1) Balanced chemical equation:
C(s)+O2(g)→CO2(g), δh∘rxn=−393.5kj
2) Meaning: When burned 1 mol of C(s), this is solid pure charcoal, produces 1 mol of CO2 and liberates 393.5 kJ of heat
Ratio: 1 mol CO2 : 393.5 kJ
3) Proportion:
1 mol CO2 x
--------------- = -------------------
393.5 kJ 4.6 * 10^2 kJ
4) Solve for x:
x = 460 kJ * 1 mol CO2 / 393.5 kJ = 1.1690 mol CO2
5) convert moles to grams
mass in grams = number of moles * molar mass
mass in grams = 1.1690 mol * 44.01 g / mol = 51.4 g
Answer: 51.4 g