What does Boyles law state?

Each day, hundreds of weather balloons are launched. Made of a synthetic rubber and carrying a box of instruments, each helium-filled balloon rises up into the sky. As a balloon gains altitude, the atmospheric pressure becomes less and the balloon expands. At some point the balloon bursts due to the expansion; the instruments drop (aided by a parachute) to be retrieved and studied for information about the weather.

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Topics Covered in Other Articles
Important Things to Consider
Relationship Between Pressure and Volume
Change in Pressure and Volume
Boyle’s Law Equation – Example Problem

Robert Boyle (1627-1691), an English chemist, is widely considered to be one of the founders of the modern experimental science of chemistry. He discovered that doubling the pressure of an enclosed sample of gas, while keeping its temperature constant, caused the volume of the gas to be reduced by half. Boyle's law states that the volume of a given mass of gas varies inversely with the pressure when the temperature is kept constant. An inverse relationship is described in this way. As one variable increases in value, the other variable decreases.

Physically, what is happening? The gas molecules are moving and are a certain distance apart from one another. An increase in pressure pushes the molecules closer together, reducing the volume. If the pressure is decreased, the gases are free to move about in a larger volume.

Figure \(\PageIndex{1}\): Robert Boyle. (CC BY-NC; CK-12)

Mathematically, Boyle's law can be expressed by the equation:

\[P \times V = k\nonumber \]

The \(k\) is a constant for a given sample of gas and depends only on the mass of the gas and the temperature. The table below shows pressure and volume data for a set amount of gas at a constant temperature. The third column represents the value of the constant \(\left( k \right)\) for this data and is always equal to the pressure multiplied by the volume. As one of the variables changes, the other changes in such a way that the product of \(P \times V\) always remains the same. In this particular case, that constant is \(500 \: \text{atm} \cdot \text{mL}\).

Table \(\PageIndex{1}\): Pressure-Volume Data

Pressure \(\left( \text{atm} \right)\)	Volume \(\left( \text{mL} \right)\)	\(P \times V = k\) \(\left( \text{atm} \cdot \text{mL} \right)\)
0.5	1000	500
0.625	800	500
1.0	500	500
2.0	250	500
5.0	100	500
8.0	62.5	500
10.0	50	500

A graph of the data in the table further illustrates the inverse relationship nature of Boyle's Law (see figure below). Volume is plotted on the \(x\)-axis, with the corresponding pressure on the \(y\)-axis.

Figure \(\PageIndex{2}\): The pressure of a gas decreases as the volume increases, making Boyle's law an inverse relationship. (CC BY-NC; CK-12)

Boyle's Law can be used to compare changing conditions for a gas. We use \(P_1\) and \(V_1\) to stand for the initial pressure and initial volume of a gas. After a change has been made, \(P_2\) and \(V_2\) stand for the final pressure and volume. The mathematical relationship of Boyle's Law becomes:

\[P_1 \times V_1 = P_2 \times V_2\nonumber \]

This equation can be used to calculate any one of the four quantities if the other three are known.

A sample of oxygen gas has a volume of \(425 \: \text{mL}\) when the pressure is equal to \(387 \: \text{kPa}\). The gas is allowed to expand into a \(1.75 \: \text{L}\) container. Calculate the new pressure of the gas.

Solution

Step 1: List the known quantities and plan the problem.

Known

\(P_1 = 387 \: \text{kPa}\)
\(V_1 = 425 \: \text{mL}\)
\(V_2 = 1.75 \: \text{L} = 1750 \: \text{mL}\)

Use Boyle's Law to solve for the unknown pressure \(\left( P_2 \right)\). It is important that the two volumes (\(V_1\) and \(V_2\)) are expressed in the same units, so \(V_2\) has been converted to \(\text{mL}\).

First, rearrange the equation algebraically to solve for \(P_2\).

\[P_2 = \frac{P_1 \times V_1}{V_2}\nonumber \]

Now substitute the known quantities into the equation and solve.

\[P_2 = \frac{387 \: \text{kPa} \times 425 \: \text{mL}}{1750 \: \text{mL}} = 94.0 \: \text{kPa}\nonumber \]

The volume has increased to slightly over 4 times its original value and so the pressure is decreased by about one fourth. The pressure is in \(\text{kPa}\) and the value has three significant figures. Note that any pressure or volume units can be used as long as they are consistent throughout the problem.

Summary

This page titled 14.3: Boyle's Law is shared under a CK-12 license and was authored, remixed, and/or curated by CK-12 Foundation via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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In this tutorial, you will learn about the Boyle’s law formula, and how this equation can be used to determine relationships between changes in pressure and changes in volume in a given closed system.

Robert Boyle, sometimes called the “Father of Modern Chemistry” worked in the fields of physics and chemistry. In 1660, Boyle published The Spring and Weight of the Air in which he described different experiments he created using a vacuum pump which he designed.

In 1662, Boyle published version two of The Spring and Weight of the Air. This is were he described the inverse relationship between pressure and volume, now known as Boyle’s Law. Boyle’s Law states that pressure and volume are inversely proportional to each other. As the pressure increases the volume decreases, and as the pressure decreases the volume increases. He made these observations by using mercury in a J-tube, and then made measurements of the volume of the gas at pressures both lower and higher than standard atmospheric pressure.

Boyle expressed his results in a relationship that is known as Boyle’s law equation or Boyle’s law formula: P1V1 = P2V2 . This law assumes the temperature remains constant.

Topics Covered in Other Articles

Important Things to Consider

The gas law described in this article only applies to ideal gases, which you can read about on our article, The Ideal Gas Law.

Relationship Between Pressure and Volume

Consider a sample of gas in a 1-liter container. From our article, What is Pressure, we know that the pressure exerted on the container from the gas is the sum of the collisions of the particles, divided by the surface area of the container,

. We also know that the volume is related to the surface area, and if the volume decreases, the surface area will decrease as well.

From these two relations, we can see that as the volume decreases, the total pressure is going to increase. This leads us to Boyle’s law formula,

We can make a graph of this relationship as follows:

Change in Pressure and Volume

This proportionality can enable us to solve specific problems relating to the changes in pressure and volume in a closed system.

Consider, for example, a piston full of oxygen. From this proportionality, we know that if the piston is compressed, the pressure of the gas will increase.

Boyle’s Law Equation – Example Problem

Here is an example of how you can solve a Boyle’s Law problem.

An ideal gas exerts a pressure of 3 atm in a 2 L container. What will the pressure be if the volume of the container is changed to 1 L at constant temperature?

Solution:

You can read about how a student used Boyle’s original data to verify Boyle’s Law.