Kinetic theory of gases – problems and solutions
1. Ideal gases in a closed container initially have volume V and pressure P. If the final pressure is 4P and the volume is kept constant, what is the ratio of the initial kinetic energy with the final kinetic energy.
Initial pressure (P1) = P
Final pressure (P2) = 4P
Initial volume (V1) = V
Final volume (V2) = V
Wanted: The ratio of the initial kinetic energy with the final kinetic energy (KE1 : KE2)
The relation between pressure (P), volume (V) and kinetic energy (KE) of ideal gases :
The ratio of the initial kinetic energy with the final kinetic energy :
2. What is the average translational kinetic energy of molecules in an ideal gas at 57oC.
Temperature of gas (T) = 57oC + 273 = 330 Kelvin
Boltzmann‘s constant (k) = 1.38 x 10-23 Joule/Kelvin
Wanted: The average translational kinetic energy
The relation between kinetic energy (KE) and the temperature of the gas (T) :
The average translational kinetic energy :
3. A gas at 27oC in a closed container. If the kinetic energy of the gas increases 2 times the initial kinetic energy, thus the final temperature of the gas is…
Initial temperature (T1) = 27oC + 273 = 300 K
Initial kinetic energy = KE
Final kinetic energy = 4 KE
Wanted: The final temperature (T2)
4. An ideal gas is in a closed container, is heated so that the final average velocity of particles of gas increases by 3 times the initial average velocity. If the initial gas temperature is 27oC, then the final temperature of the ideal gas is…
Initial temperature = 27oC + 273 = 300 Kelvin
Initial velocity = v
Final velocity = 2v
Wanted : The final temperature of ideal gas
The final average velocity = 2 x the initial average velocity
5. Three moles of gas are in a 36 liters volume space. Each gas molecule has a kinetic energy of 5 x 10-21 Joule. Universal gas constant = 8.315 J/mole.K and Boltzmann’s constant = 1.38 x 10-23 J/K. What is the gas pressure in the container.
Number of moles (n) = 3 moles
Volume = 36 liters = 36 dm3 = 36 x 10-3 m3
Boltzmann’s constant (k) = 1.38 x 10-23 J/K
Kinetic energy (KE) = 5 x 10–21 Joule
Universal gas constant (R) = 8.315 J/mole.K
Wanted : Gas pressure (P)
Calculate the temperature using the equation of kinetic energy of gas.
Calculate the gas pressure using th equation of ideal gas law (in number of moles, n) :
P V = n R T
P (36 x 10-3) = (3)(8.315)(241.5)
P (36 x 10-3) = 6024.22
The gas pressure is 1.67 x 105 Pascal or 1.67 atmospheres.