kinetic theory急

Larry

2010-10-30 11:57 pm

calculate the root-mean-square speed of the molecules of hydrogen at
(a)273K and (b)373K. Density of hydrogen at s.t.p.=9x10^-2 kg/m^3 and one standard atmosphere=1.01x10^5 Pa

回答 (1)

天同

2010-10-31 7:29 am

✔ 最佳答案

Use the formula: P = (1/3).d.v^2
where P is the pressure of gas, with density d, and root-mean-square (rms) speed of v

but density d = m/V, where m is the mass of gas and V is the gas volume
hence, P = (1/3).(m/V).v^2
or PV = (m/3).v^2

From ideal gas equation, PV = nRT
where n is the no. of moles of the gas (= m/M, M is the molar mass of gas), R is the Universal Gas Constant and T is the absolute temperature.

Thus, nRT = (m/3),v^2
(m/M)RT = (m/3)v^2
i.e. v^2 = 3RT/M
v = square-root[3RT/M]

(a) At 273 K, v = square-rrot[3 x 8.31 x 273/2x10^-3] m/s = 1845 m/s

(b) At 373 K, v = square-root[3x8.31x373/2x10^-3] m/s = 2156 m/s

👍 0 👎 0