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

20.6 K

Step-by-step 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{(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{(3RT)/(M) }\\T=(v_(rms)^(2)M )/(3R) =((505m/s)^(2)2.0159 * 10^(-3) kg/mol)/(3 * (8.314 J/mol.K)) =20.6 K`