If the volume of the original sample in Part A (P 1 = 272torr , V 1 = 32.0L ) changes to 76.0L , without a change in the temperature or moles of gas molecules, what is the new pressure, P 2 ?
To determine the new pressure, P₂, we can use the combined gas law, which states that the initial pressure, volume, and final pressure, volume are related by the equation:
P₁V₁ = P₂V₂
Given:
P₁ = 272 torr
V₁ = 32.0 L
V₂ = 76.0 L
Substituting these values into the equation, we can solve for P₂:
P₁V₁ = P₂V₂
(272 torr)(32.0 L) = P₂(76.0 L)
Divide both sides of the equation by 76.0 L to solve for P₂:
(272 torr)(32.0 L) / 76.0 L = P₂
Calculating this expression will give us the new pressure, P₂.
To find the new pressure, P2, you can use Boyle's law, which states that the pressure and volume of a gas are inversely proportional at constant temperature and moles of gas. Boyle's law can be written as P1*V1 = P2*V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Given:
P1 = 272 torr (initial pressure)
V1 = 32.0 L (initial volume)
V2 = 76.0 L (final volume)
We need to find P2, the new pressure.
Using Boyle's law:
P1*V1 = P2*V2
Substituting the given values:
272 torr * 32.0 L = P2 * 76.0 L
Simplifying the equation:
(272 torr * 32.0 L) / 76.0 L = P2
Calculating the result:
P2 = (8704 torr * L) / 76.0 L
P2 ≈ 114.53 torr
Therefore, the new pressure, P2, is approximately 114.53 torr.