Question

A gas is heated from 213.0 K to 298.0 K and the volume is increased from 14.0 liters to 35.0 liters by moving a large piston within a cylinder. If the original pressure was 3.15 atm, what would the final pressure be?

Include the following with your answer:

Which Gas Law did you use?
The numerical answer to the question.
An explanation of the correct number of significant figures you will use for the numerical answer.

Answer 1

Using the combined gas law, the final pressure of the gas when heated from 213.0 K to 298.0 K and the volume increased from 14.0 liters to 35.0 liters is 1.12 atm. The significant figures in the final answer are based on the given data, which leads to three significant figures for the final pressure.

Step-by-step explanation:

To find the final pressure of a gas after a change in temperature and volume, we use the combined gas law, which is derived from Boyle's, Charles's, and Gay-Lussac's laws. It states that for a fixed amount of gas, the pressure times the volume divided by the temperature is a constant value (P1V1/T1 = P2V2/T2). Given that the original pressure is 3.15 atm, temperature is 213.0 K, and volume is 14.0 liters, and the final temperature is 298.0 K and volume is 35.0 liters, we can rearrange the formula and solve for the unknown final pressure P2.

Using the combined gas law, P2 can be calculated as follows:

P2 = (P1V1T2) / (T1V2)

P2 = (3.15 atm × 14.0 L × 298.0 K) / (213.0 K × 35.0 L)

P2 = 1.12 atm

The numerical answer is 1.12 atm, which is the final pressure of the gas. The significant figures in the final answer are dictated by the original pressure, which is given to three significant figures. Therefore, the final answer should also be reported to three significant figures.