A sample of gas at a pressure of 1.5 atm has a volume of 22.4 L. What is the new volume if the pressure is lowered to 0.75 atm?

P1V1 = P2V2

To solve this problem, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas.

The combined gas law formula is:

P₁V₁/T₁ = P₂V₂/T₂

Where:
P₁ and P₂ are the initial and final pressures, respectively
V₁ and V₂ are the initial and final volumes, respectively
T₁ and T₂ are the initial and final temperatures, respectively

In this problem, we are given the initial pressure (P₁ = 1.5 atm) and volume (V₁ = 22.4 L), and we are asked to find the final volume (V₂) when the pressure is lowered to 0.75 atm.

Since the temperature is not given and assuming it remains constant, we can cancel out the temperature terms (T₁/T₂) in the formula, leaving us with:

P₁V₁ = P₂V₂

Substituting the given values:

(1.5 atm)(22.4 L) = (0.75 atm)(V₂)

Simplifying the equation:

33.6 atm·L = 0.75 atm·V₂

To find V₂, we can rearrange the equation:

V₂ = (33.6 atm·L) / (0.75 atm)

V₂ ≈ 44.8 L

Therefore, the new volume when the pressure is lowered to 0.75 atm is approximately 44.8 L.