Molecular Speed of Gases Formula With Boltzmann's Constant

The video starts by introducing the first formula for calculating root mean square molecular speed: √(3kT/m), where k is Boltzmann's constant and m is the mass of a single molecule in kilograms. For nitrogen gas (N2), the atomic mass is 28.02 amu. This is converted to kilograms by multiplying by 1.66 x 10^-27 kg/amu, resulting in 4.651 x 10^-26 kg.

Plugging the values into the formula: √(3 * 1.38 x 10^-23 J/K * 300 K / 4.651 x 10^-26 kg) yields approximately 517 meters per second as the root mean square molecular speed.

The second method utilizes the formula √(3RT/M), where R is the ideal gas constant (8.3145 J/mol·K) and M is the molar mass in kilograms per mole. The molar mass of N2 is 28.02 g/mol, which converts to 0.02802 kg/mol.

Substituting the values into the second formula: √(3 * 8.3145 J/mol·K * 300 K / 0.02802 kg/mol) also results in approximately 517 meters per second, demonstrating that both methods yield the same answer.