Question

A gas occupies a volume of 4.50 L at 760.0 mmHg and a temperature of 25.0°C. What would be the new volume at 200.0 mmHg, assuming temperature and the number of moles are held constant?

a) 3.14 L
b) 1.47 L
c) 2.38 L
d) 6.02 L

Answer 1

Using Boyle's Law, which indicates an inverse relationship between pressure and volume for a gas at constant temperature and moles, the new volume of the gas when pressure is reduced from 760.0 mmHg to 200.0 mmHg, with temperature and moles unchanged, is found to be 17.1 L.

Step-by-step explanation:

The question involves applying the gas law that describes the relationship between pressure and volume, known as Boyle's Law. This law states that at constant temperature and number of moles, the pressure and volume of a gas have an inverse relationship. In mathematical terms, P1V1 = P2V2 where P represents pressure, V represents volume, and subscripts 1 and 2 refer to the initial and final states of the gas respectively.

To find the new volume (V2) of the gas when the pressure is changed from 760.0 mmHg to 200.0 mmHg, while keeping temperature and the number of moles constant, we use the formula:

V2 = (P1 × V1) / P2

Substituting the given values we have:

V2 = (760.0 mmHg × 4.50 L) / 200.0 mmHg

Cancelling out the units and calculating gives us:

V2 = 17.1 L