We are given for a diatomic Hydrogen, H2: its root-mean-square speed at 50°C is 2000 m/s, and the translational kinetic energy of 1 mole at 50°C is 4000 J.
We are asked to calculate the root-mean-square speed (vrms) of diatomic oxygen which has a molar mass that is 16 times that of the diatomic hydrogen at 50°C.
Recall that the root-mean-square speed is the measure of the speed of particles in a gas, defined as the square root of the average velocity-squared of the molecules in gas.
This is calculated as follows:
μrms = rms speed
R = 8.314 J/mol∙K
T = Temperature, Kelvin
M = molar mass, kg/mol
T = 50°C
(Convert to Kelvin)
T = 50 + 273.15
T = 323.15 K
The rms (root-mean-square) speed of a diatomic hydrogen molecule at 50°C is 2000 m/s. Note that 1.0 mol of diatomic hydrogen at 50°C has a total translational kinetic energy of 4000 J.
(A) Diatomic oxygen has a molar mass 16 times that of diatomic hydrogen. The root-mean-square speed vrms for diatomic oxygen at 50°C is:
(B) The total translational kinetic energy of 1.0 mole of diatomic oxygen at 50°C is:
(C) The temperature of the diatomic hydrogen gas sample is increased to 100°C. The root-mean-square speed vrms for diatomic hydrogen at 100°C is:
i. (16)(4000 J) = 64000 J
ii. (4)(4000 J) = 16000 J
iii. 4000 J
iv. (1/4)(4000 J) = 1000 J
v. (1/16)(4000 J) = 150 J
vi. (√2)(2000 m/s) = 2800 m/s
vii. (2)(2000 m/s) = 4000 m/s
viii. (1/√2) (2000 m/s) = 1400 m/s
ix. (1/2)(2000 m/s) = 1000 m/s
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