This histogram (Figure 1) shows a theoretical distribution of speeds of molecule

Question

This histogram (Figure 1) shows a theoretical distribution of speeds of molecules in a sample of nitrogen (N2) gas. In this problem, you'll use the histogram to compute properties of the gas.

Part B:

Because the kinetic energy of a single molecule is related to its velocity squared, the best measure of the kinetic energy of the entire gas is obtained by computing the mean squared velocity, (v2)avg, or its square root vrms. The quantity vrms is more common than (v2)avg because it has the dimensions of velocity instead of the less-familiar velocity-squared.

What is the rms speed vrms of the molecules in the nitrogen gas?

Express your answer numerically to three significant digits.

Part C:

What is the temperature T of the sample of N2 gas described in the histogram?

Express your answer in degrees Celsius to three significant figues.

Explanation / Answer

For calculation of the V2rms , we will use the above histogram
V2rms = (1002*6 + 3002*34 + 5002*36 + 7002*17 + 9002*5 + 11002*2) /100
Vrms = 518.8 m/s = 519 m/s
(c) Vrms = (3RT /M)1/2
   519 = (3*8.314*T /(0.028))1/2
T = 302.385 K = 29.385 C = 29.4 C

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