The volume of a gas sample is 200 L at 740 torr. What is its volume at 760 torr?
at constant temperature?
P1V1=P2V2
V2=P1V1/P2
To find the volume of a gas sample at a different pressure, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. The formula for Boyle's Law is:
P₁V₁ = P₂V₂
Where:
P₁ = initial pressure
V₁ = initial volume
P₂ = final pressure
V₂ = final volume
In this case:
P₁ = 740 torr
V₁ = 200 L
P₂ = 760 torr (final pressure)
V₂ = unknown (final volume)
We can rearrange the formula to solve for V₂:
V₂ = (P₁ • V₁) / P₂
Substituting the given values:
V₂ = (740 torr • 200 L) / 760 torr
V₂ ≈ 194.21 L
Therefore, the volume of the gas sample at 760 torr is approximately 194.21 L.
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas sample are inversely proportional at a constant temperature.
Boyle's Law equation: P₁V₁ = P₂V₂
Where:
P₁ = initial pressure (740 torr)
V₁ = initial volume (200 L)
P₂ = final pressure (760 torr)
V₂ = final volume (unknown)
First, we can rearrange the equation to solve for V₂:
V₂ = (P₁V₁) / P₂
Now, substitute the given values into the equation:
V₂ = (740 torr * 200 L) / 760 torr
Simplify the equation:
V₂ = (148,000 torr * L) / 760 torr
V₂ ≈ 194.736 L
Therefore, the volume of the gas sample at 760 torr is approximately 194.736 liters.