# Boyle's Law: Volume and Pressure

## Boyle's Law states that for a fixed amount of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional.

#### Key Points

• According to Boyle's Law, if pressure doubles, volume halves.

• Boyle's Law holds true only if the number of molecules n and the temperature are both constant.

• Boyle's Law is used to predict the result of introducing a change, in volume and pressure only, to the initial state of a fixed quantity of gas.

#### Terms

• Boyle's law (sometimes referred to as the Boyle–Mariotte law) states that the absolute pressure and volume of a given mass of confined gas are inversely proportional, if the temperature remains unchanged within a closed system.

• An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles.

• In thermodynamics, a curve on a p-V diagram for an isothermal process

#### Examples

• In an industrial process, a gas confined to a volume of 1 L at a pressure of 20 atm is allowed to flow into a 12-L container by opening the valve that connects the two containers. What will be the final pressure of the gas? Solution: The final volume of the gas is . The gas expands in inverse proportion two volumes.

#### Figures

1. ##### Boyle's Law

An animation of Boyle's Law, showing the relationship between volume and pressure when mass and temperature are held constant.

2. ##### Boyle's Law

An introduction to the relationship between pressure and volume, and an explanation of how to solve gas problems with Boyle's Law

Boyle's Law Figure 2 (sometimes referred to as the Boyle-Mariotte Law) states that the absolute pressure and volume of a given mass of confined gas are inversely proportional, if the temperature remains unchanged within a closed system Figure 1. That is to say, the product of pressure and volume is a constant for a given mass of confined gas as long as the temperature is constant. The law was named after chemist and physicist Robert Boyle, who published the original law in 1662. Boyle showed that the volume of air trapped by a liquid in the closed short limb of a J-shaped tube decreased in exact proportion to the pressure produced by the liquid in the long part of the tube.

The trapped air acted much like a spring, exerting a force opposing its compression. Boyle called this effect "the spring of the air" and published his results in a pamphlet with that title. The difference between the heights of the two mercury columns gives the pressure (76 cm = 1 atm), and the volume of the air is calculated from the length of the air column and the tubing diameter.

The law itself can be stated as follows: for a fixed amount of an ideal gas kept at a fixed temperature, P (pressure) and V (volume) are inversely proportional (when one doubles, the other halves).

Remember that these relations hold true only if the number of molecules n and the temperature are both constant. This is a relation of inverse proportionality; any change in the pressure is exactly compensated by an opposing change in the volume. As the pressure decreases toward zero, the volume will increase without limit. Conversely, as the pressure is increased, the volume decreases (but it can never reach zero). There will be a separate P-V plot for each temperature; a single P-V plot is therefore called an isotherm. Here is a graph with some isotherms for one mole of an ideal gas at several different temperatures:

Each plot has the shape of a hyperbola, where the locus of all points has the property xy = a.

#### Key Term Glossary

closed system
A system that can exchange heat and work, but not matter, with its surroundings.
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constant
Consistently recurring over time; persistent
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gas
Matter in a state intermediate between liquid and plasma that can be contained only if it is fully surrounded by a solid (or held together by gravitational pull); it can condense into a liquid, or can (rarely) become a solid directly.
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ideal gas
a hypothetical gas whose molecules exhibit no interaction and undergo elastic collision with each other and with the walls of the container
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Ideal gas
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles.
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isotherm
In thermodynamics, a curve on a p-V diagram for an isothermeral process.
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Isotherm
In thermodynamics, a curve on a p-V diagram for an isothermal process
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liquid
A substance that flows and keeps no definite shape, such as water. A substance whose molecules, while not tending to separate from one another like those of a gas, readily change their relative position, and which therefore retains no definite shape, except that determined by the containing receptacle; an inelastic fluid.
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mass
The quantity of matter that a body contains, irrespective of its bulk or volume. It is one of four fundamental properties of matter. It is measured in kilograms in the SI system of measurement.
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mole
In the International System of Units, the base unit of the amount of substance; the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kg of carbon-12. Symbol: mol. The number of atoms in a mole is known as Avogadro’s number.
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molecule
the smallest particle of a specific element or compound that retains the chemical properties of that element or compound; two or more atoms held together by chemical bonds
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Pressure
the amount of force that is applied over a given area divided by the size of this area
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product
a chemical substance formed as a result of a chemical reaction
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solution
A homogeneous mixture, which may be liquid, gas or solid, formed by dissolving one or more substances.
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Solution
A homogeneous mixture, which may be liquid, gas or solid, formed by dissolving one or more substances.
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state
The physical property of matter as solid, liquid, gas or plasma
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system
the part of the universe being studied, arbitrarily defined to any size desired
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temperature
A measure of cold or heat, often measurable with a thermometer.
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volume
A unit of three-dimensional measure of space that comprises a length, a width, and a height. It is measured in units of cubic centimeters in metric, or cubic inches or cubic feet in English measurement.