Question

When a gas is kept at a constant temperature and pressure on it changes, its volume changes according to the following formula, known as Boyle’s law

where P1 and V1 are the pressure (in atm) and the volume (in litres) at the beginning, and P2 and V2 are the pressure and the volume at the end. Find the final pressure P2 if V1 = 1.5 litres, P1 = 4.5 atm and V2 = 3.5 litres. Round to the nearest tenth of a atm.

Answer 1

Answer: Approximately 1.9 atm

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Work Shown:

`P_1*V_1 = P_2*V_2 \ \text{ ... Boyle's Law}\\\\4.5*1.5 = P_2*3.5\\\\6.75 = P_2*3.5\\\\P_2*3.5 = 6.75\\\\P_2 = (6.75)/(3.5)\\\\P_2 \approx 1.92857142857142\\\\P_2 \approx 1.9\\\\`

If the volume is 3.5 liters, then the pressure is approximately 1.9 atm.

Note the increase in volume leads to the reduction of pressure, and vice versa. The two variables have an inverse relationship.

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As a check,

`P_1*V_1 = P_2*V_2\\\\4.5*1.5 \approx 1.9*3.5\\\\6.75 \approx 6.65\\\\`

We don't get the exact thing on both sides, but the two sides are close enough. We have rounding error due to P2 being not exact.

A more accurate check could be

`P_1*V_1 = P_2*V_2\\\\4.5*1.5 \approx 1.92857*3.5\\\\6.75 \approx 6.749995\\\\`

which has the two sides much closer to one another. This helps us verify the answer.