Question

For a cylinder of hydrogen (H2) gas, you have been informed that the rms speed of the molecules is 505 m/s. Determine the temperature of the gas in degrees K. Use 2.0159 ✕ 10−3 kg as the mass of a mole of hydrogen molecules.

Answer 1

Answer:

20.6 K

Explanation:

The root mean square velocity is the square root of the average of the square of the velocity. It can be calculated using the following expression.

$v_{rms}=\sqrt{\frac{3RT}{M} }$

where,

$v_{rms}$: root mean square velocity

R: ideal gas constant

T: absolute temperature

M: molar mass

Then, we can find the temperature,

$v_{rms}=\sqrt{\frac{3RT}{M} }\\T=\frac{v_{rms}^{2}M }{3R} =\frac{(505m/s)^{2}2.0159 \times 10^{-3} kg/mol}{3 \times (8.314 J/mol.K)} =20.6 K$