The rms (root-mean-square) speed of a diatomic hydrogen molecule at 50C is 2000

Question

The rms (root-mean-square) speed of a diatomic hydrogen molecule at 50C is 2000 m/s. Note that 1.0 mol of diatomic hydrogen at 50C has a total translational kinetic energy of 4000 J. Part A

diatomic oxygen has a molar mass 16 times that of diatomic hydrogen. the root-mean-square speed Vrme for diatomic oxygen at 50 degrees celsius is:

A. (16)(2000 m/s) = 32000 m/s

B. (4)(2000 m/s) = 8000 m/s

C. 2000 m/s

D. (1/4)(2000 m/s)= 500 m/s

E. (1/16)(2000 m/s) = 125 m/s

F. none of the above

Part B

the temperature of the diatomic hydrogen gas sample is increased to 100 degrees celsius. the root-mean-square speed Vrms for diatomic hydrogen at 100 degrees celsius is:

A. (2)(2000 m/s) = 4000 m/s

B. (sqrt 2)(2000) = 2800 m/s

C. 2000 m/s

D. (1/sqrt2) (2000 m/s) = 1400 m/s

E (1/2)(2000 m/s) = 1000 m/s

F. None of the above

Explanation / Answer

In accordance with equipartition theorem, the average translational energy of molecules is the same at thermal equilibrium. It implies that the average square of speed of molecules ( here hydrogen and oxygen ) varies inversely with their molecular masses.

As ratio of molecular masses of oxygen to hydrogen is 16:1, the sqaure of speeds are 16:1 and hence the speeds ratio is 4:1. In the given case, the rms speed of hydrgen molecule is 2000 m/s, thus, the rms speed of oxygen is

(1/4)(2000 m/s)= 500 m/s

Thus, the correct option is (D)

-----------------------------------------------------------------------------------------------------

Use the fcat that the rms speed is proportional to the square-root of the absolute temperature.

hence, speed of hydrogen at 100'C ( or = 473 K )

= 2000 x ( 473/323 )

= 2928 m/s

Thus, the correct option is ( F )

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.