Answer
Molar mass of $C_{2}H_{6}=30.0684\,g/mol$
Mass percent of carbon= $79.8892\%$
Mass percent of hydrogen= $20.1109\%$
Work Step by Step
Molar mass of $C_{2}H_{6}=$
$2(12.0107\,g/mol)+6(1.00784\,g/mol)$
$=30.0684\,g/mol$
Mass percent of carbon= $\frac{2\times12.0107\,g }{30.0684\,g}\times100\%$
$=79.8892\%$
Mass percent of hydrogen= $\frac{6\times1.00784\,g}{30.0684\,g}\times100\% $
$=20.1109\%$