Helium (He) is the lightest noble gas component of air, and xenon (Xe) is the he

Question

Helium (He) is the lightest noble gas component of air, and xenon (Xe) is the heaviest. Perform the following calculations, using R = 8.314 J/(mol middot K) and m in kg/mol. Find the rms speed of He in winter (0.degreeC) and in summer (30.degreeC). Enter your answers in scientific notation. Times 10 m/s times 10 m/s Find the ratio of the rms speed of He to that of Xe at 30.degreeC. (rate He)/(rate Xe) Find the average kinetic energy per mole of He and of Xe at 30.degreeC. Enter your answers in scientific notation. times 10 J/mol for He times 10 J/mol for Xe

Explanation / Answer

(a) Vrms= (3RT/Mm)1/2, where Mm = is the molar mass of the gas in kilograms per mole, T = temperature in Kelvin

at 00 C, temp = 273 K, Mm = 0.004 Kg/mol

therefore Vrms= (3 X 8.314 X 273/0.004)1/2 = 1304.7 m/s

At 300 C; Vrms= (3 X 8.314 X 303/0.004)1/2 = 1374.5 m/s

(b) At 300C, Vrms of Xe = (3 X 8.314 X 303/0.131)1/2  = 240.2

ratio of Vrms (He)/Vrms (Xe) at 300 C = 1374.5/240.2 = 5.7

(c) K.E.avg per mole = (3/2) X RT

For at 300 C K.E.avg per mole for both He and Xe = (3/2) X 8.314 X 303 =   3778.7 m/s

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