# At room temperature (27°C) the rms speed of molecules of a certain diatomic gas is found to be 1930 m/sec. The gas is:

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At room temperature (27°C) the rms speed of molecules of a certain diatomic gas is found to be 1930 m/sec. The gas is:

1. H2
2. F2
3. O2
4. Cl2

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Correct Answer - Option 1 : H2

Concept:

• Root Mean Square Speed: It is defined as the square root of the mean of squares of the speed of different molecules.
• The root-mean-square speed takes into account both molecular weight and temperature, two factors that directly affect the kinetic energy of a material.

From the expansion of pressure,

$P = \frac{1}{3}{\rm{\rho v}}_{rms}^2$

${v_{rms}} = \sqrt {\frac{{3P}}{\rho }}$

$V_{rms}= \sqrt {\frac{{3PV}}{{Mass\;of\;gas}}} = \sqrt {\frac{{3RT}}{M}}$

$[\because \rho = \frac{M}{V}]$

⇒ vrms ∝ T

Where, R = universal gas constant, M = molar mass, P = pressure due to density,ρ = density.

Calculation:

Given that, T = 27°C = 27+273 = 300 K, Vrms = 1930 m/sec

$V_{rms}= \sqrt {\frac{{3PV}}{{Mass\;of\;gas}}} = \sqrt {\frac{{3RT}}{M}}$

$1930 = \sqrt {\frac{{3 \times 8.31 \times {{10}^3} \times 300}}{M}}$

Mass = 2g, Hence the gas is H2.