Question

If at stp velocity of sound in a gas is 600m/s the rms velocity of the gas molecule at stp will be

Answer 1

rms is a measure of the average speed of particles in a gas given by

$u_r_m_s=\sqrt{}\frac{3RT}{M}$, where R is the ideal gas constant $\frac{8.314J}{mol^-^1K^-^1}$, T is the temperature and M is the molar mas of that specific gas.

For instance if we use oxygen, which has a molar mas of 0.032kg/mol. and we know the gas is at stp, hence temperature is $25^{0}C + 273.15K = 298.15K$,

$u_r_m_s=\sqrt{}\frac{3RT}{M}=  \sqrt{}\frac{3 \times 8.314 |times 298.15}{0.032}= 482.1 m/s$

If we use carbon-dioxide ($CO_2$), which has molar mass 0.044kg/mol, then

$u_r_m_s= \sqrt{}\frac{3 \times 8.314 \times 298.15}{0.044} = 411 m/s$

Answer 2

The solution is provided in the attachment.

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