The molecular weight of nitrogen,N₂,is 28 g/mol.What is the rms speed of nitrogen molecules in a cooler at 8.0°C? The Boltzmann constant is 1.38 × 10^-23 J/K and N_A = 6.022 × 10²³ molecules/mol. A)450 m/s B)500 m/s C)550 m/s D)600 m/s E)650 m/s

Question

Quizplus · Accepted Answer

We can use the formula for root-mean-square (rms) speed of gas molecules:

vrms = sqrt ((3kT) / M)

where k is the Boltzmann constant, T is the temperature in Kelvin, and M is the molar mass in kg/mol.

Converting the given temperature from Celsius to Kelvin:

T = 8.0°C + 273 = 281 K

Converting the molar mass of nitrogen from g/mol to kg/mol:

M = 28 g/mol / 1000 g/kg = 0.028 kg/mol

Putting in the values:

vrms = sqrt ((3 x 1.38 x 10^-23 J/K x 281 K) / 0.028 kg/mol)

vrms = 500 m/s (rounded to the nearest integer)

Therefore, the answer is B) 500 m/s.

The Molecular Weight of Nitrogen,N2,is 28 G/mol

The Molecular Weight of Nitrogen,N₂,is 28 G/mol