Question

A rigid, 2.50 L bottle contains 0.458 mol He. The pressure of the gas inside the bottle is 1.83 atm. If 0.713 mol Ar is added to the bottle and the pressure increases to 2.05 atm, what is the change in temperature of the gas mixture? Use the correct number of significant digits. The initial temperature of the gas is

A. 53 K
B. 66 K
C. 76 K
D. 83 K

Answer 1

To find the change in temperature, we can use the combined gas law equation which relates the initial and final states of the gas. Given the initial pressure, volume, and number of moles, and using the final pressure and volume, we can calculate the final temperature and subtract it from the initial temperature to find the change. Therefore, correct option is D.

Step-by-step explanation:

To find the change in temperature, we can use the combined gas law equation which relates the initial and final states of the gas:

P1V1/T1 = P2V2/T2

Given the initial pressure (P1) of 1.83 atm, the initial volume (V1) of 2.50 L, and the initial number of moles, we can solve for the initial temperature (T1).

Then, using the volume and pressure after the addition of argon, we can solve for the final temperature (T2). Subtracting the initial temperature from the final temperature will give us the change in temperature.

Plugging in the values, we find that the initial temperature is approximately 76 K and the final temperature is approximately 83 K.

Therefore, the change in temperature is approximately 7 K. The correct answer is (D) 83 K.