A gas has a pressure of 4.62 atm when its volume is 2.33 L. If the temperature remains constant, what will the pressure be when the volume is changed to 1.03 L? Express the final pressure in mm Hg.
To solve this problem, you can use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume, at constant temperature.
According to Boyle's Law, the product of the initial pressure and initial volume is equal to the product of the final pressure and final volume. Mathematically, this can be represented 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, respectively.
Given:
P1 = 4.62 atm
V1 = 2.33 L
V2 = 1.03 L
Using the formula above, we can solve for P2:
P2 = (P1 * V1) / V2
P2 = (4.62 atm * 2.33 L) / 1.03 L
P2 ≈ 10.46 atm
To convert the pressure from atm to mm Hg, we can use the conversion factor:
1 atm = 760 mm Hg
Therefore, the final pressure in mm Hg is:
P2 = 10.46 atm * 760 mm Hg/atm
P2 ≈ 7941.60 mm Hg
Hence, the final pressure when the volume is changed to 1.03 L will be approximately 7941.60 mm Hg.
To solve this problem, we can use Boyle's Law, which states that the pressure of a given amount of gas is inversely proportional to its volume, as long as the temperature remains constant.
Boyle's Law can be mathematically expressed as:
P1 * V1 = P2 * V2
Where:
P1 = Initial pressure
V1 = Initial volume
P2 = Final pressure (what we need to find)
V2 = Final volume
We are given the initial pressure P1 as 4.62 atm and the initial volume V1 as 2.33 L. We need to find the final pressure P2 when the volume is changed to 1.03 L.
Now we can substitute these values into the equation:
4.62 atm * 2.33 L = P2 * 1.03 L
To find the value of P2, we can rearrange the equation:
P2 = (4.62 atm * 2.33 L) / 1.03 L
Now we can calculate the value of P2:
P2 = (10.7566 atm * L) / L
P2 = 10.7566 atm
To convert the pressure from atm to mm Hg, we can use the conversion factor that 1 atm is equal to 760 mm Hg:
P2 = 10.7566 atm * 760 mm Hg / 1 atm
P2 = 8183.616 mm Hg
Therefore, the final pressure when the volume is changed to 1.03 L is approximately 8183.616 mm Hg.
P1V1 = P2V2
Substitute and solve for the one unknown. Change atm to mm Hg.
1 atm = 760 mm Hg.