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# Boyle's Law Formula

Boyle's law developed by Robert Boyle in 1662, states that if we keep the temperature of a gas constant in a sealed container. Its pressure (P) varies inversely with its volume (V). In other words at any given temperature if we pressurize a gas its volume will be reduced proportionately to the pressure change. If we increase the volume of a gas its pressure will increase.

"For a fixed mass of ideal gas at fixed temperature the product of pressure and volume is constant".

Boyle's Law Formula is expressed symbolically as

Another way to express Boyle's Law Formula is

Where
• P is pressure of the gas
• V is volume of the gas
• k is a constant, and has units of force times distance

 Related Calculators Boyle's Law Calculator Beer Lambert Law Calculator Charles Law Calculator Combined Gas Law Calculator

## Boyle's Law Problems

Solved problems based on Boyle's law are given below.

### Solved Examples

Question 1: A sample of gaseous nitrogen in a 65.0 L automobile air bag has a pressure of 745 mm Hg. If this sample is transferred to a 25.0 L bag at the same temperature. what is the pressure of the gas in the 25.0 L bag?
Solution:

It is often useful to make a table of the information provided.

 Initial conditions Final conditions P1 = 745 mm Hg P2 = ? V1 = 65.0 L V2 = 25.0L

We know that P1V1 = P2V2

Therefore,

P1 = $\frac{P_{1}V_{1}}{V_{2}}$

P1 = $\frac{[745\ mm\ Hg][65.0\ L]}{25.0\ L}$

P1 = 1940 mm Hg

Question 2: A sample of neon (Ne) occupies 4.00L at a pressure of 5.00 $\times$ 104 Pa and a temperature of 273K. Determine the volume of the sample at STP?
Solution:

The initial conditions are

P1 = 5.00 $\times$ 104 Pa, V1 = 4.00L

The final conditions are

P2 = 101325Pa, V2 = unknown

Rearrange

to solve for V2

V2 = $\frac{P_{1}V_{1}}{P_{2}}$

V2 = $\frac{[5.00 \times 10^{4} Pa][4.00\ L]}{1.01325 \times 10^{5} Pa}$

V2 = $\frac{2.00 \times 10^{5}}{1.01325 \times 10^{5}}$ L

V2 = 1.97L

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