Calculating Pressure with Boyle's Law

Understanding Boyle's Law

Boyle's Law states that the pressure and volume of a gas are inversely proportional to each other, as long as the temperature remains constant. This means that as the volume of a gas increases, the pressure decreases, and vice versa.

Problem Statement

5. A flask containing 90.0 mL of hydrogen gas was collected under a pressure of 97.5 atm. At what pressure, at atm, would the volume be 070 L?

Solution

To solve this problem, we can use Boyle's Law formula: PV = P'V', where P is the initial pressure, V is the initial volume, P' is the final pressure, and V' is the final volume.

First, rearrange the formula to isolate P':

P' = PV/V'

Given: P = 97.5 atm, V = 90 mL = 0.09 L, V' = 70 L.

Substitute these values into the formula:

P' = 97.5 × 0.09 / 70

P' = 0.125 atm

Therefore, the pressure at which the volume would be 0.70 L is 0.125 atm.

What is Boyle's Law and how is it applied to solve the given problem?

Boyle's Law states the inverse relationship between the pressure and volume of a gas at constant temperature. In the given problem, we used Boyle's Law formula PV = P'V' to calculate the pressure at which the volume of hydrogen gas would be 0.70 L. By substituting the given values into the formula and isolating for P', we found that the pressure would be 0.125 atm.