Question

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 ethane molecules does the sample of gas contain?

• A. $0.8\times {10}^{20}$ molecules
• B. $1.5\times {10}^{22}$ molecules
• C. $0.8\times {10}^{26}$ molecules
• D. $1.5\times {10}^{20}$ molecules

Answer 1

The correct option is A $0.8\times {10}^{20}$ molecules

Mass of $1$ molecule of $C{H}_4=\frac{16}{N_A}g$
Mass of $1.5\times {10}^{20}$ molecules of methane $=\frac{1.5\times {10}^{20}\times 16}{N_A}g$

Mass of $x$ molecules of $C_2{H}_6$ is $=\frac{1.5\times {10}^{20}\times 16}{N_A}g$
We know that mass of $1$ molecule of $C_2{H}_6=\frac{30}{N_A}g$
$\therefore$ Number of molecules of ethane $\left(x\right)$ $=\frac{1.5\times {10}^{20}\times 16}{N_A}\times \frac{N_A}{30}=0.8\times {10}^{20}$