A 2.50-liter sample of a gas is collected at a pressure of 1.50 atm. Calculate the pressure needed to reduce the volume of the gas to 1.00 liters. The temperature remains unchanged.
Question
A 2.50-liter sample of a gas is collected at a pressure of 1.50 atm. Calculate the pressure needed to reduce the volume of the gas to 1.00 liters. The temperature remains unchanged.
Solution
This problem can be solved using Boyle's Law, which states that the pressure and volume of a gas have an inverse relationship when temperature is held constant.
Boyle's Law formula is: P1V1 = P2V2
Where: P1 = initial pressure V1 = initial volume P2 = final pressure V2 = final volume
Given in the problem: P1 = 1.50 atm V1 = 2.50 L V2 = 1.00 L
We need to find P2.
Substitute the given values into Boyle's Law formula:
1.50 atm * 2.50 L = P2 * 1.00 L
Solve for P2:
P2 = (1.50 atm * 2.50 L) / 1.00 L
P2 = 3.75 atm
So, the pressure needed to reduce the volume of the gas to 1.00 liters is 3.75 atm.
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