# Consider a mixture of gas molecule of types

Question:

Consider a mixture of gas molecule of types $A, B$ and $\mathrm{C}$ having masses $\mathrm{m}_{\mathrm{A}}<\mathrm{m}_{\mathrm{B}}<\mathrm{m}_{\mathrm{C}}$. The ratio of their root mean square speeds at normal temperature and pressure is :

1. $\mathrm{v}_{\mathrm{A}}=\mathrm{v}_{\mathrm{B}}=\mathrm{v}_{\mathrm{C}}=0$

2. $\frac{1}{\mathrm{~V}_{\mathrm{A}}}>\frac{1}{\mathrm{~V}_{\mathrm{B}}}>\frac{1}{\mathrm{v}_{\mathrm{C}}}$

3. $\mathrm{v}_{\mathrm{A}}=\mathrm{v}_{\mathrm{B}} \neq \mathrm{v}_{\mathrm{C}}$

4. $\frac{1}{\mathrm{v}_{\mathrm{A}}}<\frac{1}{\mathrm{v}_{\mathrm{B}}}<\frac{1}{\mathrm{v}_{\mathrm{C}}}$

Correct Option: , 4

Solution:

$\mathrm{V}_{\mathrm{RMS}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}$

$m_{\mathrm{A}}<\mathrm{m}_{\mathrm{B}}<\mathrm{m}_{\mathrm{C}}$

$\Rightarrow \mathrm{V}_{\mathrm{A}}>\mathrm{V}_{\mathrm{B}}>\mathrm{V}_{\mathrm{C}}$

$\Rightarrow \frac{1}{\mathrm{~V}_{\mathrm{A}}}<\frac{1}{\mathrm{~V}_{\mathrm{B}}}<\frac{1}{\mathrm{~V}_{\mathrm{C}}}$