Question

A gaseous fuel mixture contains 25.3% methane (CH₄), 38.2% ethane (C₂H₆), and the rest propane (C₃H₈) by volume.

When the fuel mixture contained in a 1.76 L tank, stored at 756 mmHg and 298 K, undergoes complete combustion, how much heat is emitted? (Assume that the water produced by the combustion is in the gaseous state.)

Express your answer with the appropriate units.

Answer 1

This problem requires some literature data:

* Enthalpy of vaporization of water = 41 kJ/mol

* Enthalpy of combustion of methane = -882 kJ/mol

* Enthalpy of combustion of ethane = -1561 kJ/mol

* Enthalpy of combustion of propane = -2220 kJ/mol

Now,

Assuming ideal behavior of gases PV = nRT 756 x 1.76 760 = nx0.0821 x 298 mix = 0.072 mot Volume & no. of moles ; Tep constant naty = 0.072 x 2513 100 = 0.018 mot Nghe = 0.072 x 38.2 100 = 0.028 mot & N C₃H2 = 0.072-(0.018 +0.028) = 0.026 mol since water is assumed to be produced in the gaseous state, enthalpy of vaporisation of water needs to be subtracted from combustion enthalpies. So, adjusted ah of CH4 = 882 - 2x41 = 800 kJ/mot adjusted AH of who = 1561 – 3441 = 1438 kJ / mot adjusted Oh of Ch8 = 2220 - UX 4 = 2056 kJ/mol

Hence, total heat emitted in combustion of mixture = I no. of moles & Molar AH combustion = 0·018 X 800 + 0.028 X 1438 + 01026 X 2056 - 108.12 kJ Thus, Total heat emitted = 108.12 kJ