Air trapped in a cylinder fitted with a piston occupies 163.1 mL at 1.08 atm pressure. What is the new volume when the piston is depressed, increasing the pressure by 25%?
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To find the new volume when the pressure is increased by 25%, we need to 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:
P1 × V1 = P2 × V2
Where:
P1 = initial pressure
V1 = initial volume
P2 = final pressure
V2 = final volume
Given:
P1 = 1.08 atm
V1 = 163.1 mL
To solve for the final volume (V2), we need to find the final pressure (P2) first.
Since the pressure is increased by 25%, we can calculate the new pressure as follows:
New pressure (P2) = initial pressure (P1) + (increase in pressure × initial pressure)
New pressure (P2) = 1.08 atm + (0.25 × 1.08 atm) = 1.08 atm + 0.27 atm = 1.35 atm
Now that we have the final pressure (P2), we can substitute the values into the Boyle's Law equation:
P1 × V1 = P2 × V2
1.08 atm × 163.1 mL = 1.35 atm × V2
Now solve for V2:
V2 = (1.08 atm × 163.1 mL) / 1.35 atm
V2 ≈ 130.1 mL
Therefore, the new volume when the piston is depressed, increasing the pressure by 25%, is approximately 130.1 mL.