A sample of gas has an initial volume of 15 L and an initial pressure of 4.5 atm. If the pressure changes to 1.8 atm, what is the new volume, assuming that the temperature remains constant?

37.5 L

Explanation:

Initial Volume, V1 = 15L

Initial Pressure P1 = 4.5 atm

Final Pressure, P2 = 1.8 atm

Final Volume V2 = ?

The relationship between these variables is given as;

P1V1 = P2V2

V2 = PIV1 / P1

Inserting the values;

V2 = 4.5 * 15 / 1.8

V2 = 37.5 L

The new volume is 37.5L

Explanation:

The question is solved using the principle and formula of a gas law known as the Boyle's law. Boyle's law states that provided the temperature remains constant, the volume of a given mass of gas is inversely proportional to its pressure. Expressing the statement mathematically:

P ∝ 1/V, (where p is equal to pressure and V is volume)

Therefore PV = a constant

If a gas at pressure P1 and Volume V1 changes at constant temperature to pressure P2 and volume V2 then:

P1V1 = P2V2.

Using the formula to solve the question:

P1 = 4.5atm

P2 = 1.8atm

V1= 15L

V2 = ?

V2 = P1V1/P2

V2= 4.5 × 15 /1.8

V2 = 67.5/1.8

V2 = 37.5 L

Therefore the new volume is 37.5L

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