HENRY'S LAW: EQUATION, DEVIATION, APPLICATIONS - CHEMISTRY - 2025

The Henry 's law states that at constant temperature, the amount of dissolved gas in a liquid is directly proportional to its partial pressure on the surface of the liquid.

It was postulated in 1803 by the English physicist and chemist William Henry. His law can also be interpreted in this way: if the pressure on the liquid is increased, the greater will be the amount of gas dissolved in it.

Here the gas is considered as the solute of the solution. Unlike solid solute, temperature has a negative effect on its solubility. Thus, as the temperature increases, the gas tends to escape from the liquid more easily towards the surface.

This is due to the fact that the increase in temperature contributes energy to the gaseous molecules, which collide with each other to form bubbles (upper image). These bubbles then overcome the external pressure and escape from the sinus of the liquid.

If the external pressure is very high, and the liquid is kept cold, the bubbles will dissolve and only a few gaseous molecules will "hover" on the surface.

Henry's Law Equation

It can be expressed by the following equation:

P = K _H ∙ C

Where P is the partial pressure of the dissolved gas; C is the gas concentration; and K _H is Henry's constant.

It is necessary to understand that the partial pressure of a gas is that exerted individually by a species of the rest of the total gas mixture. And the total pressure is nothing more than the sum of all the partial pressures (Dalton's Law):

P _Total = P ₁ + P ₂ + P ₃ +… + P _n

The number of gaseous species that make up the mixture is represented by n. For example, if there is water vapor and CO ₂ on the surface of a liquid, n is equal to 2.

Deviation

For gases poorly soluble in liquids, the solution is close to ideal, complying with Henry's law for the solute.

However, when the pressure is high, there is a deviation with respect to Henry, because the solution stops behaving as an ideal dilute.

What does it mean? That solute-solute and solute-solvent interactions begin to have their own effects. When the solution is very dilute, the gas molecules are “exclusively” surrounded by solvent, neglecting the possible encounters between themselves.

Therefore, when the solution is no longer ideally diluted, the loss of linear behavior is observed in the graph P _i vs X _i.

In conclusion to this aspect: Henry's law determines the vapor pressure of a solute in an ideal dilute solution. While for the solvent, Raoult's law applies:

P _A = X _A ∙ P _A ^*

Solubility of a gas in the liquid

When a gas is well dissolved in a liquid, such as sugar in water, it cannot be distinguished from the environment, thus forming a homogeneous solution. In other words: no bubbles are observed in the liquid (or sugar crystals).

However, the efficient solvation of gaseous molecules depends on some variables such as: the temperature of the liquid, the pressure that affects it, and the chemical nature of these molecules compared to those of the liquid.

If the external pressure is very high, the chances of gas penetrating the liquid surface are increased. And on the other hand, dissolved gaseous molecules find it more difficult to overcome the incident pressure to escape to the outside.

If the liquid-gas system is under agitation (as in the sea and in the air pumps inside the fish tank), the absorption of gas is favored.

And how does the nature of the solvent affect the absorption of a gas? If this is polar, like water, it will show affinity for polar solutes, that is, for those gases that have a permanent dipole moment. Whereas if it is apolar, such as hydrocarbons or fats, it will prefer apolar gaseous molecules

For example, ammonia (NH ₃) is a very soluble gas in water due to hydrogen bonding interactions. While hydrogen (H ₂), whose small molecule is apolar, interacts weakly with water.

Also, depending on the state of the gas absorption process in the liquid, the following states can be established in them:

Unsaturated

The liquid is unsaturated when it is able to dissolve more gas. This is because the external pressure is greater than the internal pressure of the liquid.

Saturated

The liquid establishes an equilibrium in the solubility of the gas, which means that the gas escapes at the same rate as it enters the liquid.

It can also be seen as follows: if three gaseous molecules escape into the air, another three will return to the liquid at the same time.

Oversaturated

The liquid is supersaturated with gas when its internal pressure is higher than the external pressure. And, with a minimal change in the system, it will release excess dissolved gas until equilibrium is restored.

Applications

- Henry's law can be applied to calculate the absorption of inert gases (nitrogen, helium, argon, etc.) in the different tissues of the human body, and that together with Haldane's theory are the basis of the tables decompression.

- An important application is the saturation of gas in the blood. When blood is unsaturated the gas dissolves in it, until it becomes saturated and stops dissolving more. Once this happens, the gas dissolved in the blood passes into the air.

- The gasification of soft drinks is an example of Henry's law applied. Soft drinks have CO ₂ dissolved under high pressure, thus maintaining each of the combined components that make it up; and in addition, it retains the characteristic flavor for much longer.

When the soda bottle is uncapped, the pressure on top of the liquid decreases, releasing the pressure instantly.

Because the pressure on the liquid is now lower, the solubility of CO ₂ drops and it escapes into the environment (it can be noticed in the rise of the bubbles from the bottom).

- As a diver descends to greater depths, the inhaled nitrogen cannot escape because the external pressure prevents it, dissolving in the individual's blood.

When the diver rises rapidly to the surface, where the external pressure drops again, nitrogen begins to bubble into the blood.

This causes what is known as decompression sickness. It is for this reason that divers are required to ascend slowly, so that nitrogen escapes more slowly from the blood.

- Study of the effects of the decrease in molecular oxygen (O ₂) dissolved in the blood and tissues of mountain climbers or practitioners of activities that involve prolonged stay at high altitudes, as well as in the inhabitants of fairly high places.

- Research and improvement of the methods used to avoid natural disasters that can be caused by the presence of gases dissolved in huge bodies of water that can be released violently.

Examples

Henry's law applies only when the molecules are in equilibrium. Here are some examples:

- In the dissolution of oxygen (O ₂) in the blood fluid, this molecule is considered poorly soluble in water, although its solubility increases considerably due to the high content of hemoglobin in it. Thus, each hemoglobin molecule can bind to four oxygen molecules that are released in the tissues to be used in metabolism.

- In 1986 there was a thick cloud of carbon dioxide that was suddenly expelled from Lake Nyos (located in Cameroon), suffocating approximately 1700 people and a large number of animals, which was explained by this law.

- The solubility that a given gas manifests in a liquid species tends to increase as the pressure of said gas increases, although at high pressures there are certain exceptions, such as nitrogen molecules (N ₂).

- Henry's law is not applicable when there is a chemical reaction between the substance that acts as a solute and that which acts as a solvent; such is the case of electrolytes, such as hydrochloric acid (HCl).

References

1. Crockford, HD, Knight Samuel B. (1974). Fundamentals of physicochemistry. (6th ed.). Editorial CECSA, Mexico. P 111-119.
2. The editors of Encyclopaedia Britannica. (2018). Henry's law. Retrieved on May 10, 2018, from: britannica.com
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4. Leisurepro & Aquaviews. (2018). Henry's Law Retrieved on May 10, 2018, from: leisurepro.com
5. Annenberg Foundation. (2017). Section 7: Henry's Law. Retrieved on May 10, 2018, from: learner.org
6. Monica Gonzalez. (April 25, 2011). Henry's Law. Retrieved on May 10, 2018, from: quimica.laguia2000.com
7. Ian Myles. (July 24, 2009). Diver.. Retrieved on May 10, 2018, from: flickr.com