Question

Question 43
A sample of ethane $\left(C_2{H}_6\right)$ gas has the same mass as $1.5\times {10}^{20}$ molecules of methane $\left(C{H}_4\right)$. How many $C_2{H}_6$ molecules does the sample of gas contain?

Answer 1

Avagadro Number, $N_A$=$6.022\times {10}^{23}$ atoms/ions/molecules
Mass of 1 molecule of $C{H}_4=\frac{16g}{N_A}$
Mass of $1.5\times {10}^{20}$ molecules of methane = $\frac{1.5\times {10}^{20}\times 16}{N_A}g$
Mass of 1 molecule of $C_2{H}_6$ is = $\frac{30}{N_A}g$
Mass of molecules of $C_2{H}_6=\frac{1.5\times {10}^{20}\times 16}{N_A}g$
$\therefore$ Number of molecules of ethane $\frac{1.5\times {10}^{20}\times 16}{N_A}\times \frac{N_A}{30}=0.8\times {10}^{20}$