Question

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?

Answer 1

`v_(rms) = 516.8 m/s`

Step-by-step explanation:

RMS speed is root mean square speed of ideal gas molecules

It is defined as the average value of the speed of gas molecules which is given as

`v_(rms) = \sqrt{(v_1^2 + v_2^2 + v_3^2...........................)/(N)}`

this above expression can be also calculated by the kinetic energy of the gas molecules

`v_(rms) = \sqrt{(3RT)/(M)}`

here we know that

T = temperature of gas

M = molar mass

now for nitrogen molecule at room temperature the RMS speed is given as

`v_(rms) = \sqrt{(3(8.31)(300))/(0.028)}`

`v_(rms) = 516.8 m/s`