Question

Sample of $C_2H_6$ has same mass as $10^7$ molecules of $CH_y$. Howmany no. of molecules does the sample contain.

Answer 1

$\frac{10^7 (12+y)}{30}$ molecules

Answer 2

Let the number of molecules of $C_2H_6$ in the sample be $N$. The mass of one molecule of any compound is proportional to its molecular mass (in atomic mass units). Thus,

$$\begin{array}{rcl} \text{Mass of one } C_2H_6 &\propto& 2(12) + 6(1) = 30 \\ \text{Mass of one } CH_y &\propto& 12 + y \end{array}$$

Since the mass of the $C_2H_6$ sample equals the mass of $10^7$ molecules of $CH_y$:

$$N \times 30 = 10^7 \times (12 + y)$$

Solving for $N$:

$$N = \frac{10^7 \times (12+y)}{30}$$

Explanation (Minimal):

1. Calculate molecular mass: $C_2H_6 = 30$ and $CH_y = 12+y$.
2. Using the equality of masses: $N \cdot 30 = 10^7(12+y)$.
3. Solve: $N = \frac{10^7(12+y)}{30}$.