A gaseous fuel containing methane and ethane is burned with excess air. The fuel enters the furnace at 25°C and 1 atm, and the air enters at 200.0°C and 1 atm. The stack gas leaves the furnace at 900.0°C and 1 atm and contains 5.45 mole% CO2, 2.14% CO, 6.44% O2, 12.91% H2O, and the balance N2.

a) Calculate the molar percentages of methane and ethane in the fuel gas and the

percentage excess air fed to the reactor.

b) Calculate the heat (kJ) transferred from the reactor per mole of fuel gas fed.

57.33%, 38.3%

Explanation:

The stack gas leaves the furnace with

5.45 mole% CO2, 2.14% CO, 6.44% O2, 12.91% H2O

Basis: 100 moles of stack gas

The molecular formula of methane is CH4 and ethane is C2H6,

Assume x = number of moles of methane

y = number of moles of ethane

Hence we have the carbon balance

x + 2y = 5.45 + 2.14 = 7.59

And we have the hydrogen balance

4x + 6y = 2 (12.91) = 25.82

Simultaneously solving the two equations, we obtain

x = 3.05 and y = 2.27

Hence, the molar percentage of methane in the fuel = 3.05 / (3.05+2.27) * 100% = 57.33%

Similarly, molar percentage of ethane is 42.67%

The oxygen entering = (100 - 5.45 - 2.14 - 6.44 - 12.91) * (21/79) = 19.42

And oxygen required = 2 (3.05) + 3.5 (2.27) = 14.045

Hence, excess air feed = 100 * (19.42 - 14.045) / 14.045 = 38.3%