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A container of nitrogen (an ideal diatomic gas, molecular weight=28) is at a pressure of 2 atm and has a mass density of 1.6 grams per liter. What is the typical speed of the nitrogen molecules in the container? What is the root-mean-square velocity (vrms) of the center of mass of one of the molecules?

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Answer:

Explanation:What is the root-mean-square velocity (vrms) of the center of mass of one of the molecules?

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The root-mean-square velocity (vrms) of the center of mass of one of the molecules is; V_rms = 616.4 m/s

What is the root mean square velocity?

Formula for root mean square velocity is;

V_rms = √(3RT/M)

Where;

R = 8.314 J/mol.K

M is molecular weight = 28g/mol = 0.028kg/mol

T is temperature

mass density; ρ = 1.6 g/L

Recall that;

PV = (m/M)RT

Thus;

T = PM/ρR

V_rms = √(3R(PM/ρR)/M)

V_rms = √(3P/ρ)

V_rms = √(3 * 2 * 101325/1.6)

V_rms = 616.4 m/s

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