Find the maximum temperature (for cases a and b) that can be attained in the bur

ID: 790887 • Letter: F

Question

Find the maximum temperature (for cases a and b) that can be attained in the burning of methane at constant P according to the reaction

CH4(g) + 2O2(g) --> CO2(g) + 2H2O(g)

a.) in O2

b.) in air, which is 80% N2 and 20% O2.

Assume the reaction goes to completion. The reagents are initially at 298K, and there is no energy loss from the flame.

Standard heats of formation for the products in the vapor phase:

CH4 = -74.7 kJ/mol

CO2 = -395.5 kJ/mol

H2O = -241.8 kJ/mol

Heat capacities:

O2 = 25.7 J/mol K

N2 = 27.3 J/mol K

CO2 = 26.0 J/mol K

H2O = 30.5 J/mol K

a) Heat released is difference of heat of formation

= 2*241.8 + 395.5 - 74.7 = 804.4 kJ

Therefore new temperature of all gases be T

total heat liberated = total heat taken

For maximum temperature to happen, Oxygen shouldn't take heat

2*30.5*(T-298) + 26*(T-298) = 804400

T = 9543.98 K

b) For 2 moles of Oxygen we need 2/0.2 = 10 moles of air

10 mole air has 8 moles Nitrogen.

Therefore though heat released = 804.4 kJ/mol

Heat will also be taken by N2

8*27.3*(T-298) + 2*30.5*(T-298) + 26*(T-298) = 804400

T = 2931.92 K

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