Q. A gas at 300 K has an RMS speed of 400 m/s. What will be its RMS speed at 600 K?
A.400 m/s
B.400 sqrt(2) m/s
C.800 m/s
D.200 m/s
Solution
The RMS speed is proportional to the square root of the temperature. Therefore, at 600 K, the RMS speed will be 400 * sqrt(600/300) = 400 * sqrt(2) m/s.
Correct Answer: B — 400 sqrt(2) m/s
Q. A gas has an RMS speed of 500 m/s. If the molar mass of the gas is 0.02 kg/mol, what is the temperature of the gas?
A.250 K
B.500 K
C.1000 K
D.2000 K
Solution
Using the formula v_rms = sqrt((3RT)/M), we can rearrange to find T = (v_rms^2 * M) / (3R). Substituting v_rms = 500 m/s and M = 0.02 kg/mol gives T = 500 K.
Correct Answer: B — 500 K
Q. According to the kinetic theory of gases, the pressure exerted by a gas is due to:
A.the gravitational force on the gas
B.the collisions of gas molecules with the walls of the container
C.the temperature of the gas
D.the volume of the gas
Solution
The pressure exerted by a gas is due to the collisions of gas molecules with the walls of the container, which transfers momentum to the walls.
Correct Answer: B — the collisions of gas molecules with the walls of the container
Q. According to the kinetic theory, the pressure exerted by a gas is due to which of the following?
A.The weight of the gas molecules.
B.The collisions of gas molecules with the walls of the container.
C.The temperature of the gas.
D.The volume of the gas.
Solution
The pressure of a gas is caused by the collisions of gas molecules with the walls of the container, which exert force on the walls.
Correct Answer: B — The collisions of gas molecules with the walls of the container.
Q. At absolute zero, what is the expected volume of an ideal gas?
A.Zero
B.Infinite
C.Constant
D.Undefined
Solution
At absolute zero, the volume of an ideal gas is expected to be zero according to Charles's Law.
Correct Answer: A — Zero
Q. At absolute zero, what is the theoretical volume of an ideal gas?
A.Zero
B.Infinite
C.Constant
D.Undefined
Solution
At absolute zero, the volume of an ideal gas is theoretically zero according to Charles's Law.
Correct Answer: A — Zero
Q. At constant pressure, if the temperature of a gas is increased, what happens to its volume?
A.It decreases
B.It increases
C.It remains constant
D.It becomes zero
Solution
According to Charles's Law, at constant pressure, the volume of a gas increases with an increase in temperature.
Correct Answer: B — It increases
Q. At what temperature will the RMS speed of a gas be 300 m/s if its molar mass is 28 g/mol?
A.300 K
B.600 K
C.900 K
D.1200 K
Solution
Using the formula v_rms = sqrt((3RT)/M), we can rearrange to find T. Setting v_rms = 300 m/s and M = 28 g/mol, we find T = (M * v_rms^2)/(3R) = 600 K.
Correct Answer: B — 600 K
Q. For a gas at a certain temperature, if the molar mass is halved, what happens to the RMS speed?
A.Increases by a factor of 2
B.Increases by a factor of sqrt(2)
C.Decreases by a factor of 2
D.Remains the same
Solution
RMS speed is inversely proportional to the square root of molar mass. Halving the molar mass increases the RMS speed by a factor of sqrt(2).
Correct Answer: B — Increases by a factor of sqrt(2)
Q. For a gas at constant pressure, if the volume is doubled, what happens to the temperature?
A.It remains the same
B.It doubles
C.It halves
D.It triples
Solution
According to Charles's law, for a gas at constant pressure, if the volume is doubled, the temperature also doubles.
Correct Answer: B — It doubles
Q. For a gas at constant pressure, if the volume is halved, what happens to the temperature?
A.It remains the same
B.It doubles
C.It is halved
D.It is quartered
Solution
According to Charles's law, for a gas at constant pressure, if the volume is halved, the temperature must also be halved.
Correct Answer: C — It is halved
Q. For a gas mixture, how is the RMS speed calculated?
A.Using the average molar mass of the mixture
B.Using the molar mass of the heaviest gas
C.Using the molar mass of the lightest gas
D.Using the molar mass of the most abundant gas
Solution
The RMS speed for a gas mixture is calculated using the average molar mass of the mixture.
Correct Answer: A — Using the average molar mass of the mixture
Q. For a gas with a molar mass of 32 g/mol at a temperature of 300 K, what is the RMS speed?
A.273 m/s
B.400 m/s
C.500 m/s
D.600 m/s
Solution
Using the formula v_rms = sqrt((3RT)/M), where R = 8.314 J/(mol·K), M = 0.032 kg/mol, and T = 300 K, we find v_rms ≈ 400 m/s.
Correct Answer: B — 400 m/s
Q. For a gas with molar mass M at temperature T, what is the relationship between RMS speed and molar mass?
A.v_rms is directly proportional to M
B.v_rms is inversely proportional to M
C.v_rms is independent of M
D.v_rms is proportional to M^2
Solution
The RMS speed is given by v_rms = sqrt((3RT)/M). This shows that v_rms is inversely proportional to the square root of the molar mass M.
Correct Answer: B — v_rms is inversely proportional to M
Q. For a gas with molar mass M, what is the relationship between RMS speed and molar mass?
A.v_rms is directly proportional to M
B.v_rms is inversely proportional to M
C.v_rms is independent of M
D.v_rms is proportional to M^2
Solution
The RMS speed is inversely proportional to the square root of the molar mass (v_rms = sqrt((3RT)/M)). Thus, as molar mass increases, RMS speed decreases.
Correct Answer: B — v_rms is inversely proportional to M
Q. For a gas with molar mass M, what is the relationship between RMS speed and molecular mass?
A.v_rms is directly proportional to M
B.v_rms is inversely proportional to M
C.v_rms is independent of M
D.v_rms is proportional to M^2
Solution
The RMS speed is inversely proportional to the square root of the molar mass (v_rms = sqrt((3RT)/M)). Thus, as molar mass increases, RMS speed decreases.
Correct Answer: B — v_rms is inversely proportional to M
Q. For a monoatomic ideal gas, the RMS speed is given by which of the following expressions?
A.sqrt((3kT)/m)
B.sqrt((3RT)/M)
C.Both of the above
D.None of the above
Solution
Both expressions are valid for calculating the RMS speed of a monoatomic ideal gas.
Correct Answer: C — Both of the above
Q. For an ideal gas, if the volume is halved while keeping the temperature constant, what happens to the pressure?
A.It remains the same
B.It doubles
C.It halves
D.It quadruples
Solution
According to Boyle's law, for a given mass of gas at constant temperature, the pressure is inversely proportional to the volume. Halving the volume will double the pressure.
Correct Answer: B — It doubles
Q. For an ideal gas, the equation of state is given by:
A.PV = nRT
B.PV = NkT
C.PV = mRT
D.PV = kT
Solution
The equation of state for an ideal gas is given by PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.
Correct Answer: A — PV = nRT
Q. For an ideal gas, which equation relates pressure, volume, and temperature?
A.PV = nRT
B.PV = nR
C.PV = RT
D.PV = nT
Solution
The ideal gas law is given by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.
Correct Answer: A — PV = nRT
Q. If 1 mole of an ideal gas occupies 22.4 L at STP, what is the pressure exerted by the gas?
A.1 atm
B.2 atm
C.0.5 atm
D.4 atm
Solution
At STP (Standard Temperature and Pressure), 1 mole of an ideal gas occupies 22.4 L at a pressure of 1 atm.
Correct Answer: A — 1 atm
Q. If 2 moles of an ideal gas at 300 K occupy a volume of 10 L, what is the pressure of the gas? (Use R = 0.0821 L·atm/(K·mol))
A.0.5 atm
B.1.0 atm
C.2.0 atm
D.3.0 atm
Solution
Using the Ideal Gas Law, P = nRT/V = (2 moles * 0.0821 L·atm/(K·mol) * 300 K) / 10 L = 4.926 atm.
Correct Answer: B — 1.0 atm
Q. If the molar mass of a gas is halved, what happens to its RMS speed?
A.Increases by a factor of sqrt(2)
B.Increases by a factor of 2
C.Decreases by a factor of sqrt(2)
D.Remains the same
Solution
If the molar mass is halved, the RMS speed increases by a factor of sqrt(2) because RMS speed is inversely proportional to the square root of molar mass.
Correct Answer: A — Increases by a factor of sqrt(2)
Q. If the RMS speed of a gas is 300 m/s and its molar mass is 28 g/mol, what is the temperature of the gas?
A.300 K
B.600 K
C.900 K
D.1200 K
Solution
Using the formula v_rms = sqrt((3RT)/M), we can rearrange to find T = (v_rms^2 * M)/(3R). Plugging in the values gives T = 600 K.
Correct Answer: B — 600 K
Q. If the RMS speed of a gas is 300 m/s at 300 K, what will be its RMS speed at 600 K?
A.300 m/s
B.600 m/s
C.300√2 m/s
D.600√2 m/s
Solution
The RMS speed is proportional to the square root of the temperature. Therefore, at 600 K, the RMS speed will be 300 * sqrt(2) m/s.
Correct Answer: C — 300√2 m/s
Q. If the RMS speed of a gas is 300 m/s at 400 K, what will be the RMS speed at 200 K?
A.150 m/s
B.300 m/s
C.600 m/s
D.100 m/s
Solution
The RMS speed is proportional to the square root of the temperature. Therefore, at 200 K, the RMS speed will be 300 * sqrt(200/400) = 150 m/s.
Correct Answer: A — 150 m/s
Q. If the RMS speed of a gas is 500 m/s, what is the speed of the gas molecules at 1/2 of the RMS speed?
A.250 m/s
B.500 m/s
C.1000 m/s
D.125 m/s
Solution
The speed at 1/2 of the RMS speed is simply 500 m/s / 2 = 250 m/s.
Correct Answer: A — 250 m/s
Q. If the RMS speed of a gas is 500 m/s, what is the speed of the gas molecules in terms of average speed?
A.500 m/s
B.250 m/s
C.400 m/s
D.600 m/s
Solution
The average speed of gas molecules is related to the RMS speed by the relation v_avg = (v_rms * sqrt(8/3)). Therefore, the average speed is approximately 400 m/s.
Correct Answer: C — 400 m/s
Q. If the RMS speed of a gas is 500 m/s, what is the speed of the molecules in the gas?
A.500 m/s
B.250 m/s
C.1000 m/s
D.It varies
Solution
The RMS speed is an average measure; individual molecular speeds will vary around this value.
Correct Answer: D — It varies
Q. If the temperature of a gas is doubled, how does its RMS speed change?
A.Increases by a factor of sqrt(2)
B.Increases by a factor of 2
C.Increases by a factor of 4
D.Remains the same
Solution
The RMS speed is proportional to the square root of the temperature. If the temperature is doubled, the RMS speed increases by a factor of sqrt(2).
Correct Answer: A — Increases by a factor of sqrt(2)
