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Solutions to Mole Concept Exercises

1. (a). Molality = number of moles/mass of solvent (kg)

Number of moles = mass (g)/molar mass 

Molar mass of C₁₂H₂₂O₁₁ (relative atomic mass; C = 12, H = 1, O = 16)

Molar mass = 12x12 + 22x1 + 11x16 = 342g/mol

Number of moles of sugar dissolved = 300/342 = 0.8772

Therefore, Molality of solution = 0.8772 mole / 1.5 kg = 0.5848 mol/kg

(b). Molarity of solution = number of moles/volume (dm³)

Number of moles (n) = molarity x volume (dm³)

n = 0.25 x 0.5 = 0.125

Number of moles = mass/molar mass

mass (g) = number of moles x molar mass

mass of sugar needed = 0.125 x 342 = 42.75g

2. (a). From the balanced equation: CH_4(g) + 2O_2(g) → CO_2(g) + 2H₂O_(l)

the mole ratio of methane CH₄ and oxygen is 1 : 2

1 mole of methane needs 2 moles of oxygen for combustion, therefore 3 moles of methane will require 6 moles of oxygen.

(b). Convert 100g of methane to moles:

number of moles = mass / molar mass

Molar mass of methane CH₄  (taking relative atomic mass C = 12, H= 1)

Molar mass of methane = 12x1 + 1x4 = 16g/mol

Number of moles of methane = 100/16   = 6.25

If 1 mole of methane require 2 moles of oxygen, 6.25 moles of methane will require 12.5 moles of oxygen.

(c). From the stoichiometry, 8 moles of oxygen are required to burn 4 moles of methane.

Converting 8 moles of oxygen to mass.

mass = number of moles x molar mass

mass of oxygen = 8 x 32 = 256g

Note that the molar mass of a diatomic molecule is the atomic mass of its element multiplied by the number of atoms it contains. Therefore molar mass of oxygen is 16 x 2 = 32g/mol.

(d). Converting 50g of methane to moles

number of moles = mass/molar mass = 50/16 = 3.125

From the stoichiometry, 1 mole of methane require 2 moles of oxygen, therefore, 3.125 moles of methane will require 3.125x2 = 6.250 moles of oxygen.

converting 6.250 moles of oxygen to mass,

mass = number of moles x molar mass

mass of oxygen required = 6.250 x 32 = 200g

3. (a). (i). The mass of 1 mole of sulphur, S₈ is same as its molar mass, which is its atomic mass multiplied by its number of atoms = 32 x 8 = 256g

(ii). mass of carbon = 2.5 moles x molar mass

2.5 x 12 = 30g

(iii). mass of tungsten = 0.003 mole x molar mass

0.003 x 184 = 0.552g

(iv). mass of iron = 4.2 x 10^-13 mole x molar mass

4.2 x 10^-13 x 56 = 2.35 x 10^-11 g

(b). (i). number of moles of nitrogen = mass/molar mass

= 100/28 = 3.57

(ii). number of moles of potassium trioxonitrate(V) - KNO₃ = 1000/molar mass

molar mass of KNO₃ (atomic mass: K = 39, N = 14, O = 16) = 39 + 14 + 16X3 = 101

number of moles = 1000/101 = 9.90

(c).  (i). mass = number of moles x molar mass

molar mass of carbon(II) oxide - CO = 12 + 16 = 28

mass = 1 x 28 = 28g

(ii). molar mass of water - H₂O = 1X2 + 16 = 18

mass = number of moles x molar mass

= 5 x 18 = 90g

(d). number of moles = mass/molar mass

molar mass of nitrogen molecule - N₂ = 14 x 2 = 28

number of moles = 500/28 = 17.86 

4. Al(NO₃)₃ → Al³⁺  + 3NO₃^-1

From the balanced equation above, 1 mole of Al(NO₃)₃ produces 1 mole of Al³⁺ ions 

number of moles of Al(NO₃)₃ = mass/molar mass

molar mass (atomic mass: Al = 27, N = 14, O = 16) = 27 + (14+48)X3 = 213

number of moles of Al(NO₃)₃ = 1000/213 = 4.69

Therefore, number of moles of Al³⁺ ions = 4.69

(ii). Al₂(SO₄)₃ → 2Al³⁺  + 3SO₄^-2

1 mole of Al₂(SO₄)₃ produces  2 moles of Al³⁺

number of moles of Al₂(SO₄)₃ = mass/molar mass

molar mass of Al₂(SO₄)₃ (atomic mass: Al = 27, S = 32, O =16) = 27X2 + (32 + 64)x 3 = 342

number of moles of Al₂(SO₄)₃ = 1000/342 = 2.92

Therefore number of moles of Al³⁺ ions = 2 x 2.92 = 5. 84

(b). Al(NO₃)₃ → Al³⁺  + 3NO₃^-1

The stoichiometry is 1 mole of Al(NO₃)₃ produces 3 moles of NO₃^-1

number of moles of Al(NO₃)₃ = 1000/213 = 4.69

Therefore, number of moles of  NO₃^-1 = 3 x 4.69 = 14.07

 See Tutorial on the mole here