Question

Methane and ethane are the two simplest hydrocarbons. What is the mass % C in a mixture that is 40.0% methane and 60.0% ethane by mass?

Short answer

The mass % of C in a mixture is 77.8% C.

Step-by-step solution

Calculating the mass from C (CH4) 

It can be denoted as,

$Mass of C (from C{H}_4)=40 g C{H}_4\times \frac{1 mol C{H}_4}{16.05 g C{H}_4}\times \frac{1 mol C}{1 mol C{H}_4}\times \frac{12.01 g C}{1 molC}=29.9 g C$

Calculating the mass from C (C2H6)

It can be denoted as,

$Mass of C (from C_2{H}_6)=60 g C_2{H}_6\times \frac{1 mol C_2{H}_6}{30.08 g C_2{H}_6}\times \frac{2 mol C}{1 mol{C}_2{H}_6}\times \frac{12.01 g C}{1 molC}=47.9 g C$

Calculating the mass percent of C

The mass percent in the mixture can be denoted as,

$$\begin{gathered} Mass \% of C=\frac{29.9 g C+47.9 g C}{100 g mixture}\times 100 \\ Mass \% of C=77.8\% C \end{gathered}$$