The volume V of an enclosure contains a mixture of three gases,

Question:

The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T. Consider R as universal gas constant. The pressure of the mixture of gases is :

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

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

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

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


Correct Option: , 3

Solution:

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

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

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

$\mathrm{P}=\frac{5}{2} \frac{\mathrm{RT}}{\mathrm{V}}$

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