A sample of gas in a 25.0-L containter exerts a pressure of 3.20 atm. Calculate the pressure exerted by the gas if the volume is changed to 45.0-L at constant temperature.
P1V1 = P2V2
To calculate the pressure exerted by the gas when the volume is changed, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
Boyle's Law can be mathematically expressed as:
P₁V₁ = P₂V₂
Where:
P₁ = initial pressure
V₁ = initial volume
P₂ = final pressure
V₂ = final volume
Given:
P₁ = 3.20 atm
V₁ = 25.0 L
V₂ = 45.0 L
We can rearrange the equation to solve for P₂:
P₂ = (P₁V₁) / V₂
Now we can substitute the given values into the equation:
P₂ = (3.20 atm * 25.0 L) / 45.0 L
Calculating the result:
P₂ = 1.77778 atm
Therefore, the pressure exerted by the gas when the volume is changed to 45.0 L at constant temperature is approximately 1.78 atm.