mole fraction

A gaseous mixture of CO(g) and O2(g) contains 0.30 mole fraction of oxygen. Combustion occurs according to:
2CO(g) + O2(g) → 2CO2(g)
What is the mole fraction of CO2(g) in the final mixture, when the reaction is complete?

Before reaction:
Let n be the total number of moles.
No. of moles of O2 = 0.3n mol
No. of moles of CO = n - 0.3n = 0.7n mol

Equation: 2CO(g) + O2(g) → 2CO2(g)

Mole ratio CO : O2 : CO2 = 2 : 1 : 2
For complete reaction of 0.3n mol of O2,
no. of moles of CO needed = 0.3n x 2 = 0.6n mol
Hence, CO is in excess, O2 is completely reacted (limiting reactant).
No. of moles of CO2 formed = 0.3n x 2 = 0.6n mol

In the final mixture after reaction:
No. of moles of O2 left = 0.3n - 0.3n = 0 mol
No. of moles of CO left = 0.7n - 0.6n = 0.1n mol
No. of moles of CO2 formed = 0.6n mol
Total number of moles of the mixture = 0.1n + 0.6n = 0.7n
Mole fraction of CO2 = 0.6n/0.7n = 6/7