First slide

Gaseous state

Question

The molecular velocities of two gases at same temperature are u₁ and u₂, their molar masses are m₁ and m₂respectively. Which of the following expression is correct?

Moderate

A

$\frac{m_{1}}{u_{1}^{2}} = \frac{m_{2}}{u_{2}^{2}}$
B

$m_{1} u_{1} = m_{2} u_{2}$
C

$\frac{m_{1}}{u_{1}} = \frac{m_{2}}{u_{2}}$
D

$m_{1} u_{1}^{2} = m_{2} u_{2}^{2}$

Solution

If molecular velocities are root mean square type at ternperature T K, then
$u_{1} = \sqrt{\frac{3 RT}{m_{1}}} \Rightarrow u_{2} = \sqrt{\frac{3 RT}{m_{2}}} \Rightarrow \frac{u_{1}^{2}}{u_{2}^{2}} = \frac{m_{2}}{m_{1}}$
$∴ m_{1} u_{1}^{2} = m_{2} u_{2}^{2}$

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