The solubility of \(\mathrm{N}_{2}\) in blood at \(37^{\circ} \mathrm{C}\) and at a partial pressure of \(0.80 \mathrm{~atm}\) is \(5.6 \times 10^{-4} \mathrm{~mol} / \mathrm{L}\). A deepsea diver breathes compressed air with the partial pressure of \(\mathrm{N}_{2}\) equal to \(4.0 \mathrm{~atm} .\) Assume that the total volume of blood in the body is 5.0 L. Calculate the amount of \(\mathrm{N}_{2}\) gas released (in liters) when the diver returns to the surface of the water, where the partial pressure of \(\mathrm{N}_{2}\) is \(0.80 \mathrm{~atm}\)

When we talk about the solubility of gases, we're referring to how well a gas dissolves in a liquid under various conditions. Henry's Law plays a critical role here by providing a simple relationship: the amount of gas dissolved in a liquid is proportional to the pressure of the gas above the liquid. It's an important concept to understand when considering how environmental changes, like depth and pressure in scuba diving, affect gas solubility in our body fluids.

For divers, as they descend deeper underwater, the increased pressure can significantly increase the solubility of gases like nitrogen in their blood, leading to potential dangers such as decompression sickness if they ascend too quickly. The exercise solved above uses this principle to calculate how much nitrogen gas would be released from a diver's blood when they return to the surface, where pressure is comparatively lower.

The term partial pressure is key when dissecting Henry's Law. It refers to the pressure contribution of a single gas within a mixture of gases. In our atmosphere, for example, nitrogen makes up about 78% of the air, therefore it contributes approximately 78% of the atmospheric pressure. This concept becomes very tangible when considering scenarios like the textbook problem, where a diver's exposure to high partial pressure of nitrogen at depth means more nitrogen dissolves in their blood.

Understanding partial pressure is not only important academically but also practically, as it affects our everyday activities such as breathing and is considered in industries involving carbonated drinks, where the escape of carbon dioxide is dictated by its partial pressure.

Henry's Law is just one of several gas laws that describe how gases behave under various circumstances. Other gas laws such as Boyle's Law, which states that pressure and volume of a gas are inversely proportional at constant temperature, and Charles's Law, which shows how gas volume is proportional to temperature, are all part of the puzzle. Together, these laws form the foundation for understanding thermodynamics and fluid behavior in chemistry and physics.

Gas laws are essential for numerous real-world applications, ranging from the design of respiratory therapy equipment to the production of gas-powered engines. They're also pivotal in calculating how gases will respond to changes such as when divers adjust their depths, similar to the described exercise, or when assessing the behavior of gases in chemical reactions.