# Boyle-Mariotte law

The law says that: The pressure exerted by a physical force is inversely proportional to the volume of a gaseous mass, as long as its temperature remains constant. Or in simpler terms: At constant temperature, the volume of a fixed mass of gas is inversely proportional to the pressure it exerts. Mathematically it can be expressed thus: PV = k where k is constant if the temperature and mass of the gas remain constant.

## Summary

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• 1 History
• 2 Definition of the Boyle – Mariotte Law
• 1 Why does this happen?
• 2 Example
• 3 Exercise
• 3 Boyle’s experiment
• 4 Sources

## History

It was discovered by Robert Boyle in 1662. Edme Mariotte also reached the same conclusion as Boyle, but he did not publish his works until 1676. This is why in many books we find this law under the name of Boyle and Mariotte’s Law. Boyle’s law states that the pressure of a gas in a closed container is inversely proportional to the volume of the container, when the temperature is constant. The mathematical expression of Boyle’s law indicates that the product of the pressure of a gas by its volume is constant:
PV = K
P1V1 = P2V2
As shown in figure 1, When a gas is subjected to a pressure of 4 atmospheres the volume of the gas decreases. Therefore, the higher the pressure, the lower the volume.

Figure 1. Gas under pressure of 4 atmospheres.

In figure 2, it is observed that when the pressure is decreased to 1 atmosphere, the volume increases, because the gases are compressible. Therefore At lower pressure Greater volume.

Figure 2. Gas under pressure of 1 atmosphere.

## Definition of the Boyle – Mariotte Law

The volume is inversely proportional to the pressure: • If the pressure increases, the volume decreases. • If the pressure decreases, the volume increases.

### Why does this happen?

As the volume increases, the gas particles (atoms or molecules) take longer to reach the walls of the container and therefore collide less times per unit time against them. This means that the pressure will be less since it represents the frequency of gas strikes against the walls.

When the volume decreases the distance that the particles have to travel is less and therefore more shocks occur in each unit of time: the pressure increases.

What Boyle discovered is that if the quantity of gas and the temperature remain constant, the product of the pressure by the volume always has the same value.

As we have seen, the mathematical expression of this law is:

PV = k

(the product of pressure times volume is constant)

Suppose we have a certain volume of gas V1 that is at a pressure P1 at the beginning of the experiment. If we vary the gas volume to a new value V2, then the pressure will change to P2, and it will be true:

P1V1 = P2V2

which is another way of expressing Boyle’s law.

### Example

4.0 L of a gas is at 600.0 mmHg of pressure. What will its new volume be if we increase the pressure to 800.0 mmHg?

Solution: We substitute the values ​​in the equation P1V1 = P2V2.

(600.0 mmHg) (4.0 L) = (800.0 mmHg) (V2)

If you clear V2 you will get a value for the new volume of 3L.

### Exercise

1. You want to compress 10 liters of oxygen, at room temperature and a pressure of 30 kPa, to a volume of 500 mL. What pressure in atmospheres must be applied?

P1 = 30 kPa (1 atm / 101.3kPa) = 0.3 atm

500 mL = 0.5L.

P1V1 = P2V2

P1 = 0.3 atm

V1 = 10 L

V2 = 0.50 L

We clear P2 and substitute.

P2 = P1 (V1 / V2)

P2 = 0.3 atm (10L / 0.50L) ​​= 6 atm

## Boyle’s experiment

In order to verify his theory, he introduced a gas into a cylinder with a piston and checked the different pressures when the piston was lowered. Below is a table that shows some of the results that this phenomenon obtained:

Boyle’s experiment

 x p (atm) V (L) PV 0.5 60 30 1.0 30 30 1.5 twenty 30 2.0 fifteen 30 2.5 12 30 3.0 10 30

Looking at the data in the table, it can be seen that as the volume increases, the pressure decreases. Therefore, an isothermal diagonal is used to represent it on a graph. , increases and that by multiplying y you get atm · L.