The Problem
A gas mixture contains hydrogen, carbon monoxide, and carbon dioxide. Calculate:
a) The mass% hydrogen if the mixture contains 15 mol% $\ce{CO}$ and no $\ce{CO2}$;
b) The molar composition if the mass fraction of $\ce{CO}$ and $\ce{CO2}$ are both 0.35.
My Attempt
I first calculated the molar masses:
molar_mass$\ce{H2}$ = 2.01588 g
molar_mass$\ce{CO2}$ = 44.0095 g
molar_mass$\ce{CO}$ = 28.0101 g
a) The mass% hydrogen if the mixture contains 15 mol% $\ce{CO}$ and no $\ce{CO2}$;
Since the mixture contains 15 mol% $\ce{CO}$ and no $\ce{CO2}$, then the mol% of $\ce{H2}$ must be 85.
I set the mixture equal to 10 mols. This means that there are 1.5 moles $\ce{CO}$ and 8.5 moles $\ce{H2}$. I then converted these values to grams.
1.5 mol $\ce{CO}$ = 42.015 g $\ce{CO}$
8.5 mol $\ce{H2}$ = 17.135 g $\ce{H2}$
The total grams is 59.15 g. The percent of $\ce{H2}$ would then be 29% since 17.135 / 59.15 = 0.29.
b) The molar composition if the mass fraction of $\ce{CO}$ and $\ce{CO2}$ are both 0.35.
Since the mass fractions of $\ce{CO}$ and $\ce{CO2}$ are both 0.35, the mass fraction of $\ce{H2}$ must be 0.3.
I set the mixture equal to 100 g. This means that there would be 35 g $\ce{CO}$, 35 g $\ce{CO2}$, and 30 g $\ce{H2}$.
Converting these to mols:
35 g $\ce{CO}$ = 1.25 mol $\ce{CO}$
35 g $\ce{CO2}$ = 0.795 mol $\ce{CO2}$
30 g $\ce{H2}$ = 14.88 mol $\ce{H2}$
This gives us a molar composition of 0.88 $\ce{H2}$; 0.07 $\ce{CO}$; and 0.05 $\ce{CO2}$.
My answers matched up with the solution key, but did I solve this question in the 'right' way? Or is there a better/quicker alternative?