Question

the root mean square speed of oxygen at 27°c is 760cm-s the root mean square speed of hydrogen at the same temperature will be

Answer 1

RMS speed is directly prpotional to 1\under root of molecoular mass.

solve and u will get 4286.4 cm-s

Answer 2

Concept:

The square root of the average of the square of velocity is the root mean square (R.M.S.) velocity of a gas.

$R.M.S. =\sqrt{\frac{3 R T}{M}}$

R = gas constant, T = temperature (in K), M = molar mass of the gas.

Given:

R.M.S speed of oxygen = $760 cm/s$

Temperature=  $27{\°} C$

To Find:

R.M.S  speed of Hydrogen

Answer:

Root mean square speed is calculated by v= $\sqrt{\frac{3 R T}{M}}$

At the same temperature, R.M.S of oxygen = R.M.S of hydrogen

i.e., $\frac{v_{1} }{v_{2} } = \sqrt{\frac{M_{2}}{M_{1}}}$

$or \frac{760}{v_{2}}=\sqrt{\frac{2}{32}} or v_{2}=760 \times 4=3040 \mathrm{~cm} \mathrm{~s}^{-1}$

The R.M.S speed of hydrogen is $3040 cm/s$.

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