Question

find the rms speed v rms of the molecules of a sample of N₂ (diatomic nitrogen) gas at a temperature of 35.5 degrees celsius. the atomic mass of nitrogen is 14.0 g/mol and the boltzmann constant is 1.3806 x 10⁻²³ j/k

Answer 1

The rms speed of nitrogen molecules in N2 gas at 35.5 degrees Celsius is found using the formula v_rms = sqrt(3kT/m).

Step-by-step explanation:

To find the rms speed (vrms) of nitrogen molecules in N2 gas at a temperature of 35.5 degrees Celsius, we utilize the equation vrms = √(3kT/m), where k is the Boltzmann constant (1.3806 x 10-23 J/K), T is the absolute temperature in kelvin, and m is the mass of a single nitrogen molecule in kilograms.

Firstly, the molecular mass of N2 is 28.0 g/mol (since nitrogen is diatomic and each atom has a mass of 14.0 g/mol). To obtain m, we convert this mass to kilograms per molecule, using Avogadro's number: m = (28.0 g/mol) / (6.022 x 1023 mol-1).

Next, we convert the Celsius temperature to Kelvin: T = 35.5 + 273.15 = 308.65 K. Finally, we substitute the values into our formula to calculate vrms: vrms = √[(3×1.3806 x 10-23 J/K×308.65 K) / (28.0 g/mol × (1 kg/1000 g) / (6.022 x 1023 mol-1))].