AP Chemistry: 3.4 Ideal Gas Law – Exam Style questions with Answer- MCQ

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Question

A gaseous air‑fuel mixture in a sealed car engine cylinder has an initial volume of 600.mL at 1.0atm. To prepare for ignition of the fuel, a piston moves within the cylinder, reducing the volume of the air‑fuel mixture to 50.mL at constant temperature. Assuming ideal behavior, what is the new pressure of the air‑fuel mixture?

A About 0.083atm , because the initial volume of the gas mixture was 12 times larger than its final volume.
B About 12atm , because the volume of the gas mixture decreased by a factor of 12.
C About 120.atm , because the initial volume of the gas mixture was 120 times larger than its final volume.
D About 550.atm , because the change in the volume of the gas mixture was 550.mL.
▶️Answer/Explanation

Ans:B

 For a gas or gas mixture that behaves ideally, pressure and volume are inversely proportional. Therefore, since n and T remained constant, a 12-fold decrease in volume should result in a 12-fold increase in pressure.

Question

At 10.°C, 20.g of oxygen gas exerts a pressure of 2.1atm in a rigid, 7.0L cylinder. Assuming ideal behavior, if the temperature of the gas was raised to 40.°C , which statement indicates the new pressure and explains why?

A 1.9atm, because the pressure P decreases by the proportion \(\frac{283}{313}\)
 
B 2.3atm, because the pressure P increases by the proportion \(\frac{313}{283}\)
 
C 0.52atm , because the pressure P decreases by the proportion \(\frac{10}{40}\)
 
D 8.4atm , because the pressure P increases by the proportion \(\frac{40}{10}\)
▶️Answer/Explanation

Ans: B

 Rearranging the ideal gas law equation yields the equation \(P=\frac{nRT}{V}\)

Since the number of moles of oxygen (n), the gas constant (R), and the volume (V) are all constant in this case, the relationship reduces to P=kT, where T is the absolute temperature (in kelvins). Therefore, increasing the temperature to 313 K from 283 K results in a pressure that is larger by the factor \(\frac{313}{283}\)

Question

 

Two sealed, rigid 5.0L containers each contain a gas at the same temperature but at a different pressure, as shown above. Also shown are the results of transferring the entire contents of container 1 to container 2. No gases escape during the transfer. Assuming ideal behavior, which statement is correct regarding the total pressure of the gases after they are combined?

A The total pressure of the gases in the mixture is the sum of the initial pressures of oxygen gas and nitrogen gas because pressure only depends on the total amount of gas when volume and temperature are held constant.
 
B The total pressure of the gases in the mixture is lower than the sum of the initial pressures of oxygen and nitrogen because some of the energy of the particles will be lost due to an increase in the number of collisions.
 
C The total pressure of the gases in the mixture is higher than the sum of the initial pressures of oxygen and nitrogen because of the intermolecular forces that develop between oxygen and nitrogen molecules.
 
D The total pressure of the gases in the mixture cannot be determined because the actual value of the temperature is not given.
▶️Answer/Explanation

Ans: A

 Under conditions of constant T and V, the pressure of a gas or a mixture of gases only depends on the total number of moles of gas, regardless of the identity of the gas. From the ideal gas law, thus P is directly proportional to n, since R, T, and V are constant. Since the total amount of gas in the mixture is the sum of the original amounts of each gas, meaning that the total pressure of the gas mixture is simply the sum of the initial pressures of each gas.

Question

Under which of the following conditions of temperature and pressure will \(H_2\) gas be expected to behave most like an ideal gas’?

(A)50 K and 0.10 atm

(B)50 K and 5.0 atm

(C)500 K and 0.10 atm 

(D) 500 K and 50 atm 

▶️Answer/Explanation

Ans:C     

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