Question

The ratio of rms velocity of o2 at 27c to that of o2 at 327c is

Answer 1

Answer:

: At 327K, the root mean square velocity of both the gases will be equal.

Explanation: Root mean square velocity is related to the temperature and molar mass of the gas. It's expression is given by:

V_{rms}=\sqrt{\frac{3RT}{M}}

Where,

R = Gas constant

T = Temperature (in Kelvin)

M = Molar mass of gas

Now, we need to find the temperature at which root mean square velocity of SO_2 and O_2 is same

V_{rms}_1=V_{rms}_2

Squaring and cancelling the terms on both the sides.

\sqrt{\not{3}\not{R}\frac{T_1}{M_1}}=\sqrt{\not{3}\not{R}\frac{T_2}{M_2}}

\frac{T_1}{M_1}=\frac{T_2}{M_2}

M_1=\text{Molar mass of }SO_2=64g/mol

M_2=\text{Molar mass of }O_2=32g/mol

T_2=\text{Temperature at which }O_2\text{ is present}=27\°C=(27+273)K=300K

T_1=?K

Putting values in above equation:

\frac{T_1}{64g/mol}=\frac{300K}{32g/mol}

T_1=600K

T_1=327 \°C

This is the temperature of SO_2 at which root mean square vales of both the gases will be equal.