Question

The temperature of an open room of volume $30 \, m^3$ increases from $17^{\circ}C$ to $27^{\circ}C$ due to the sunshine. The atmospheric pressure in the room remains $1 \times 10^5 \, Pa$. If $n_i$ and $n_f$ are the number of molecules in the room before and after heating, then $n_f-n_i$ will be :

• A. $- 1.61 \times 10^{23}$
• B. $1.38 \times 10^{23}$
• C. $2.5 \times 10^{25}$
• D. $- 2.5 \times 10^{25}$

Answer 1

Answer: (D)

$- 2.5 \times 10^{25}$

Answer 2

$n_1$ = initial number of moles $n_{1} = \frac{P_{1}V_{1}}{RT_{1}} = \frac{10^{5} \times30}{8.3 \times290}$ $\approx 1.24 \times10^{3}$ $n_2$ = final number of moles $=\frac{P_{2}V_{2}}{RT_{2}} = \frac{10^{5} \times30}{8.3 \times300}$ $\approx 1.20 \times10^{3}$ Change of number of molecules : $n_{f} - n_{i} = \left(n_{2} - n_{1}\right)\times6.023 \times10^{23}$ $\approx - 2.5 \times10^{25}$