Inorganic chemistry

How do you graph Boyle’s law? Boyle’s law Explanation for Pressure and Volume

Boyle's law graph

Boyle’s law states that at constant temperature the volume occupied by a certain amount of gas is inversely proportional to pressure — meaning as we increase the pressure, the quantity of the gas decreases.

Boyle Mariotte’s law

Boyle-Mariotte’s law, also called Boyle’s law, are postulates that were carried out independently by physicists Robert Boyle in 1662 and Edme Mariotte in 1676. This law belongs to the so-called gas laws, which associate the volume and pressure of a specific quantity of gas contained at a continuous temperature.

This law determines the following:

The pressure exerted by a chemical force is inversely proportional to the mass of gas, as long as its temperature is kept permanent.

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This means then, that if the volume were to go up, the pressure would go down and if the pressure went up, the volume would go down.

This law was initially proposed by Robert Boyle in the year 1662. Edme Mariotte, for his part, through his research, also reached the same conclusion as Boyle, however, the publication of his work was only possible in the year 1676. It is for this reason that this law appears in many texts with the names of both scientists.

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Now, in order to demonstrate his theory Boyle carried out the following experiment: he injected gas into a container with a plunger and verified the different pressures that were manifested when the plunger was lowered, since by doing this, the pressure on the gas increased proportionally, to the decrease in its volume.

Regarding its field of application, its most frequent use is in the diving area, where through the application of the law, it is possible to specify the duration of a container filled with compressed air and its productivity at a certain depth.

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It should be added that this law, together with Graham’s law and Charles and Gay Lussac’s law, make up the gas laws and which explain the behavior of an ideal gas. These three laws can be generalized into the general equation for gases.

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It is important to remember that despite the fact that the study of the characteristics of gases may be of little value and interest to some, one must consider the fact that technological evolution has been possible, in large part, due to the wise ability to manipulate these elements, starting from the domain of the oceans to outer space. 

How to graph Boyle’s law?

The graph of Boyle’s law is familiar as a pressure-volume graph or PV curve. It is as below:

As seen in the graph above, pressure increases with decreasing volume and vice versa. Therefore, pressure is inversely proportional to volume. Other parameters (temperature and amount of gas) are shown in the previous graph.

Mathematical explanation

Volume is on the x-axis and pressure is on the y-axis. The curve equation is PV = k, which is Boyle’s law equation. The curve is hyperbolic in nature and has two asymptotes: P = 0 (horizontal) and V = 0 (vertical).

Note: An asymptote is a line or curves such that the distance between it and a given curve tends to zero when the x and/or y coordinates tend to infinity.

As the volume tends to positive infinity, the pressure tends to zero and we get the horizontal asymptote, P = 0.

When the volume reaches zero, the pressure approaches infinity and results in the vertical asymptote, V = 0.

Graphs at different temperatures

Boyle’s Law graphs can be drawn at different temperatures. Each curve in the graphs below is at a constant temperature and these curves are called isotherms.

The graph above is a pressure-volume graph plotted at three different temperatures (T1, T2, and T3). As can be seen from the graph, as the temperature increases, the curves shift upwards. This is due to the increase in the value of k.

The pressure vs. inverse volume is a straight line through the origin and has a positive slope, k.

The graph above is a straight line parallel to the x-axis. This proves that the product of pressure and volume at a constant temperature and the amount of gas is constant. The lines on the graph are independent of volume (or pressure).

Logarithmic graphs

The equation of Boyle’s law is PV = k. Proceeding the logarithm to both sides.

The plots are a straight line with the y-intercept of log k.

Boyle’s law graph:

Boyle’s law graph is listed below the relationship between volume and pressure by which you can easily understand it.

The relationship between volume and pressure (Boyle-Mariotte’s Law)

The law Boyle describes the relationship between the pressure and volume of a gas. It stipulates that, at a constant temperature, the volume occupied by a certain quantity of gas is inversely proportional to its pressure.

The Irish physicist and chemist Robert Boyle (1627-1691) and the French physicist Edme Mariotte (1620-1684) have shown that there is a relationship between the pressure and the volume of a gas.

At a constant temperature and for the same number of molecules, they observed that the pressure of a gas increases when its volume decreases, and vice versa. The opposite is also true: a decrease in the volume of gas results in an increase in its pressure. This relationship is called Boyle-Mariotte’s Law.

The volume of a gas is therefore inversely proportional to its pressure. For example, doubling the gas pressure will reduce the volume by half. This variation can be explained by the kinetic theory of gas.

At constant temperature, if the external pressure exerted on a gas increases, its volume of it decreases. As a result, the gas particles become closer and clash further.

As a result, collisions are more frequent, which increases the pressure. Conversely, if the volume of the container is increased, the collision frequency is lower and the pressure of the gas becomes lower.

The graph of pressure versus volume forms a typical curve of an inversely proportional relationship. We can therefore say that the pressure is directly proportional to the inverse of the volume. Mathematically, we can write this relation as follows:

As the product of the pressure by the volume is equal to a constant, one can compare two situations for the same gas, as long as the quantity of gas and the temperature do not vary. This results in the following relation:



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