Examkin

Question

Difficulty: HardCarbon: Allotropes, Coal Distillation, and Industrial Fuel Gases

An industrial chemist passes steam over incandescent coke at 1000∘C1000^\circ\text{C} to synthesize water gas. If 120 g120\text{ g} of pure carbon is completely consumed in this reaction, what is the total volume of the resulting fuel gas mixture collected at s.t.p.? [Relative atomic mass: C=12;Molar volume of gas at s.t.p.=22.4 dm3 mol−1][\text{Relative atomic mass: } C = 12; \text{Molar volume of gas at s.t.p.} = 22.4\text{ dm}^3\text{ mol}^{-1}]

  1. A
    224 dm3224\text{ dm}^3
  2. 448 dm3448\text{ dm}^3Answer
  3. C
    672 dm3672\text{ dm}^3
  4. D
    112 dm3112\text{ dm}^3

Answer

The total volume of the resulting water gas mixture collected at s.t.p. is 448 dm3448\text{ dm}^3.
Water gas is produced by passing steam over incandescent carbon at high temperatures according to the equation C(s)+H2O(g)→CO(g)+H2(g)C_{(s)} + H_2O_{(g)} \rightarrow CO_{(g)} + H_{2(g)}. One mole of carbon yields two moles of gaseous products (1 mole CO1\text{ mole } CO and 1 mole H21\text{ mole } H_2). Given 120 g120\text{ g} of carbon (10 moles10\text{ moles}), the total moles of gas produced is 20 moles20\text{ moles}. Multiplying by the molar volume at s.t.p. (22.4 dm3 mol−122.4\text{ dm}^3\text{ mol}^{-1}) gives 448 dm3448\text{ dm}^3.

Step-by-Step Solution

1
Write the balanced thermochemical equation for water gas formation
C(s)+H2O(g)→CO(g)+H2(g)C_{(s)} + H_2O_{(g)} \rightarrow CO_{(g)} + H_{2(g)}
Passing steam over red-hot coke produces water gas, which is an equimolar mixture of carbon(II) oxide and hydrogen gas.
2
Calculate the moles of carbon reacted
Moles of C=120 g12 g mol−1=10 mol\text{Moles of } C = \frac{120\text{ g}}{12\text{ g mol}^{-1}} = 10\text{ mol}
Moles equal mass divided by molar mass.
3
Determine the total moles of gaseous products generated
From stoichiometry, 1 mol C→1 mol CO+1 mol H2=2 mol of gas mixture1\text{ mol } C \rightarrow 1\text{ mol } CO + 1\text{ mol } H_2 = 2\text{ mol of gas mixture}. Therefore, 10 mol C→20 mol of gas mixture10\text{ mol } C \rightarrow 20\text{ mol of gas mixture}.
Water gas comprises both COCO and H2H_2 gases.
4
Calculate total volume at s.t.p.
Volume=20 mol×22.4 dm3 mol−1=448 dm3\text{Volume} = 20\text{ mol} \times 22.4\text{ dm}^3\text{ mol}^{-1} = 448\text{ dm}^3
At s.t.p., 1 mole1\text{ mole} of any gas or gas mixture occupies 22.4 dm322.4\text{ dm}^3.

Key Concept

Manufacture and Stoichiometry of Industrial Fuel Gases (Water Gas)
Estimated Time:2m 0s
Rate this question

Topics

Carbon: Allotropes, Coal Distillation, and Industrial Fuel Gases

More questions from this topic