Be sure to answer all parts. Helium (He) is the lightest noble gas component of

Question

Be sure to answer all parts. Helium (He) is the lightest noble gas component of air, and xenon Ce) is the heaviest. Perform the following calculations, usingR E 8.314 J/Cmol K) and M in kg/mol. (a) Find the rms speed of He in winter (0.°C) and in summer 30. C). Enter your answers in scientific notation. x 10 x 10 m/s m/s (summer) (winter) (b) Find the ratio of the rms speed of He to that of Xe at 30. C. Crate He)/Crate Xe) (c) Find the average kinetic energy per mole of He and of Xe at 30. C. Enter your answers in scientific notation. x 10 J/mol for He x 10 J/mol for Xe

Explanation / Answer

A) rms velocity = sqrt(3RT/M)

in winter = sqrt(3*8.314*273.15/(4*10^-3)) = 1305 m/s

    = 1.305*10^3 m/s

in summer = sqrt(3*8.314*303.15/(4*10^-3)) = 1374.9 m/s

   = 1.374*10^3 m/s

b) ratio (rHe/rXe) = sqrt(131.293/4) = 5.73

rHe: rXe = 1:5.73

c) averagevelocity = sqrt(8RT/3.14M)

He averagevelocity = sqrt(8*8.314*303.15/(3.14*4*10^-3))

      = 1267 m/s

xe averagevelocity = sqrt(8*8.314*303.15/(3.14*131.293*10^-3))

      = 221.15 m/s

KE of Xe = 1/2mv^2

      = 1/2*131.293*10^-3*221.153

      = 1.45*10^1 joule

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