A sample of methane gas at a pressure of 1.02 atm and a temperature of 29.1 °C, occupies a volume of 10.1 liters. If the gas is compressed at constant temperature to a volume of 6.61 liters, the pressure of the gas sample will be_____ atm.
Use P1V1 = P2V2. Substitute and solve. Post your work if you get stuck.
To find the final pressure of the gas sample after it is compressed, we can use Boyle's Law, which states that the product of pressure and volume of a gas is constant at constant temperature.
Boyle's Law equation:
P₁V₁ = P₂V₂
Where:
P₁ = Initial pressure
V₁ = Initial volume
P₂ = Final pressure (to be found)
V₂ = Final volume
Given values:
P₁ = 1.02 atm
V₁ = 10.1 liters
V₂ = 6.61 liters
Now we can substitute the known values into the equation and solve for P₂:
(1.02 atm)(10.1 liters) = P₂(6.61 liters)
To solve for P₂, divide both sides of the equation by 6.61 liters:
(1.02 atm)(10.1 liters) / 6.61 liters = P₂
Calculating the expression:
P₂ ≈ 1.56 atm
Therefore, the pressure of the gas sample when compressed to a volume of 6.61 liters would be approximately 1.56 atm.