9.96 | The root mean square speed of H2 molecules at 25 °C is about 1.6 km/s. What is the root mean

The root mean square speed of H2 molecules at 25 °C is about 1.6 km/s. What is the root mean square speed of a N2 molecule at 25 °C?``.
The root mean square speed (rms speed) of a gas molecule is given by the equation:

rms speed = √(3RT / M)

Where:
- R = 8.314 J/mol·K (universal gas constant)
- T = temperature in Kelvin
- M = molar mass of the gas in kg/mol

The ratio of the rms speeds of two gases can be derived from the equation:

rms speed of gas 1 / rms speed of gas 2 = √(M2 / M1)

Given:
- rms speed of H2 = 1.6 km/s
- Molar mass of H2 = 2.016 g/mol = 0.002016 kg/mol
- Molar mass of N2 = 28.014 g/mol = 0.028014 kg/mol

Now, applying the ratio:

rms speed of N2 / rms speed of H2 = √(M_H2 / M_N2)

rms speed of N2 = rms speed of H2 × √(M_H2 / M_N2)
rms speed of N2 = 1.6 km/s × √(0.002016 kg/mol / 0.028014 kg/mol)

rms speed of N2 = 1.6 km/s