This questions concerns stoichiometry and the percent yield.

Question

The process of coal gasification is used to convert coal, which is pure carbon, into methane gas according to the following reaction: 2C(s) + 2H2O(l) yields CH4(g) + CO2(g). If the reaction has 82% yield, determine the mass of methane produced from 100.0 kg coal. 

Answer 1

2C(s) + 2H2O(l) ==> CH4(g) + CO2(g) .. balanced equation

Determine moles of coal (C)

100.0 kg C x 1000 g / kg x 1 mol C / 12.01 g = 8326.4 mols C

Determine moles of methane (CH4) theoretically produced

8326.4 mols c x 1 mol CH4 / 2 mol C = 4163.2 mols CH4

Determine theoretical mass of methane (CH4)

4163.2 mols CH4 x 16.04 g / mol = 66777.7 g CH4

Determine mass of methane (CH4) assuming 82% yield

66777.8 g x 0.82 = 54,758 g

Round answer to 2 significant figures (based on 82%)

55,000 g