A sample of a gas (5.0 mol)at 1.0 atm is expanded at constant temperature from 10.0 L to 15 L. The final pressure is _______ atm.
.67
P1V1=P2V2
- P1 = 1.0 atm
- V1 = 10L
- V2 = 15L
- P2 = ?
(1.0 atm)(10L)=(P2)(15L)
10=(P2)(15L)
P2=10/15
P2 = 0.67 atm
To determine the final pressure when a gas is expanded at constant temperature, we can use Boyle's Law. Boyle's Law states that the product of the initial pressure and initial volume is equal to the product of the final pressure and final volume, as long as temperature remains constant.
Mathematically, Boyle's Law can be written as:
P₁V₁ = P₂V₂
where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume.
In this case, we are given:
Initial pressure (P₁) = 1.0 atm
Initial volume (V₁) = 10.0 L
Final volume (V₂) = 15 L
To find the final pressure (P₂), we rearrange the equation and solve:
P₂ = (P₁ * V₁) / V₂
Substituting the given values, we have:
P₂ = (1.0 atm * 10.0 L) / 15 L
P₂ = 10.0 atm / 15 L
P₂ ≈ 0.67 atm
Therefore, the final pressure is approximately 0.67 atm.