Chemistry - Thermochemistry Question with Solution | TestHub
When 0.1 mole of C8H18(l) at 300 K is completely burned at constant pressure in some oxygen gas at 300 K, yielding products gaseous H2O, CO and CO2 at 800 K, the process yielding 87.3 kcal of heat to the surrounding. Given:
Δf H (kcal/mol): C8H18(l) = -74.0, CO2(g) = -94.0, CO(g) = -26.5, H2O(g) = -58.0
Molar heat capacity at constant pressure (cal/K-mol): CO(g) = 7.0, CO2(g) = 8.0, H2O(g) = 6.0
Assume that all Δr H are independent of temperature.
What is the magnitude work done by the system?
Options:
Answer:
Solution:
The number of O atoms in the products is 2(0.4) + 0.4 + 0.9 = 2.1. Therefore, the amount of O₂ used is 1.05 mol.
The gaseous moles in the products are 0.4 + 0.4 + 0.9 = 1.7 at 800 K. The reactant O₂ is 1.05 mol at 300 K (C₈H₁₈ is a liquid).
The magnitude of work, |w|, is calculated as:
|w| = PΔ V = nf R Tf - ni R Ti
Substituting the values, we get:
|w| = R(1.7 × 800 - 1.05 × 300)
|w| = R(1360 - 315)
|w| = 1045 R
Given R ≈ 1.98 cal/(K·mol), the work done is approximately 1045 × 1.98 = 2069.1 cal, which is about 2.07 kcal. This corresponds to option (b).
