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Root Mean Square Velocity

At same tempe...

Question

At same temperature, calculate the ratio of average velocities of $S O_{2}$ and $C H_{4}$ :

A

2 : 3

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B

3 : 4

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C

1 : 2

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D

1 : 6

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Solution

The correct option is C 1 : 2
$v_{avg} = \sqrt{\frac{8 R T}{π M}}$
where T is the temperature and Mis the molar mass of the gas.
Since $S O_{2}$ and $C H_{4}$ are at same temperature,
$\frac{v_{S O_{2}}}{v_{C H_{4}}} = \sqrt{\frac{M_{C H_{4}}}{M_{S O_{2}}}}$
$= \sqrt{\frac{16}{64}} = \frac{1}{2}$

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