Question

A mixture of carbon monoxide and methane gases with a total mass of 1.00 g was combusted in excess oxygen gas to produce carbon dioxide gas, liquid water, and 15.0 kJ of heat. Using the thermodynamic data, determine the mass percentage composition of the initial gas mixture (with two significant figures).

Answer 1

CO + CH4 = 1 g

CO2, H2O, H = 15 kJ

use thermo data

% mass of each species

CO + 1/2O2 = CO2

HRxn = CO2 - (CO + 1/2O2) = -393.5 - (-110.5 + 1/2*0 ) = -283 kJ

CH4 + O2 = CO2 + H2O

HRxn = CO2 + H2O - (CH4 + O2) = -393.5 + -285.8 - (-74.6 +0) = -604.7 kJ

Now...

mol of CO = x

mol of CH4 = y

energy balance

x*283 + y*604.7 = 15

mass balance

x*28 + y*16 = 1

y = (1 - 28x)/16

x*283 + (1 - 28x)/16*604.7 = 15

283x + 37.79 - 1058.12x = 15

(283 - 1058.12)x = 15 - 37.79

x = ( 15 - 37.79 ) /(283 - 1058.12)) = 0.02940

y = (1 - 28x)/16

y =  (1 - 28*0.02940)/16

y = 0.01105

x*28 + y*16 = 1

mass of CO = x*28 = 28*0.02940 = 0.8232 g --> 0.82 g

mass of CH4 = 16*y = 16*0.01105 = 0.1768 g --> 0.18 g