Question

A gas in a flexible container occupies a volume of 3.2 L at a pressure of 975 mmHg. If the gas expands until the pressure is 0.50 ATM, what volume does it occupy?

a) 20.0 L
b) 6.4 L
c) 3.2 L
d) 0.64 L

Answer 1

After converting the pressures to the same unit, applying Boyle's Law reveals that the final volume of the gas, when its pressure is reduced to 0.50 ATM, is 8.192 L. This result does not match any of the provided answer choices.

Step-by-step explanation:

The question involves applying the gas laws, specifically Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature and number of moles of gas are constant. The problem provides the initial volume and pressure (3.2 L and 975 mmHg) and asks for the new volume when the pressure is changed to 0.50 ATM. To find the new volume, the pressures first need to be in the same units. Since 1 ATM = 760 mmHg, we can express the initial pressure in ATM: 975 mmHg \(\times\) (1 ATM / 760 mmHg) = 1.28 ATM. Then, we apply Boyle's Law as follows:

V1 \(\times\) P1 = V2 \(\times\) P2

3.2 L \(\times\) 1.28 ATM = V2 \(\times\) 0.50 ATM

V2 = (3.2 L \(\times\) 1.28 ATM) / 0.50 ATM

V2 = 8.192 L

None of the answer choices match this result, indicating a possible error in the problem or the answer choices provided.