Mole Concept & Stoichiometry Miscellaneous Exercises

From the equation for burning of hydrogen and oxygen

2H₂ + O₂ ⟶ 2H₂O (Steam)

Write down the number of mole (or moles) of steam obtained from 0.5 moles of oxygen.

Answer

$\begin{matrix} 2\text{H}_2 & + &\text{O}_2 & \longrightarrow & 2\text{H}_2\text{O} \\ 2\text{ mole} & & 1\text{ mole}& & 2\text{ mole} \end{matrix}$

1 mole of oxygen gives 2 moles of steam

∴ 0.5 mole of oxygen will give $\dfrac{2}{1}$ × 0.5

= 1 mole of steam

From the equation

3Cu + 8HNO₃ ⟶ 3Cu(NO₃)₂ + 4H₂O + 2NO

(At. mass Cu=64, H=1, N=14, O=16)

Calculate:

(a) Mass of copper needed to react with 63 g of HNO₃

(b) Volume of nitric oxide at S.T.P. that can be collected.

Answer

$\begin{matrix} 3\text{Cu} & + &8\text{HNO}_3 & \longrightarrow & 3\text{Cu(NO}_3)_2 + 4\text{H}_2\text{O} + 2\text{NO} \\ 3(64) && 8(1 + 14 + 3(16)) \\ = 192 \text{g} & & = 8(63) \\ &&= 504 \text{g} \\ \end{matrix}$

(a) 504 g nitric acid reacts with 192 g of copper

∴ 63 g of nitric acid reacts with $\dfrac{192}{504}$ x 63 = 24 g of copper

Hence, 24 g of copper is required.

(b) 504 g of nitric acid gives 2 × 22.4 litre volume of NO

∴ 63 g of nitric acid gives $\dfrac{2 × 22.4}{504}$ x 63

= 5.6 litre of NO

5.6 L of NO is collected.

(a) Calculate the number of moles in 7 g of nitrogen.

(b) What is the volume at S.T.P. of 7.1 g of chlorine?

(c) What is the mass of 56 cm³ of carbon monoxide at S.T.P?

Answer

(a) Gram molecular mass of N₂ = 2 x 14 = 28 g

28 g of nitrogen = 1 mole

∴ 7 g of nitrogen = $\dfrac{1}{28}$ x 7

= 0.25 moles

(b) Gram molecular mass of Cl₂ = 2 x 35.5 = 71 g

71 g of chlorine at S.T.P. occupies 22.4 litres

∴ 7.1 g of chlorine will occupy $\dfrac{22.4}{71}$ x 7.1

= 2.24 litre = 2.24 dm³

(c) Gram molecular mass of carbon monoxide (CO) = 12 + 16 = 28 g

28 g of carbon monoxide at S.T.P. occupies 22,400 cm³ volume

So, 22,400 cm³ volume have mass = 28 g

∴ 56 cm³ volume will have mass $\dfrac{28}{22,400}$ x 56 = 0.07 g

Some of the fertilizers are sodium nitrate NaNO₃, ammonium sulphate (NH₄)₂SO₄ and urea CO(NH₂)₂. Which of these contains the highest percentage of nitrogen?

Answer

(i) Molar mass of NaNO₃ = 23 + 14 + 3(16) = 23 + 14 + 48 = 85 g

Nitrogen in 85 g NaNO₃ = 14 g

∴ Percentage of Nitrogen in NaNO₃ = $\dfrac{14}{85}$ x 100 = 16.47%

(ii) Molar mass of (NH₄)₂SO₄ = 2[14 + 4(1)] + 32 + 4(16) = 36 + 32 + 64 = 132 g

Nitrogen in 132 g of (NH₄)₂SO₄ = 28 g

∴ Percentage of Nitrogen in (NH₄)₂SO₄ = $\dfrac{28}{132}$ x 100 = 21.21%

(iii) Molar mass of CO(NH₂)₂ = 12 + 16 + 2[14 + (2 x 1)]

= 28 + 2(16)

= 28 + 32

= 60 g

Nitrogen in 60 g of CO(NH₂)₂ = 2 x 14 = 28 g

∴ Percentage of Nitrogen in CO(NH₂)₂ = $\dfrac{28}{60}$ x 100 = 46.66%

So, the highest percentage of Nitrogen is in Urea.

Water decomposes to O₂ and H₂ under suitable conditions as represented by the equation below:

2H₂O ⟶ 2H₂ + O₂

(a) If 2500 cm³ of H₂ is produced, what volume of O₂ is liberated at the same time and under the same conditions of temperature and pressure?

(b) The 2500 cm³ of H₂ is subjected to $2\dfrac{1}{2}$ times increase in pressure (temp. remaining constant). What volume will H₂ now occupy?

(c) Taking the value of H₂ calculated in 5(b), what changes must be made in Kelvin (absolute) temperature to return the volume to 2500 cm³ pressure remaining constant.

Answer

$\begin{matrix} 2\text{H}_2\text{O} & \longrightarrow & 2\text{H}_2 & + &\text{O} \\ 2\text{ Vol.} & & 2\text{ Vol.}& & 1\text{ Vol.} \end{matrix}$

2 Vol. of water gives 2 Vol. of H₂ and 1 Vol. of O₂

∴ If 2500 cm³ of H₂ is produced, volume of O₂ produced = $\dfrac{2500}{2}$ = 1250 cm³

(b) V₁ = 2500 cm³

P₁ = 1 atm = 760 mm

T₁ = T

T₂ = T

P₂ = [760 x 2 $\dfrac{1}{2}$] + [760] = 760 [$\dfrac{5}{2}$ + 1] = 760 x $\dfrac{7}{2}$ = 2660 mm

V₂ = ?

Using formula:

$\dfrac{\text{P}_1\text{V}_1}{\text{T}_1}$ = $\dfrac{\text{P}_2\text{V}_2}{\text{T}_2}$

$\dfrac{760 \times 2500}{\text{T}}$ = $2660 \times \dfrac{\text{V}_2}{\text{T}}$

V₂ = $\dfrac{760 \times 2500 }{2660}$ = $\dfrac{5000}{7}$

(c) V₁ = $\dfrac{5000}{7}$ = 714.29 cm³

P₁ = P₂ = P

T₁ = T

V₂ = 2500 cm³

T₂ = ?

Using formula:

$\dfrac{\text{P}_1\text{V}_1}{\text{T}_1}$ = $\dfrac{\text{P}_2\text{V}_2}{\text{T}_2}$

$\dfrac{\text{P} \times 714.29}{\text{T}}$ = $\dfrac{\text{P} \times 2500}{\text{T}_2}$

T₂ = $\dfrac{2500 }{714.29}$ x T

T₂ = 3.5 x T

Hence, T₂ = 3.5 times T or temperature should be increased by 3.5 times

Urea (CO(NH₂)₂) is an important nitrogenous fertilizer. Urea is sold in 50 kg sacks. What mass of nitrogen is in one sack of urea?

Answer

Molar mass of urea [CO(NH₂)₂] = 12 + 16 + 2[14 + (2 x 1)]

= 28 + 2(16)

= 28 + 32

= 60 g

50 kg of urea = 50,000 g of urea

Nitrogen in 60 g of CO(NH₂)₂ = 2 x 14 = 28 g

∴ Nitrogen in 50,000 g urea = $\dfrac{28 \times 50,000 }{60}$

= 23,333 g = 23.3 kg

Find the molecular formula of a hydrocarbon having vapour density 15, which contains 20% of Hydrogen.

Answer

Simplest ratio of whole numbers = C : H = 1 : 3

Hence, empirical formula is CH₃

Empirical formula weight = 12 + 3(1) = 15

V.D. = 15

Molecular weight = 2 x V.D. = 2 x 15

$\text{n} = \dfrac{\text{Molecular weight}}{\text{Empirical formula weight}} \\[0.5em] = \dfrac{2 \times 15}{15} = 2$

∴ Molecular formula = n[E.F.] = 2[CH₃] = C₂H₆

The following experiment was performed in order to determine the formula of a hydrocarbon. The hydrocarbon X is purified by fractional distillation.

0.145 g of X was heated with dry copper (II) oxide and 224 cm³ of carbon dioxide was collected at S.T.P.

(a) Which elements does X contain?

(b) What was the purpose of copper (II) oxide?

(c ) Calculate the empirical formula of X by the following steps:

(i) Calculate the number of moles of carbon dioxide gas.

(ii) Calculate the mass of carbon contained in this quantity of carbon dioxide and thus the mass of carbon in sample X.

(iii) Calculate the mass of hydrogen in sample X.

(iv) Deduce the ratio of atoms of each element in X (empirical formula).

Answer

(a) X contains carbon and hydrogen as it is a hydrocarbon.

(b) The purpose of copper (II) oxide is to act as an oxidizing agent.

(c) (i) 22400 cm³ CO₂ has mass = 44 g

∴ 224 cm³ CO₂ will have mass = $\dfrac{44}{22400}$ x 224 = 0.44 g

Molar mass of CO₂ = 12 + 2(16) = 12 + 32 = 44 g

Moles of CO₂ = $\dfrac{\text{Mass}}{\text{{Molecular mass}}}$ = $\dfrac{0.44}{44}$ = 0.01 moles

(ii) Mass of carbon in 44 g CO₂ = 12 g

∴ Mass of carbon in 0.44 g CO₂ = $\dfrac{12}{44}$ x 0.44 = 0.12 g

As X contains carbon and hydrogen, so sample X has 0.12 g of carbon

(iii) Mass of Hydrogen in X = 0.145 - 0.12 = 0.025 g

(iv) Ratio of moles of C : H

= $\dfrac{0.01}{0.01}$ : $\dfrac{0.025}{0.01}$

= 1 : $\dfrac{25}{10}$

= 1 : $\dfrac{5}{2}$

= 2 : 5

Hence, ratio of C : H = 2 : 5

so, the empirical formula of hydrocarbon is C₂H₅

Compound is formed by 24 g of X and 64 g of oxygen. If atomic mass of X = 12 and O = 16, calculate the simplest formula of compound.

Answer

Simplest ratio of whole numbers = X : O = 1 : 2

Hence, simplest formula of compound is XO₂

A gas cylinder filled with hydrogen holds 5 g of the gas. The same cylinder holds 85 g of gas X under the same temperature and pressure. Calculate:

(a) Vapour density of gas X.

(b) Molecular weight of gas X.

Answer

(a) V.D. = $\dfrac{\text{mass of certain volume of gas at S.T.P.}}{\text{mass of equal volume of H}_2\text{ at S.T.P.}}$ = $\dfrac{85}{5}$ = 17

(b) Molecular weight = 2 x V.D. = 2 x 17 = 34 a.m.u.

(a) When carbon dioxide is passed over red hot carbon, carbon monoxide is produced according to the equation :

CO₂ + C ⟶ 2CO

What volume of carbon monoxide at S.T.P. can be obtained from 3 g of carbon?

(b) 60 cm³ of oxygen was added to 24 cm³ of carbon monoxide and mixture ignited. Calculate:

(i) volume of oxygen used up and

(ii) Volume of carbon dioxide formed.

Answer

$\begin{matrix} \text{CO}_2 & + &\text{C} & \longrightarrow & 2\text{CO} \\ 1\text{ vol.} & : & 1 \text{ vol.} & \longrightarrow & 2 \text{ vol.} \\ \end{matrix}$

[By Gay Lussac's law]

1 Vol. of C produces 2V of CO

12 g of C produces 2 x 22.4 L of CO

∴ 3 g of C will produce $\dfrac{2 \times 22.4}{12}$ x 3

= 11.2 L of CO

(b)

$\begin{matrix} \text{O}_2 & + &\text{2CO} & \longrightarrow & 2\text{CO}_2 \\ 1\text{ vol.} & : & 2 \text{ vol.} & \longrightarrow & 2 \text{ vol.} \\ \end{matrix}$

(i) 2 Vol. of CO requires 1 Vol. of oxygen

∴ 24 cm³ CO will require $\dfrac{1}{2}$ x 24

= 12 cm³ of oxygen

(ii) 2 Vol. of CO gives 2 vol. of CO₂

∴ 24 cm³ of CO will give 24 cm³ of CO₂

How much calcium oxide is obtained by heating 82 g of calcium nitrate? Also find the volume of NO₂ evolved:

2Ca(NO₃)₂ ⟶ 2CaO + 4NO₂ + O₂

Answer

$\begin{matrix} 2\text{Ca(NO}_3)_2 & \longrightarrow & 2\text{CaO} & + &\space 4\text{NO}_2 \space + & \text{O}_2 \\ 2[40 + 2[14 + 3(16)]] & & 2[40 + 16] \\ = 2[40 + 28 + 96] & & = 2(56) \\ = 328 \text{ g} & & = 112 \text{ g} \end{matrix}$

328 g of calcium nitrate produces 112 g of CaO

∴ 82 g of calcium nitrate will produce $\dfrac{112}{328}$ x 82

= 28 g of CaO

328 g of calcium nitrate produces 4 x 22.4 L of NO₂

∴ 82 g of calcium nitrate will produce $\dfrac{4 \times 22.4}{328}$ x 82

= 22.4 L of NO₂

The equation for the burning of octane is:

2C₈H₁₈ + 25O₂ ⟶ 16CO₂ + 18H₂O

(i) How many moles of carbon dioxide are produced when one mole of octane burns?

(ii) What volume at S.T.P. is occupied by the number of moles determined in (i)?

(iii) If the relative molecular mass of carbon dioxide is 44, what is the mass of carbon dioxide produced by burning two moles of octane?

(iv) What is the empirical formula of octane?

Answer

$\begin{matrix} 2\text{C}_8\text{H}_{18} & + &25\text{O}_2 & \longrightarrow & 16\text{CO}_2 & + & 18\text{H}_2\text{O} \\ 2\text{ Vol.}&& 25\text{ Vol.} && 16\text{ Vol.}&& 18\text{ Vol.} \\ &&&&16[12 + 2(16)] \\ &&&&16[12 + 32] \\ &&&&16[44] = 704 \text{g} \\ \end{matrix}$

(i) 2 moles of octane produces 16 moles of CO₂

∴ 1 mole octane produces $\dfrac{16}{2}$ x 1

= 8 moles of CO₂

(ii) 1 mole CO₂ occupies volume = 22.4 L

As 2 moles of octane produces 8 moles of carbon dioxide which will occupy volume $\dfrac{22.4}{1}$ x 8

= 179.2 dm³ of CO₂

(iii) 1 mole CO₂ has mass = 44 g

∴ 16 moles will have mass $\dfrac{44}{1}$ x 16

= 704 g of CO₂

(iv) Molecular formula is C₈H₁₈

∴ Ratio of C and H is 8 : 18

Simple ratio is 4 : 9

Hence, empirical formula = C₄H₉

Ordinary chlorine gas has two isotopes ³⁵₁₇Cl and ³⁷₁₇Cl in the ratio of 3:1. Calculate the relative atomic mass of chlorine.

Answer

The relative atomic mass of Cl = $\dfrac{(35 × 3) + (1 × 37)}{4}$ = 35.5

Silicon (Si = 28) forms a compound with chlorine (Cl = 35.5) in which 5.6 g of silicon combines with 21.3 g of chlorine. Calculate the empirical formula of the compound.

Answer

Simplest ratio of whole numbers = Si : Cl = 1 : 3

Hence, empirical formula is SiCl₃

An acid of phosphorus has the following percentage composition; Phosphorus = 38.27%; hydrogen = 2.47%; oxygen = 59.26%. Find the empirical formula of the acid and it's molecular formula, given that it's relative molecular mass is 162.

Answer

Simplest ratio of whole numbers = P : H : O = 1 : 2 : 3

Hence, empirical formula is H₂PO₃

Empirical formula weight = 31 + 2(1) + 3(16) = 31 + 2 + 48 = 81

Molecular weight = 162

$\text{n} = \dfrac{\text{Molecular weight}}{\text{Empirical formula weight}} \\[0.5em] = \dfrac{162}{81} = 2$

So, molecular formula = 2(H₂PO₃) = H₄P₂O₆

(a) Calculate the mass of substance 'A' which in gaseous form occupies 10 litres at 27°C and 700 mm pressure. The molecular mass of 'A' is 60.

(b) A gas occupied 360 cm³ at 87°C and 380 mm Hg pressure. If the mass of gas is 0.546 g, find it's relative molecular mass.

Answer

(a) Given, molecular mass of 'A' is 60

V₁ = 10 L

T₁ = 27 + 273 K = 300 K

P₁ = 700 mm

T₂ = 273 K

P₂ = 760 mm

V₂ = ?

Using formula:

$\dfrac{\text{P}_1\text{V}_1}{\text{T}_1}$ = $\dfrac{\text{P}_2\text{V}_2}{\text{T}_2}$

Substituting in the formula,

$\dfrac{700 \times 10}{300}$ = $\dfrac{760 \times\text{V}_2}{273}$

V₂ = $\dfrac{700 \times10 \times 273}{300 \times760}$ = $\dfrac{1911}{228}$ = 8.38 L

As, 22.4 L of A weighs 60 g

∴ 8.38 L of A will weigh $\dfrac{60}{22.4}$ x 8.38

= 22.446 = 22.45 g

(b) V₁ = 360 cm³

T₁ = 87 + 273 K = 360 K

P₁ = 380 mm Hg pressure

T₂ = 273 K

P₂ = 760 mm Hg pressure

V₂ = ?

Using formula:

$\dfrac{\text{P}_1\text{V}_1}{\text{T}_1}$ = $\dfrac{\text{P}_2\text{V}_2}{\text{T}_2}$

Substituting in the formula,

$\dfrac{380\times 360}{360}$ = $\dfrac{760 \times\text{V}_2}{273}$

V₂ = $\dfrac{380 \times 273}{760}$ = $\dfrac{10,374}{760}$ = 136.5 cm³

136.5 cm³ of gas weigh = 0.546 g

22400 cm³ of gas weigh $\dfrac{0.546}{136.5}$ x 22400

= 89.6 amu

A gas cylinder can hold 1 kg of hydrogen at room temperature and pressure.

(a) What mass of carbon dioxide can it hold under similar conditions of temperature and pressure?

(b) If the number of molecules of hydrogen in the cylinder is X, calculate the number of carbon dioxide molecules in the cylinder. State the law that helped you to arrive at the above result

Answer

(a) Given, cylinder can hold = 1 kg of hydrogen

Molar mass of hydrogen = 2[1] = 2g

Number of moles of hydrogen present in cylinder = $\dfrac{1000}{2}$ = 500

According to avogadro's law : cylinder will hold 500 moles of carbon dioxide gas

Molar mass of CO₂ = C + 2(O) = 12 + 2(16) = 44 g

1 mole of carbon dioxide = 44 g

∴ 500 moles of carbon dioxide = 44 x 500 = 22,000 g = 22 kg.

Hence, Weight of carbon dioxide in cylinder = 22 kg

(b) According to Avogadro's law — Equal volumes of all gases under similar conditions of temperature and pressure contain equal number of molecules.

∴ molecules in the cylinder of carbon dioxide = X

Avogadro's law helped to arrive at this result.

Following questions refer to one mole of chlorine gas.

(a) What is the volume occupied by this gas at S.T.P.?

(b) What will happen to the volume of gas, if pressure is doubled?

(c) What volume will it occupy at 273°C?

(d) If the relative atomic mass of chlorine is 35.5, what will be the mass of 1 mole of chlorine gas?

Answer

(a) According to Avogadro's law : The volume occupied by 1 mole of chlorine is 22.4 dm³

(b) According to Boyle's Law: PV = constant

Hence, if pressure is doubled then volume will become half i.e. $\dfrac{22.4}{2}$ = 11.2 dm³

(c) V₁ = 22.4 dm³

T₁ = 273 K

T₂ = 273 + 273 K = 546 K

V₂ = ?

According to charles law:

$\dfrac{\text{V}_1}{\text{T}_1}$ = $\dfrac{\text{V}_2}{\text{T}_2}$

Substituting to we get,

$\dfrac{ 22.4}{273}$ = $\dfrac{\text{V}_2}{546}$

Hence, V₂ = $\dfrac{ 22.4}{273}$ x 546 = 44.8 dm³

(c) Mass of 1 mole Cl₂ gas = 35.5 × 2 = 71 g

(a) A hydrate of calcium sulphate CaSO4.xH₂O contains 21% water of crystallisation. Find the value of x.

(b) What volume of hydrogen and oxygen measured at S.T.P. will be required to prepare 1.8 g of water.

(c) How much volume will be occupied by 2g of dry oxygen at 27°C and 740 mm pressure?

(d) What would be the mass of CO₂ occupying a volume of 44 litres at 25°C and 750 mm pressure?

(e) 1 g of a mixture of sodium chloride and sodium nitrate is dissolved in water. On adding silver nitrate solution, 1.435 g of AgCl is precipitated.

AgNO₃ (aq) + NaCl (aq) ⟶ AgCl (s) + NaNO₃

Calculate the percentage of NaCl in the mixture.

Answer

Relative molecular mass of CuSO₄.xH₂O

= 40 + 32 + (4×16) + [x(2+16)]

= 40 + 32 + 64 + 18x

= 136 + 18x

∴ 21% water of crystallization = 18 x

$\Rightarrow \dfrac{18x}{136 + 18x } = \dfrac{21}{100} \\[1em] 1800x = 21(136 + 18x) \\[1em] 1800x = 2856 + 378x \\[1em] 1800x - 378x = 2856 \\[1em] 1422x = 2856 \\[1em] x = \dfrac{2856}{1422} \\[1em] x = 2$

Hence, water of crystallization = 2

(b) Molar mass of H₂O = 2(1) + 16 = 18 g

For 18 g water, vol. of hydrogen needed = 22.4 litre

∴ For 1.8 g, vol. of H₂ needed = $\dfrac{22.4}{18}$ x 1.8 = 2.24 L

According to Gay Lussac's Law, 2 vol of hydrogen requires 1 vol of oxygen

When 2 vol of hydrogen in 1.8 g H₂O is 2.24 L, then one vol. of oxygen will be:

$\dfrac{2.24}{2}$ = 1.12 L

(c) Gram molecular mass of O₂ = 2 x 16 = 32 g

1 mole of O₂ weighs 32 g and occupies 22.4 lit. vol.

∴ 2 g of O₂ occupies = $\dfrac{22.4}{32} \times 2 = 1.4 \text{ lit.}$

Volume occupied by 2 g of O₂ gas at 27°C and 740 mm pressure:

Using the gas equation,

$\dfrac{P_{1}V_{1}}{T_{1}} = \dfrac{P_{2}V_{2}}{T_{2}}$

Substituting the values we get,

$\dfrac{760 \times 1.4}{273} = \dfrac{740 \times x}{300} \\[0.5em] x = \dfrac{760 \times 1.4 \times 300}{740 \times 273 } \\[0.5em] x = \dfrac{3,19,200}{2,02,020} \\ \\[0.5em] x = 1.58 \text{ lit}$

Hence, the volume occupied by 2 g of O₂ gas at 27°C and 740 mm pressure is 1.58 lit.

(d) Gram molecular mass of CO₂ = 12 + 2(16) = 12 + 32 = 44 g

Using the gas equation,

$\dfrac{P_{1}V_{1}}{T_{1}} = \dfrac{P_{2}V_{2}}{T_{2}}$

Substituting the values we get,

$\dfrac{750 \times 44}{298} = \dfrac{760 \times x}{273} \\[0.5em] x = \dfrac{750 \times 44 \times 273}{760 \times 298 } \\[0.5em] x = \dfrac{9,009,000}{226,480} \\ \\[0.5em] x = 39.78 \text{ lit}$

22.4 litre of CO₂ at S.T.P. has mass = 44 g

39.78 litre of CO₂ at S.T.P. has mass $\dfrac{44}{22.4}$ x 39.78

= 78.14 g

(e)

$\begin{matrix} \text{AgNO}_3 & + &\text{NaCl} & \longrightarrow & \text{AgCl} & + & \text{NaNO}_3 \\ && 23 + 35.5 && 108 + 35.5 \\ && = 58.5 \text{g}&& = 143.5\text{g} \\ \end{matrix}$

(i) 143.5 g AgCl is formed by 58.5 g NaCl

∴ 1.435 g of AgCl will be formed by $\dfrac{58.5}{143.5}$ x 1.435 = 0.582 g

Percentage of NaCl = $\dfrac{0.582}{1}$ x 100 = 58.5%

Hence, percentage of NaCl is 58.5%

From the equation:

C + 2H₂SO₄ ⟶ CO₂ + 2H₂O + 2SO₂

Calculate:

(i) The mass of carbon oxidized by 49 g of sulphuric acid.

(ii) The volume of sulphur dioxide measured at STP, liberated at the same time.

Answer

$\begin{matrix} \text{C} & + &2\text{H}_2\text{SO}_4 & \longrightarrow & \text{CO}_2 & + & 2\text{H}_2\text{O}& + & 2\text{SO}_2 \\ 12 \text{g} && 2[2(1) + 32 + 4(16)] \\ && 2[2 + 32 + 64] \\ && 196 \text{g} \\ \end{matrix}$

(i) 196 g of sulphuric acid oxidizes 12 g carbon

∴ 49 g of sulphuric acid will oxidize = $\dfrac{12}{196}$ x 49 = 3 g

Hence, 3 g of carbon is oxidized.

(ii) 12 g carbon liberates 2 vol = (2 x 22.4) lit of SO₂

∴ 3 g of carbon will liberate $\dfrac{2 \times 22.4}{12}$ x 3 = 11.2 lit of SO₂.

Hence, 11.2 lit of SO₂ is liberated.

(i) A compound has the following percentage composition by mass: carbon 14.4%, hydrogen 1.2% and chlorine 84.5%. Determine the empirical formula of this compound. Work correct to 1 decimal place. (H = 1; C = 12; Cl = 35.5)

(ii) The relative molecular mass of this compound is 168, so what is it's molecular formula?

Answer

(i)

Simplest ratio of whole numbers = C : H : Cl = 1 : 1 : 2

Hence, empirical formula is CHCl₂

Empirical formula weight = 12 + 1 + 2(35.5) = 84 g

Relative molecular mass = 168

$\text{n} = \dfrac{\text{Molecular weight}}{\text{Empirical formula weight}} \\[0.5em] = \dfrac{168}{84} = 2$

Molecular formula = n[E.F.] = 2[CHCl₂] = C₂H₂Cl₄

∴ Molecular formula = C₂H₂Cl₄

Find the percentage of

(a) oxygen in magnesium nitrate crystals [Mg(NO₃)₂.6H₂O].

(b) boron in Na₂B₄O₇.10H₂O. H=1,B=11,O=16,Na=23.

(c) phosphorus in the fertilizer superphosphate Ca(H₂PO₄)₂

Answer

Relative molecular mass of [Mg (NO₃)₂.6H₂O]

= 24 + 2[14 + 3(16)] + 12(1) + 6(16)
= 24 + 2[14 + 48] + 12 + 96
= 24 + 28 + 96 + 12 + 96
= 256 g

Molar mass of oxygen in [Mg (NO₃)₂.6H₂O] = 96 + 96 = 192 g

Since, 256 g of [Mg(NO₃)₂.6H₂O] contains 192 g of oxygen

∴ 100 g of [Mg(NO₃)₂.6H₂O] contains

$\dfrac{192}{256}$ x 100 = 75% of oxygen

(b) Relative molecular mass of Na₂B₄O₇.10H₂O
= 2(23) + 4(11) + 7(16) + 20(1) + 10(16)
= 46 + 44 + 112 + 20 + 160
= 382 g

Molar mass of boron in Na₂B₄O₇.10H₂O = 44 g

382 g of Na₂B₄O₇.10H₂O contains 44 g of boron

∴ 100 g Na₂B₄O₇.10H₂O contains $\dfrac{44}{382}$ x 100 = 11.5%

(c) Relative molecular mass of Ca(H₂PO₄)₂
= 40 + 4(1) + 2(31) + 8(16)
= 40 + 4 + 62 + 128
= 234 g

Molar mass of phosphorus in Ca(H₂PO₄)₂ = 62 g

234g of Ca(H₂PO₄)₂ contains 62 g of phosphorus

∴ 100 g of Ca(H₂PO₄)₂ contains $\dfrac{62}{234}$ x 100 = 26.5%

What mass of copper hydroxide is precipitated by using 200 g of sodium hydroxide?

2NaOH + CuSO₄ ⟶ Na₂SO₄ + Cu(OH)₂ ↓

[Cu = 64, Na = 23, S = 32, H = 1]

Answer

$\begin{matrix} 2\text{NaOH} & + & \text{CuSO}_4 & \longrightarrow & \text{Na}_2\text{SO}_4 & + & \text{Cu(OH)}_2\downarrow \\ 2[23 + 16 & & & & & & 64 + 2[16 + 1] \\ + 1] & & & & & & = 64 + 34 \\ = 80 \text{ g} & & & & & & = 98 \text{g} \\ \end{matrix}$

80 g of sodium hydroxide precipitates 98 g of copper hydroxide.

∴ 200 g of sodium hydroxide will precipitate $\dfrac{98}{80}$ x 200 = 245 g of copper hydroxide.

Hence, 245 g. of copper hydroxide is precipitated.

Solid ammonium dichromate decomposes as under:

(NH₄)₂Cr₂O₇ ⟶ N₂ + Cr₂O₃ + 4H₂O

If 63 g of ammonium dichromate decomposes. Calculate

(a) the quantity in moles of (NH₄)₂Cr₂O₇

(b) the quantity in moles of nitrogen formed.

(c) the volume of N₂ evolved at S.T.P.

(d) the loss of mass

(iv) the mass of chromium (III) formed at the same time.

Answer

$\begin{matrix} (\text{NH}_4)_2\text{Cr}_2\text{O}_7 & \xrightarrow{\Delta} & \text{N}_2 & + & 4\text{H}_2\text{O} & + & \text{Cr}_2\text{O}_3 \\ 2[14 + 4(1)] & & & & & & 2(52) \\ + 2(52) + 7(16) & & & & & & + 3(16) \\ = 36 + 104 & & & & & & = 104 + 48 \\ + 112 = 252 \text{ g} & & & & & & = 152 \text{ g} \\ \end{matrix}$

(a) 252 g of (NH₄)₂Cr₂O₇ = 1 mole

∴ 63 g of (NH₄)₂Cr₂O₇ = $\dfrac{1}{252}$ x 63 = 0.25 moles

Hence, no. of moles = 0.25 moles

(b)

$\begin{matrix} (\text{NH}_4)_2\text{Cr}_2\text{O}_7 & : & \text{N}_2 \\ 1 \text{ mol.} & : & 1 \text{ mol.} \\ 0.25 \text{ mol.} & : & x \\ \end{matrix}$

Hence, 0.25 moles of (NH₄)₂Cr₂O₇ will produce 0.25 moles of nitrogen.

(c) 1 mole of N₂ occupies 22.4 lit.

∴ 0.25 moles of N₂ will occupy = 22.4 x 0.25 = 5.6 lit.

Hence, volume of N₂ evolved at s.t.p = 5.6 lit.

(d) 252 g of (NH₄)₂Cr₂O₇ decomposes to give 152 g of solid Cr₂O₃, loss in mass = 252 - 152 = 100 g

If 63 g of (NH₄)₂Cr₂O₇ decomposes then loss in mass is

$\dfrac{100}{252}$ x 63 = 25 g

(e) 1 mole of Cr₂O₇ = 152 g.

∴ 0.25 moles of Cr₂O₇ = 152 x 0.25 = 38 g.

Hence, mass in gms of Cr₂O₇ formed = 38 g.

Hydrogen sulphide gas burns in oxygen to yield 12.8 g of sulphur dioxide gas as under:

2H₂S + 3O₂ ⟶ 2H₂O + 2SO₂

Calculate the volume of hydrogen sulphide at S.T.P. Also, calculate the volume of oxygen required at S.T.P. which will complete the combustion of hydrogen sulphide determined in (litres).

Answer

$\begin{matrix} 2\text{H}_2\text{S} & + &3\text{O}_2 & \longrightarrow & 2\text{H}_2\text{O} & + & 2\text{SO}_2 \\ 2\text{ Vol.} && 3\text{ Vol.} && && 2\text{ Vol.} \\ 2[2(1) + 32] && 3[2(16)] &&&& 2[32 + 2(16)] \\ 68 \text{ g} && 96 \text{ g} &&&& 128 \text{ g} \end{matrix}$

128 g of SO₂ has volume 2 × 22.4 litres

∴ 12.8 g of SO₂ has volume =

$\dfrac{2 × 22.4}{128}$ x 12.8 = 4.48 L

Volume of oxygen = ?

2 × 22.4 L H₂S requires = 3 × 22.4 litre of oxygen

∴ 4.48 L H₂S will require

$\dfrac{3 × 22.4}{2 × 22.4 }$ x 4.48 = 6.72 L of oxygen.

Ammonia burns in oxygen and combustion, in the presence of a catalyst, may be represented by

2NH₃ + 2 $\dfrac{1}{2}$ O₂ ⟶ 2NO + 3H₂O

[H = 1, N = 14, O = 16]

What mass of steam is produced when 1.5 g of nitrogen monoxide is formed?

Answer

$\begin{matrix} 2\text{NH}_3 & + &2\dfrac{1}{2}\text{O}_2 & \longrightarrow & 2\text{NO} & + &3\text{H}_2\text{O} \\ &&&&2[14 + 16] && 3[2(1) + 16] \\ &&&& 60 \text{ g} && 54 \text{ g} \\ \end{matrix}$

When 60 g NO is formed then, 54 g mass of steam is produced

∴ when 1.5 g NO is formed, mass of steam produced

= $\dfrac{54}{60}$ x 1.5 = 1.35 g

If a crop of wheat removes 20 kg of nitrogen per hectare of soil, what mass of the fertilizer, calcium nitrate Ca(NO₃)₂ would be required to replace the nitrogen in a 10 hectare field ?

Answer

Molecular mass of Ca(NO₃)₂

= 40 + [2(14) + 6(16)]
= 40 + 28 + 96
= 164 g

Mass of N₂ in Ca(NO₃)₂ = 28 g

In 1 hectare of soil, 20 kg of N₂ is removed

∴ In 10 hectare field N₂ removed is 20 x 10 = 200 kg

28 g N₂ is present in 164 g of Ca(NO₃)₂

So, 200 kg or 200,000 g of N₂ is present in $\dfrac{164}{28}$ x 200,000

= 1171428 g = 1171.4 kg

Concentrated nitric acid oxidises phosphorus to phosphoric acid according to the following equation:

P + 5HNO₃ ⟶ H₃PO₄+ 5NO₂ + H₂O

If 6.2 g of phosphorus was used in the reaction calculate:

(a) Number of moles of phosphorus taken and mass of phosphoric acid formed.

(b) mass of nitric acid consumed at the same time?

(c) The volume of steam produced at the same time if measured at 760 mm Hg pressure and 273°C?

Answer

$\begin{matrix} \text{P}& + &5\text{HNO}_3 & \longrightarrow & \text{H}_3\text{PO}_4 & + & 5\text{NO}_2& + &\text{H}_2\text{O} \\ 31 \text{g} && 5[1 + 14 + 3(16)] && 3(1) + 31 + 4(16) \\ && 315 \text{ g} && 98 \text{ g} \end{matrix}$

(a) 31 g of P = 1 mole

∴ 6.2 g of P = $\dfrac{1}{31}$ x 6.2 = 0.2 mole of P

Mass of phosphoric acid formed = ?

31 g of P produces 98 g of phosphoric acid

∴ 6.2 g of P will form $\dfrac{98}{31}$ x 6.2 = 19.6 g

(b) 31 g P reacts with 315 g HNO₃

∴ 6.2 g P will react with $\dfrac{315}{31}$ x 6.2 = 63 g HNO₃

(c) 31 g P produces = 1 mole steam

∴ 6.2 g P produces $\dfrac{1}{31}$ x 6.2 = 0.2 moles

Volume of steam produced at STP = 0.2 × 22.4 = 4.48 litre

V₁ = 4.48 litre

T₁ = 273 K

P₁ = 760 mm Hg pressure

T₂ = 273 + 273 = 546 K

P₂ = 760 mm Hg pressure

V₂ = ?

Using formula:

$\dfrac{\text{P}_1\text{V}_1}{\text{T}_1}$ = $\dfrac{\text{P}_2\text{V}_2}{\text{T}_2}$

Substituting in the formula,

$\dfrac{760\times 4.48}{273}$ = $\dfrac{760 \times\text{V}_2}{546}$

V₂ = 2 x 4.48 = 8.96 L

Hence, volume of steam produced = 8.96 L

112 cm³ of a gaseous fluoride of phosphorus has a mass of 0.63 g. Calculate the relative molecular mass of the fluoride. If the molecule of the fluoride contains only one atom of phosphorus, then determine the formula of the phosphorus fluoride. [ F = 19, P = 31]

Answer

Given,

112 cm³ of gaseous fluoride has mass = 0.63 g

so, 22400 cm³ of gaseous fluoride will have mass = $\dfrac{0.63}{112}$ x 22400

= 126 g

∴ Relative molecular mass of fluoride = 126 g

The molecular mass = At mass P + At. mass of F

126 = 31 + At. Mass of F

∴ At. Mass of F = 126 - 31 = 95 g

However, At. mass of F = 19

∴ $\dfrac{95}{19}$ = 5

So, 5 atoms of F, hence, the molecular formula = PF₅

Washing soda has formula Na₂CO₃.10H₂O. What mass of anhydrous sodium carbonate is left when all the water of crystallization is expelled by heating 57.2 g of washing soda?

Answer

$\begin{matrix} \text{Na}_2\text{CO}_3.10\text{H}_2\text{O} & \xrightarrow{\Delta} & \text{Na}_2\text{CO}_3 & + & 10\text{H}_2\text{O} \\ 2(23) + 12 + 3 (16) & & 2(23) + 12 & & 10[2(1) \\ + 10[2(1) + 16] & & + 3(16) & & + 16] \\ = 46 + 12 + 48 & & = 46 + 12 & & = 180 \text{ g} \\ + 10(18) & & + 48 \\ = 286 \text{ g} & & = 106 \text{ g} \\ \end{matrix}$

286 g of washing soda had 106 g of anhydrous sodium carbonate

∴ 57.2 g will have = $\dfrac{106}{286}$ x 57.2 = 21.2 g anhydrous sodium carbonate.

Hence, 21.2 g anhydrous sodium carbonate is left.

A metal M forms a volatile chloride containing 65.5% chlorine. If the density of the chloride relative to hydrogen is 162.5, find the molecular formula of the chloride (M = 56).

Answer

Simplest ratio of whole numbers = M : Cl = 1 : 3

Hence, empirical formula is MCl₃

Empirical formula weight = 56 + 3(35.5) = 162.5 g

Molecular weight = 2 x V.D. = 2 x 162.5 = 325

$\text{n} = \dfrac{\text{Molecular weight}}{\text{Empirical formula weight}} \\[0.5em] = \dfrac{ 325}{162.5} = 2$

Molecular formula = n[E.F.] = 2[MCl₃] = M₂Cl₆

∴ Molecular formula = M₂Cl₆

A compound X consists of 4.8% carbon and 95.2% bromine by mass.

(i) Determine the empirical formula of this compound working correct to one decimal place (C = 12; Br = 80)

(ii) If the vapour density of the compound is 252, what is the molecular formula of the compound?

Answer

Simplest ratio of whole numbers = C : Br = 1 : 3

Hence, empirical formula is CBr₃

(ii) Empirical formula weight = 12 + 3(80) = 252 g

Molecular weight = 2 x V.D. = 2 x 252 = 504

$\text{n} = \dfrac{\text{Molecular weight}}{\text{Empirical formula weight}} \\[0.5em] = \dfrac{ 504}{252} = 2$

Molecular formula = n[E.F.] = 2[CBr₃] = C₂Br₆

∴ Molecular formula = C₂Br₆

The reaction: 4N₂O + CH₄ ⟶ CO₂ + 2H₂O + 4N₂ takes place in the gaseous state. If all volumes are measured at the same temperature and pressure, calculate the volume of dinitrogen oxide (N₂O) required to give 150 cm³ of steam.

Answer

$\begin{matrix} 4\text{N}_2\text{O} & + &\text{CH}_4 & \longrightarrow & \text{CO}_2 & + & 2\text{H}_2\text{O} & + &4\text{N}_2 \\ 4 \text{ Vol} && 1 \text{ Vol} && 1 \text{ Vol} && 2 \text{ Vol} && 4\text{ Vol} \\ \end{matrix}$

2 x 22400 litre steam is produced by 4 × 22400 cm³ N₂O

∴ 150 cm³ steam will be produced by

= $\dfrac{4 × 22400}{2 × 22400}$ x 150 = 300 cc of N₂O

Samples of the gases O₂, N₂, CO₂ and CO under the same conditions of temperature and pressure contain the same number of molecules x. The molecules of oxygen occupy V litres and have a mass of 8 g under the same conditions of temperature and pressure

What is the volume occupied by:

(a) x molecules of N₂

(b) 3x molecules of CO

(c) What is the mass of CO₂ in grams?

(d) In answering the above questions, which law have you used?

Answer

By Avogadro's law: Under the same conditions of temperature and pressure equal volumes of all gases contain the same number of molecules.

∴ If gases under the same conditions have same number of molecules then they must have the same volume.

(i) So, X molecules of N₂ occupy 1V litres.

(ii) 3X molecules of CO will occupies 3V litres.

(iii) Molar mass of CO₂ = C + 2(O) = 12 + 2(16) = 44 g

1 mole of O₂ weighs 32 g and occupy 22.4 lit. volume

∴ 8 g of O₂ will occupy $\dfrac{22.4}{32}$ x 8 = 5.6 lit. vol. = Molar volume

If 8 g of O₂ occupies 5.6 lit. vol.

And 1 mole of CO₂ occupy 22.4 lit and weighs = 44 g at s.t.p.

∴ 5.6 lit. vol. of CO₂ will weigh = $\dfrac{44}{22.4}$ x 5.6 = 11 g

Hence, mass of CO₂ = 11 g

(iv) Avogadro's Law is used above.

The percentage composition of sodium phosphate as determined by analysis is 42.1% sodium, 18.9% phosphorus and 39% oxygen. Find the empirical formula of the compound?

Answer

Simplest ratio of whole numbers = Na : P : O = 3 : 1 : 4

Hence, empirical formula is Na₃PO₄

What volume of oxygen is required to burn completely a mixture of 22.4 dm³ of methane and 11.2 dm³ of hydrogen into carbon dioxide and steam?

CH₄ + 2O₂ ⟶ CO₂ + 2H₂O

2H₂ + O₂ ⟶ 2H₂O

Answer

$\begin{matrix} \text{CH}_4 & + & 2\text{O}_2 & \longrightarrow & \text{CO}_2 & + & 2\text{H}_2\text{O} \\ 1 \text{ vol.} & : & 2 \text{ vol.} & \longrightarrow & 1\text{ vol.} \\ \end{matrix}$

From equation:

22.4 dm³ of methane requires oxygen = 2 x 22.4 dm³ of O₂ = 44.8 dm³

$\begin{matrix} 2\text{H}_2 & + & \text{O}_2 & \longrightarrow & 2\text{H}_2\text{O} \\ 2 \text{ vol.} & : & 1 \text{ vol.} & \longrightarrow & 2\text{ vol.} \\ \end{matrix}$

From equation,

[2 x 22.4] dm³ hydrogen requires oxygen = 22.4 dm³

∴ 11.2 dm³ hydrogen will require oxygen = $\dfrac{22.4}{2 \times 22.4}$ x 11.2 =

= 5.6 dm³

Total volume of oxygen required = 44.8 + 5.6 = 50.4 dm³

The gases hydrogen, oxygen, carbon dioxide, sulphur dioxide and chlorine are arranged in order of their increasing relative molecular masses. Given 8 g of each gas at S.T.P., which gas will contain the least number of molecules and which gas the most?

Answer

According to Avogadro's law:

Equal volumes of all gases, under similar conditions of temperature and pressure, contain equal numbers of molecules.

So, 1 mole of each gas contains = 6.02 × 10²³ molecules

Mol. Mass of :

H₂ = 2 g,

O₂ = 32 g,

CO₂ = 12 + 2(16) = 44 g,

SO₂ = 32 + 2(16) = 64 g,

Cl₂ = 2(35.5) = 71 g

(i) 2 g of hydrogen contains molecules = 6.02 × 10²³

So, 8 g of hydrogen contains molecules

= $\dfrac{6.02 × 10^{23}}{2}$ x 8

= 4 × 6.02 × 10²³molecules

= 24.08 × 10²³molecules

(ii) 32 g of oxygen contains molecules = 6.02 × 10²³

So, 8 g of oxygen contains molecules

= $\dfrac{6.02 × 10^{23}}{32}$ x 8

= 1.505 × 10²³molecules

(iii) 44 g of carbon dioxide contains molecules = 6.02 × 10²³

So, 8 g of carbon dioxide contains

= $\dfrac{6.02 × 10^{23}}{44}$ x 8

= 1.09 × 10²³molecules

(iv) 64 g of sulphur dioxide contains molecules = 6.02 × 10²³

So, 8g of sulphur dioxide contains

= $\dfrac{6.02 × 10^{23}}{64}$ x 8

= 0.75 × 10²³molecules

(v) 71 g of chlorine contains molecules = 6.02 × 10²³

So, 8g of chlorine contains

= $\dfrac{6.02 × 10^{23}}{71}$ x 8

= 0.67 × 10²³molecules

Thus Cl₂ < SO₂ < CO₂ < O₂ < H₂

(i) Least number of molecules in Cl₂

(ii) Most number of molecules in H₂

10 g of a mixture of sodium chloride and anhydrous sodium sulphate is dissolved in water. An excess of barium chloride solution is added and 6.99 g of barium sulphate is precipitated according to the equation given below:

Na₂SO₄ + BaCl₂ ⟶ BaSO₄ + 2NaCl

Calculate the percentage of sodium sulphate in the original mixture.

Answer

$\begin{matrix} \text{Na}_2\text{SO}_4 & + & \text{BaCl}_2 & \longrightarrow & \text{BaSO}_4 \downarrow & + & 2\text{NaCl} \\ 2(23) + 32 & & & & 137 + 32 \\ + 4(16) & & & & + 4(16) \\ = 46 + 32 & & & & = 137 + 32 \\ + 64 & & & & + 64 \\ = 142 \text{ g} & & & & = 233 \text{ g} \\ \end{matrix}$

233 g of BaSO₄ is obtained from 142 g of Na₂SO₄

6.99 g of BaSO₄ will be obtained from $\dfrac{142}{233}$ x 6.99 = 4.26 g of Na₂SO₄.

∴ In 10 g mixture $\dfrac{4.26}{10}$ x 100 = 42.6% Na₂SO₄ is present.

Hence, 42.6% Na₂SO₄ is present in the original mixture

When heated, potassium permanganate decomposes according to the following equation:

2KMnO₄ ⟶ K₂MnO₄ + MnO₂ + O₂

(a) Some potassium permanganate was heated in the test tube. After collecting one litre of oxygen at room temperature, it was found that the test tube had undergone a loss in mass of 1.32 g. If one litre of hydrogen under the same conditions of temperature and pressure has a mass of 0.0825 g, calculate the relative molecular mass of oxygen.

(b) Given that the molecular mass of potassium permanganate is 158. What volume of oxygen (measured at room temperature) would be obtained by the complete decomposition of 15.8 g of potassium permanganate? (Molar volume at room temperature is 24 litres)

Answer

2KMnO₄ ⟶ K₂MnO₄ + MnO₂ + O₂

Loss in mass = 1.32 g = 1 lit of oxygen

Vapour density of gas =

$\dfrac{\text{Wt. of certain volume of gas }}{\text {Wt. of same volume of H}_2} \\[0.5em] = \dfrac{1.32}{0.0825} \\[0.5em] = 16 \text{ g}$

Molecular weight = 2 x Vapour density
= 2 x 16 = 32 g

Hence, relative molecular mass of oxygen is 32 g

(b) Molar mass of 2KMnO₄ = 2[39 + 55 + 4(16)] = 2[39 + 55 + 64] = 316 g

316 g of KMnO₄ gives oxygen = 24 litres

∴ 15.8 g of KMnO₄ will give

= $\dfrac{24}{316}$ x 15.8 = 1.2 L

(a) A flask contains 3.2 g of sulphur dioxide. Calculate the following:

(i) The moles of sulphur dioxide present in the flask.

(ii) The number of molecules of sulphur dioxide present in the flask.

(iii) The volume occupied by 3.2 g of sulphur dioxide at S.T.P.

(b) An Experiment showed that in a lead chloride solution, 6.21 g of lead is combined with 4.26 g of chlorine. What is the empirical formula of this chlorine? (Pb = 207; Cl = 35.5)

Answer

(a) (i) Molar mass of sulphur dioxide = 32 + 2(16) = 64 g

64 g of sulphur dioxide = 1 mole

So, 3.2 g = $\dfrac{1}{64}$ x 3.2 = 0.05 moles

(ii) 1 mole of SO₂ = 6.02 × 10²³ molecules

So, in 0.05 moles, no. of molecules = 6.02 × 10²³ × 0.05 = 3 × 10²²

(iii) The volume occupied by 64 g of SO₂ = 22.4 dm³

3.2 g of SO₂ will be occupied by volume

$\dfrac{22.4}{64}$ x 3.2 = 1.12 L

Simplest ratio of whole numbers Pb : Cl = 1 : 4

Hence, empirical formula is PbCl₄

The volume of gases A, B, C and D are in the ratio, 1 : 2 : 2 : 4 under the same conditions of temperature and pressure .

(i) Which sample of gas contains the maximum number of molecules?

(ii) If the temperature and pressure of gas A are kept constant, then what will happen to the volume of A when the number of molecules is doubled?

(iii) If this ratio of gas volume refers to the reactants and products of a reaction, which gas law is being observed?

(iv) If the volume of A is actually 5.6 dm³ at S.T.P., calculate the number of molecules in the actual Volume of D at S.T.P. (Avogadro's number is 6 × 10²³).

(v) Using your answer from (iv), state the mass of D if the gas is dinitrogen oxide (N₂O)

Answer

(i) Volume is directly proportional to the number of molecules, hence gas D will have maximum no. of molecules as its volume is maximum.

(ii) If number of molecules of gas A is doubled, the volume will also be doubled i.e. 2V.

(iii) Gay Lussac's Law is observed.

(iv) 1 mole contains 6 x 10²³ number of molecules and occupies 22.4 lit. vol.

Given, volume of 'A' is 5.6 dm³ at s.t.p.

∴ vol. of D will be 4 × 5.6 = 22.4 lit.
No. of molecules in 22.4 lit. of D = 6 x 10²³ (Avogadro no.)

(v) As D is 1 mole hence, mass of 1 mole of D (N₂O) = 2(14) + 16 = 28 + 16 = 44 g

Hence, mass of N₂O = 44 g

The equations given below relate to the manufacture of sodium carbonate [Mol. wt. of Na₂CO₃ = 106]

(i) NaCl + NH₃ + CO₂ + H₂O ⟶ NaHCO₃ + NH₄Cl

(ii) 2NaHCO₃ ⟶ Na₂CO₃ + H₂O + CO₂

Equations (1) and (2) are based on the production of 21.2 g. of sodium carbonate.

(a) What mass of sodium hydrogen carbonate must be heated to give 21.2 g. of sodium carbonate

(b) To produce the mass of sodium hydrogen carbonate calculated in (a), what volume of carbon dioxide, measured at s.t.p., would be required.

Answer

$\begin{matrix} 2\text{NaHCO}_3 & \longrightarrow & \text{Na}_2\text{CO}_3 & + & \text{H}_2\text{O} + \text{CO}_2 \\ 2 \text{mol.} & & 1 \text{mol.} \\ 2 \times 84 & & 106\text{ g.} \\ = 168\text{ g.} & & \end{matrix}$

106 g of Na₂CO₃ is obtained from 168 g of NaHCO₃

∴ 21.2 g. of Na₂CO₃ is obtained from $\dfrac{168}{106}$ x 21.2 = 33.6 g of NaHCO₃

(ii)

$\begin{matrix} \text{NaCl} & + & \text{NH}_3 & + & \text{CO}_2 & + & \text{H}_2\text{O} \\ & & & & 1\text{mol.} & \\ & & & & 22.4 \text{lit.} \\ \longrightarrow & \text{NaHCO}_3 & + & \text{NH}_4\text{Cl} \\ & 1 \text{mol.} \\ & 84\text{ g.} \end{matrix}$

84 g of NaHCO₃ is obtained from 22.4 lit of CO₂

∴ 33.6 g. of NaHCO₃ is obtained from $\dfrac{22.4}{84}$ x 33.6 = 8.96 lit.

Hence, 8.96 lit of CO₂ is required.

A sample of ammonium nitrate when heated yields 8.96 litres of steam (measured at STP)

NH₄NO₃ ⟶ N₂O + 2H₂O

(i) What volume of di nitrogen oxide is produced at the same time as 8.96 litres of steam.

(ii) What mass of ammonium nitrate should be heated to produce 8.96 litres of steam [Relative molecular mass of NH₄NO₃ is 80]

(iii) Determine the percentage of oxygen in ammonium nitrate [O = 16]

Answer

$\begin{matrix} \text{NH}_4\text{NO}_3 &\xrightarrow{\Delta} & \text{N}_2\text{O} & + & 2\text{H}_2\text{O} \\ 1\text{ vol.} = 80 \text{g} & & 1 \text{ vol.} & & 2\text{ vol.} \\ \end{matrix}$

(i) Given,

1 vol. of di nitrogen produced at the same time as 8.96 litres of steam (2 vol)

Hence, Vol of di nitrogen = $\dfrac{8.96}{2}$ = 4.48 lit.

Hence, volume of di nitrogen oxide produced = 4.48 lit.

(ii) 2 vol = (2 x 22.4) lit steam is produced from 80 g NH₄NO₃

∴ 8.96 lit of steam will be produced by $\dfrac{80}{2 \times 22.4}$ x 8.96 = 16 g

Hence, 16 g of ammonium nitrate is required to be heated.

(iii) % of oxygen in ammonium nitrate = $\dfrac{3 \times 16}{80}$ x 100 = 60 %

Given that the relative molecular mass of copper oxide is 80, what volume of ammonia (measured at STP) is required to completely reduce 120 g of copper oxide? The equation for the reaction is:

3CuO + 2NH₃ ⟶ 3Cu + 3H₂O + N₂

Answer

$\begin{matrix} 3\text{CuO} & + & 2\text{NH}_3 \\ 3\text{ mol.} & & 2 \text{ mol.} \\ = 3 \times 80 \text{ g.} & & = 2 \times 22.4 \text{ lit.} \\ = 240 \text{ g.} & & = 44.8\text{ lit.} \\ \end{matrix}$

$\longrightarrow 3\text{Cu} + 3\text{H}_2\text{O} + \text{N}_2$

240 g of CuO is reduced by 44.8 lit of NH₃

∴ 120 g of CuO is reduced by $\dfrac{44.8}{240}$ x 120 = 22.4 lit.

Hence, 22.4 lit of NH₃ is required

(a) Calculate the number of moles and the number of molecules present in 1.4 g of ethylene gas. What is the volume occupied by the same amount of ethylene?

(b) What is the vapour density of ethylene?

Answer

Gram molecular mass of C₂H₄
= 2(12) + 4(1)
= 24 + 4 = 28 g

As,

28 g of C₂H₄ = 1 mole
∴ 1.4 g of C₂H₄ = $\dfrac{1}{28}$ x 1.4 = 0.05 moles

1 mole = 6 × 10²³ molecules
∴ 0.05 moles = 6 × 10²³ x 0.05 = 3 x 10²² molecules

Hence, no. of moles is 0.05 and no. of molecules is 3 x 10²².

Vol. occupied by 1 mole = 22.4 lit
∴ Vol. occupied by 0.05 moles = 22.4 x 0.05 = 1.12 lit.

Hence, vol. occupied is 1.12 lit

(b)
$\text{Vapour density} = \dfrac{\text{Molecular weight}}{2} = \dfrac{28}{2} = 14$

Hence, vapour density is 14

(a) Calculate the percentage of sodium in sodium aluminium fluoride (Na₃AlF₆) correct to the nearest whole number.

(F = 19; Na =23; Al = 27)

(b) 560 ml of carbon monoxide is mixed with 500 ml of oxygen and ignited. The chemical equation for the reaction is as follows:

2CO + O₂ ⟶ 2CO₂

Calculate the volume of oxygen used and carbon dioxide formed in the above reaction.

Answer

Molecular weight of sodium aluminium fluoride (Na₃AlF₆)
= 3(23) + 27 + 6(19)
= 69 + 27 + 114
= 210 g

210 g of sodium aluminium fluoride contains 69 g of Na

∴ 100 g of sodium aluminium fluoride will contain = $\dfrac{69}{210}$ x 100 = 32.85% = 33%

Hence, percentage of sodium in sodium aluminium fluoride (Na₃AlF₆) is 33%

(b)

$\begin{matrix} 2\text{CO} & + & \text{O}_2 & \longrightarrow & 2\text{CO}_2 & \\ 2 \text{ vol.} & : & 1 \text{ vol.} & \longrightarrow & 2\text{ vol.} \\ \end{matrix}$

1 mole of O₂ has volume = 22400 ml

Volume of oxygen used by 2 × 22400 ml CO = 22400 ml

∴ Vol. of O₂ used by 560 ml CO

= $\dfrac{22400}{2 × 22400}$ x 560

= 280 ml

Volume of CO₂ formed by 2 × 22400 ml CO = 2 x 22400 ml

∴ Vol. of CO₂ formed by by 560 ml CO

= 560 ml

A gas cylinder of capacity of 20 dm³ is filled with gas X the mass of which is 10 g. When the same cylinder is filled with hydrogen gas at the same temperature and pressure the mass of the hydrogen is 2 g, hence the relative molecular mass of the gas is:

i. 5

ii. 10

iii. 15

iv. 20

Answer

10

Working

Vapour density of gas =

$\dfrac{\text{Wt. of certain volume of gas }}{\text {Wt. of same volume of H}_2} \\[0.5em] = \dfrac{10}{2} \\[0.5em] = 5 \text{ g}$

Molecular weight = 2 x Vapour density
= 2 x 5 = 10 g

Hence, relative molecular mass of gas is 10 g

Calcium carbide is used for the artificial ripening of fruits. Actually the fruit ripens because of the heat evolved while calcium carbide reacts with moisture. During this reaction calcium hydroxide and acetylene gas is formed. If 200 cm³ of acetylene is formed from a certain mass of calcium carbide, find the volume of oxygen required and carbon dioxide formed during the complete combustion. The combustion reaction can be represented as below.

2C₂H₂(g) + 5O₂(g) ⟶4CO₂(g) + 2H₂O(g)

Answer

$\begin{matrix} 2\text{C}_2\text{H}_2 & + & 5\text{O}_2 \longrightarrow & 4\text{CO}_2 & + &2\text{H}_2\text{O} \\ 2\text{ mol.} & & 5 \text{ mol.} & 4\text{ mol.}\ \end {matrix}$ According to Gay-Lussac's law,

2 volume of acetylene requires 5 volume of oxygen

1 volume of acetylene requires $\dfrac{5}{2}$ = 2.5 volume of oxygen

∴ 200 cm³ of acetylene requires $\dfrac{2.5}{1}$ x 200

= 500 cm³ of oxygen

2 volume of acetylene produces 4 volume of CO₂

1 volume of acetylene produces $\dfrac{4}{2}$ = 2 volume of CO₂

∴ 200 cm³ produces $\dfrac{2}{1}$ x 200 = 400 cm³ of CO₂

A gaseous compound of nitrogen and hydrogen contains 12.5% hydrogen by mass. Find the molecular formula of the compound if its relative molecular mass is 37. (N = 14, H = 1).

Answer

Simplest ratio of whole numbers N : H = 1 : 2

Hence, empirical formula is NH₂

Empirical formula weight = 14 + 2(1) = 16

Relative molecular mass = 37

$\text{n} = \dfrac{\text{Molecular weight}}{\text{Empirical formula weight}} \\[0.5em] = \dfrac{37}{16} = 2.31 = 2$

∴ Molecular formula = n[E.F.] = 2[NH₂] = N₂H₄

A gas cylinder contains 24 × 10²⁴ molecules of nitrogen gas. If Avogadro's number is 6 × 10²³ and the relative atomic mass of nitrogen is 14, calculate :

(1) Mass of nitrogen gas in the cylinder.

(2) Volume of nitrogen at STP in dm³

Answer

(1) Gram molecular mass of N₂ = 2(14) = 28 g

6 × 10²³ molecules of N₂ weighs 28 g

∴ 24 × 10²⁴ molecules will weigh $\dfrac{28}{6 \times 10^{23}}$ x 24 × 10²⁴ = 1120 g

(2) 6 × 10²³ molecules of N₂ occupies 22.4 dm³

∴ 24 × 10²⁴ molecules of N₂ will occupy $\dfrac{22.4}{6 \times 10^{23}}$ x 24 × 10²⁴ = 896 dm³

Commercial sodium hydroxide weighing 30g has some sodium chloride in it. The Mixture on dissolving in water and subsequent treatment with excess silver nitrate solution formed a precipitate weighing 14.3 g. What is the percentage of sodium chloride in the commercial sample of sodium hydroxide? The equation for the reaction is

NaCl + AgNO₃ ⟶ AgCl + NaNO₃

(Relative molecular mass of NaCl = 58; AgCl = 143)

Answer

$\underset{58 \text{g}}{\text{NaCl}} + \text{AgNO}_3 \longrightarrow \underset{143 \text{ g}}{\text{AgCl}} + \text{NaNO}_3$

(i) 143 g AgCl is formed by 58 g NaCl

∴ 14.3 g of AgCl will be formed by $\dfrac{58}{143}$ x 14.3 = 5.8 g

Percentage of NaCl = $\dfrac{5.8}{30}$ x 100 = 19.33%

Hence, percentage of NaOH is 19.33%

A certain gas 'X' occupies a volume of 100 cm³ at S.T.P. and weighs 0.5 g. Find its relative molecular mass

Answer

100 cm³ weighs 0.5 g

∴ 22400 cm³ weighs $\dfrac{0.5}{100}$ x 22400 = 112 g

Hence, relative molecular mass of the gas = 112 g.

LPG stands for liquefied petroleum gas. Varieties of LPG are marketed including a mixture of propane (60%) and butane (40%). If 10 litre of this mixture is burnt, find the total volume of carbon dioxide gas added to the atmosphere. Combustion reactions can be represented as:

C₃H₈ + 5O₂ ⟶ 3CO₂ + 4H₂O

2C₄H₁₀ + 13O₂ ⟶ 8CO₂ + 10H₂O

Answer

Given, 10 litres of this mixture contains 60% propane and 40% butane. Hence, propane is 6 litres and butane is 4 litres

$\begin{matrix} \text{C}_3\text{H}_8 & + & 5\text{O}_2 & \longrightarrow & 3\text{CO}_2 & + & 4\text{H}_2\text{O} \\ 1 \text{ vol.} & : & 5 \text{ vol.} & \longrightarrow & 3\text{ vol.} \\ 2\text{C}_4\text{H}_{10} & + & 13\text{O}_2 & \longrightarrow & 8\text{CO}_2 & + & 10\text{H}_2\text{O} \\ 2 \text{ vol.} & : & 13 \text{ vol.} & \longrightarrow & 8\text{ vol.} \\ \end{matrix}$

1 Vol. C₃H₈ produces carbon dioxide = 3 Vol

So, 6 litres C₃H₈ will produce carbon dioxide = 3 x 6 = 18 litres

2 Vol. C₄H₁₀ produces carbon dioxide = 8 Vol

So, 4 litres C₄H₁₀ will produce carbon dioxide = $\dfrac{8}{2}$ x 4 = 16 litres

Hence, 34 (i.e., 18 + 16) litres of CO₂ is produced.

Calculate the percentage of nitrogen and oxygen in ammonium nitrate. (Relative molecular mass of ammonium nitrate is 80, H = 1, N = 14, O = 16).

Answer

Given,

molecular mass of ammonium nitrate = 80

mass of nitrogen in 1 mole of ammonium nitrate (NH₄NO₃) is 2(14) = 28 g

percentage of nitrogen in ammonium nitrate = $\dfrac{28}{80}$ x 100 = 35%

mass of oxygen in 1 mole of ammonium nitrate (NH₄NO₃) is 3(16) = 48 g

percentage of oxygen in ammonium nitrate = $\dfrac{48}{80}$ x 100 = 60%

Hence, percentage of nitrogen is 35% and percentage of oxygen is 60%

4.5 moles of calcium carbonate are reacted with dilute hydrochloric acid.

(i) Write the equation for the reaction.

(ii) What is the mass of 4.5 moles of calcium carbonate? (Relative molecular mass of calcium carbonate is 100)

(iii) What is the volume of carbon dioxide liberated at STP?

(iv) What mass of calcium chloride is formed? (Relative molecular mass of calcium chloride is 111).

(v) How many moles of HCl are used in this reaction?

Answer

(i) CaCO₃ + 2HCl ⟶ CaCl₂ + H₂O + CO₂

(ii) Given,

1 mole of CaCO₃ = molecular mass of CaCO₃ = 100 g

∴ 4.5 moles of CaCO₃ weighs $\dfrac{100}{1}$ x 4.5 = 450 g

(iii) 1 mole of CaCO₃ produces 1 mole of CO₂ and 1 mole occupies 22.4 l of volume.

∴ 4.5 moles of CaCO₃ will produce 4.5 moles of CO₂ and 4.5 moles will occupy 22.4 x 4.5 = 100.8 L

(iv) 1 mole CaCO₃ produces 111 g. CaCl₂

∴ 4.5 moles of CaCO₃ will produce = 111 x 4.5 = 499.5 g.

(v)

$\begin{matrix}\text{CaCO}_3 & : & \text{HCl} & \\ \text{ 1 mole} & : & 2 \text{ moles} \\ \text{ 4.5 mole} & : & x \text{ moles} \\ \end{matrix}$

∴ number of moles of HCl used = 2 x 4.5 = 9 moles.

Hence, moles of HCl used = 9 moles.

i. Calculate the volume of 320 g of SO₂ at STP. (Atomic mass: S = 32 and O = 16).

ii. State Gay-Lussac's Law of combining volumes

iii. Calculate the volume of oxygen required for the complete combustion of 8.8 g of propane (C₃H₈). (Atomic mass: C = 12, O = 16, H = I, Molar Volume = 22.4 dm³ at stp.)

Answer

(i) Gram molecular mass of SO₂ = 32 + 2(16) = 32 + 32 = 64 g

64 g of SO₂ occupy 22.4 lit of vol.

320 g of SO₂ will occupy = $\dfrac{22.4}{64}$ x 320 = 112 lit.

Hence, volume of 320 g of SO₂ = 112 lit.

(ii) Gay-Lussac's law Gay-Lussac's Law states "When gases react, they do so in volumes which bear a simple ratio to one another and to the volume of the gaseous product, if all the volumes are measured at the same temperature and pressure."

(iii)

$\begin{matrix} \text{C}_3\text{H}_8 & + &5\text{O}_2 & \longrightarrow & 3\text{CO}_2 & + & 4\text{H}_2\text{O} \\ 3(12) + 8(1) & & 5 \text{ vol} \\ = 44 \text{ g}& & 5 (22.4) \text{ lit} \\ \end{matrix}$

(i) 44 g propane requires 5 x 22.4 lit of oxygen

∴ 8.8 g of propane will require $\dfrac{5 \times 22.4}{44}$ x 8.8 = 22.4 lit.

Hence, 22.4 lit of Oxygen is required.

An organic compound with vapour density = 94 contains C = 12.67%, H = 2.13%, and Br = 85.11%. Find the molecular formula. (Atomic mass : C = 12, H = 1, Br = 80)

Answer

Simplest ratio of whole numbers = C : H : Br = 1 : 2 : 1

Hence, empirical formula is CH₂Br

Empirical formula weight = 12 + 2(1) + 80 = 94

Vapour density (V.D.) = 94

Molecular weight = 2 x V.D. = 2 x 94

$\text{n} = \dfrac{\text{Molecular weight}}{\text{Empirical formula weight}} \\[0.5em] = \dfrac{2 \times 94}{94} = 2$

∴ Molecular formula = n[E.F.] = 2[CH₂Br] = C₂H₄Br₂

Calculate the mass of:

1. 10²² atoms of sulphur.

2. 0.1 mole of carbon dioxide.

Answer

(i) gram molecular mass of S = 32

6 × 10²³ atoms weigh = 32 g

10²² atoms will weigh = $\dfrac{32}{6 \times 10^{23}}$ x 10²² = 0.533 g

(ii) 1 mole of carbon dioxide weighs = C + 2(O) = 12 + 2(16) = 12 + 32 = 44 g

∴ 0.1 mole of carbon dioxide weighs = 44 x 0.1 = 4.4 g.

Concentrated nitric acid oxidises phosphorus to phosphoric acid according to the following equation:

P + 5HNO₃ [conc.] ⟶ H₃PO₄ + H₂O + 5NO₂.

If 9.3 g of phosphorus was used in the reaction, calculate :

(i) Number of moles of phosphorus taken.

(ii) The mass of phosphoric acid formed.

(iii) The volume of nitrogen dioxide produced at STP.

Answer

$\begin{matrix} \text{P} & + & 5\text{HNO}_3 & \longrightarrow & \text{H}_3\text{PO}_4 & + & \text{H}_2\text{O} & + & 5\text{NO}_2 \\ 31 \text{ g} & & [conc.] & & 3(1) + 31 \\ & & & & + 4(16) \\ & & & & = 98 \text{ g} \\ \end{matrix}$

(i)

31 g of P = 1 mole

∴ 9.3 g of P = $\dfrac{1}{31}$ x 9.3 = 0.3 moles.

Hence, 0.3 moles of phosphorous was taken for the reaction.

(ii)

31 g of P forms 98 g of phosphoric acid

∴ 9.3 g will form $\dfrac{ 98}{31}$ x 9.3 = 29.4 g.

Hence, 29.4 g. of phosphoric acid is formed

(iii)

31 g of P produces 5 vol = 5 x 22.4 lit.

∴ 9.3 g will produce = $\dfrac{5 \times 22.4}{31}$ x 9.3 = 33.6 lit.

67.2 litres of hydrogen combines with 44.8 litres of nitrogen to form ammonia :

N₂(g) + 3H₂(g) ⟶ 2NH₃(g).

Calculate the vol. of ammonia produced. What is the substance, if any, that remains in the resultant mixture ?

Answer

[By Lussac's law]

$\begin{matrix} \text{N}_2 & + & 3\text{H}_2 & \longrightarrow & 2 \text{NH}_3 \\ 1 \text{ vol.} & : & 3 \text{ vol.} & \longrightarrow & 2\text{ vol.} \end{matrix}$

To calculate the volume of ammonia gas formed.

$\begin{matrix} \text{H}_2 & : & \text{NH}_3 \\ 3 & : & 2 \\ 67.2 & : & x \end{matrix}$

$\therefore \dfrac{2}{3} \times 67.2 = 44.8 \text{ lit}$

Hence, volume of NH₃ formed is 44.8 lit.

We know,

$\begin{matrix}\text{H}_2 & : & \text{N}_2 \\ 3 & : & 1 \\ 67.2 & : & x \end{matrix}$