Q. According to the kinetic theory, what is the relationship between pressure and the number of gas molecules in a container?
A.
Pressure is independent of the number of molecules
B.
Pressure decreases with more molecules
C.
Pressure increases with more molecules
D.
Pressure is inversely proportional to the number of molecules
Solution
According to the kinetic theory, pressure is directly proportional to the number of gas molecules in a container, assuming temperature and volume are constant.
Correct Answer:
C
— Pressure increases with more molecules
Q. In an ideal gas, if the temperature is doubled while keeping the volume constant, what happens to the pressure?
A.
It halves
B.
It doubles
C.
It quadruples
D.
It remains the same
Solution
According to Gay-Lussac's law, pressure is directly proportional to temperature when volume is constant. Therefore, if the temperature is doubled, the pressure also doubles.
Q. What is the average kinetic energy of a gas molecule at temperature 300 K?
A.
1.24 x 10^-21 J
B.
4.14 x 10^-21 J
C.
6.21 x 10^-21 J
D.
2.07 x 10^-21 J
Solution
The average kinetic energy of a gas molecule is given by the formula KE = (3/2)kT, where k is the Boltzmann constant (1.38 x 10^-23 J/K) and T is the temperature in Kelvin. KE = (3/2)(1.38 x 10^-23)(300) = 6.21 x 10^-21 J.
Q. What is the effect of increasing the molar mass of a gas on its average kinetic energy at a constant temperature?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
Solution
The average kinetic energy of gas molecules is independent of molar mass and is solely dependent on temperature. Therefore, it remains the same at constant temperature.
Q. What is the root mean square speed of nitrogen gas (N2) at 300 K? (Molar mass of N2 = 28 g/mol)
A.
400 m/s
B.
500 m/s
C.
600 m/s
D.
700 m/s
Solution
The root mean square speed is given by the formula v_rms = sqrt(3RT/M), where R = 8.314 J/(mol·K), T = 300 K, and M = 0.028 kg/mol. v_rms = sqrt(3 * 8.314 * 300 / 0.028) ≈ 500 m/s.
