A sealed container holds a mixture of nitrogen molecules and helium molecules at a temperature of 290K. The total pressure exerted by the gas on the container is 120 kPa.
(M) molar mass of helium = 4 x 10-3 kg / mol
R= 8.31 J / K mol
Na= 6.02 x 1023 /mol
i) calculate root mean square speed of the helium molecules.
ii) calculate average kinetic energy of a nitrogen molecule.
iii)If there are twice as many helium molecules as nitrogen molecules in the container, calculate pressure exerted on the container by helium molecules.
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Answer:
i) Average kinetic energy per mole = (1/2) * Na*m v2 = 3/2 RT
Since M = Na * m= 4 x 10-3 kg / mol,
then, v2 = ( (3 * R T) / M = 3 * 8.31 * 290 / (4 x 10-3) =1.81 x 106
v_rms = √(1.81 x 106)
= 1346 m/s
ii) Average kinetic energy of a nitrogen molecule
= 3/2 KT, where K = boltzmann constant
= 3/2 * 1.38 * 10-23 * 290
= 6.00 *10-21 J
iii) pV = nRT
From here, we can see that R is constant, T and V is same for both helium and nitrogen. The only difference is n.
So, we can expect that helium molecules will exert twice the amount of pressure as the nitrogen molecules in this question
Hence, pressure exerted on the container by helium molecules is 80 kPa.
