The volume V of an enclosure contains a
Question:

The volume $\mathrm{V}$ of an enclosure contains a mixture of three gases, $16 \mathrm{~g}$ of oxygen, $28 \mathrm{~g}$ of nitrogen and $44 \mathrm{~g}$ of carbon dioxide at absolute temperature $\mathrm{T}$. Consider $\mathrm{R}$ as universal gas constant.

The pressure of the mixture of gases is:

1. (1) $\frac{88 \mathrm{RT}}{\mathrm{V}}$

2. (2) $\frac{3 \mathrm{RT}}{\mathrm{V}}$

3. (3) $\frac{5}{2} \frac{\mathrm{RT}}{\mathrm{V}}$

4. (4) $\frac{4 \mathrm{RT}}{\mathrm{V}}$

Correct Option: , 3

Solution:

(3)

$\mathrm{PV}=\left(\mathrm{n}_{1}+\mathrm{n}_{2}+\mathrm{n}_{3}\right) \mathrm{RT}$

$\mathrm{P} \times \mathrm{V}=\left[\frac{16}{32}+\frac{28}{28}+\frac{44}{44}\right] \mathrm{RT}$

$\mathrm{PV}=\left[\frac{1}{2}+1+1\right] \mathrm{RT}$