(a) What is the average translational kinetic energy of a nitrogen molecule at S
ID: 1796509 • Letter: #
Question
(a) What is the average translational kinetic energy of a nitrogen molecule at STP? ___J
(b) What is the total translational kinetic energy of 1.00 mol of N2 molecules at 40°C? ___J
(c) Calculate the rms speed of a nitrogen molecule at 20°C.___ m/s
(d) Determine how many times per second it would move back and forth across a 7.0 m long room on the average, assuming it made very few collisions with other molecules.___ cycles/s
(e) What is the partial pressure of water on a day when the temperature is 0°C and the relative humidity is 35%?___Pa
Explanation / Answer
(a)
Kinetic energy is a function of temperature alone:
K = (3/2) · kb · T
= (3/2) · 1.38065×10²³J/K · 273.15K
= 5.65687×10²¹ J
(b)
K = (3/2) · n · R · T
= (3/2) · 1mol · 8.314472J/molK (40+273.15)K
= 3.9 x 103 J
(c)
r.m.s = square root of ( 3RT/M)
where R = 8.314 J/K/mole
T = 20 + 273.15 = 293.15 K
M = molecular mas of N2 in kg = 28 X 10^-3 kg
putting the values...
r.m.s. = square root of ( 3 X 8.314 X 293.15/(28 X 10^-3))
= 511 m/s
(d)
No. of times it would take:
= 511 / (2x7.0xsqrt3) = 21.07 cycles/s
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