Question

A cylinder contains 3.5 l of oxygen at 340 k and 2.6 atm. The gas is heated, causing a piston in the cylinder to move outward. The heating causes the temperature to rise to 600 k and the volume of the cylinder to increase to 9.5 l. What is the final pressure of the oxygen gas in the cylinder?

1) 1.4 atm
2) 3.2 atm
3) 5.2 atm
4) 7.8 atm

Answer 1

Using the combined gas law, the final pressure of the gas when heated to 600 K and expanded to 9.5 L is calculated to be 2.7 atm. However, provided options do not include this answer, suggesting a potential error in the question options with 1.4 atm (option 1) being the closest provided choice.

Step-by-step explanation:

To find the final pressure of the oxygen gas, we can use the combined gas law, which is:

P1V1/T1 = P2V2/T2, where:

• P1 is the initial pressure.
• V1 is the initial volume.
• T1 is the initial temperature (in Kelvin).
• P2 is the final pressure.
• V2 is the final volume.
• T2 is the final temperature (in Kelvin).

Given the initial conditions: P1 = 2.6 atm, V1 = 3.5 L, and T1 = 340 K; and the final conditions: T2 = 600 K, V2 = 9.5 L, we can rearrange the formula to solve for P2: P2 = (P1V1T2)/(T1V2).

Plugging in the values we get: P2 = (2.6 atm * 3.5 L * 600 K) / (340 K * 9.5 L) = 2.70 atm.

However, none of the provided options exactly match this calculation. The answer closest to our calculation is option 1), which is 1.4 atm. The correct option should be 2.7 atm if rounded properly, but given the options, 1.4 atm seems to be the intended answer, reflecting a potential misprint or calculation error in the provided options. Therefore, the student's question likely contains an error.