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Solubility refers to the ability of a substance to dissolve in a solvent. In the context of gases like nitrogen (\(\mathrm{N}_2\)) in liquids such as water or blood, solubility tells us how much of the gas can dissolve under given conditions.
One important factor affecting solubility is temperature. Generally, the solubility of gases decreases as the temperature increases. This means that, at higher temperatures, less gas can dissolve in a liquid.
Furthermore, pressure also plays a crucial role in the solubility of gases. According to Henry's Law, the concentration of a dissolved gas in a liquid is directly proportional to the partial pressure of that gas above the liquid.

• Thus, when pressure increases, more gas dissolves into the liquid until a new equilibrium is reached.
• Conversely, a decrease in pressure results in gas coming out of the solution, potentially creating bubbles, which is what happens when a scuba diver surfaces too quickly.

Therefore, understanding solubility is indispensable for applications in fields like medicine, where knowing how gases behave in blood is vital for safe diving practices and medical treatments.
In the exercise provided, nitrogen's solubility is measured as 0.015 g/L at body temperature and 1 atm, which is used as a baseline to explore how solubility changes with pressure when diving.

The Ideal Gas Law is a fundamental equation in chemistry and physics that describes the state of an ideal gas. This equation is written as:\[ PV = nRT \]where:

• \(P\) is the pressure of the gas,
• \(V\) is the volume,
• \(n\) is the number of moles of the gas,
• \(R\) is the universal gas constant (0.0821 L atm/mol K), and
• \(T\) is the temperature in Kelvin.

The Ideal Gas Law helps us predict how a gas will behave under varying conditions of pressure, volume, and temperature.
While no real gas perfectly follows this law due to intermolecular forces and volume occupied by gas particles, it provides a very close approximation for many gases under a range of conditions.
In the context of the scuba diving scenario, the Ideal Gas Law helps calculate the volume of nitrogen gas released into the diver's bloodstream when surfacing. It takes into account changes in pressure and temperature that occur during the dive.

Partial pressure is the pressure exerted by a single type of gas in a mixture of gases. It is a crucial concept when discussing the behavior of gases dissolved in liquids, as seen with nitrogen in blood.
Each gas in a mixture exerts a pressure independently of other gases. This contributes to the total pressure of the gas mixture, an idea encapsulated in Dalton's Law of Partial Pressures.

• In the air, nitrogen has a partial pressure because it makes up a certain percentage (about 78%) of the atmosphere.
• Underwater, the total pressure increases due to the weight of the water above, thus increasing the partial pressures of each gas, including nitrogen.

This concept is important in diving, as it explains why more nitrogen dissolves in the blood at higher pressures experienced at \(100 \mathrm{ft}\) depths. Divers must manage this dissolved nitrogen to avoid decompression sickness, also known as "the bends," which occurs if nitrogen comes out of solution too rapidly as they return to the surface.
In solving the exercise, partial pressures are crucial for understanding how nitrogen's solubility changes with increased depth and pressure.

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It is an essential concept for converting between mass and moles in chemical calculations.

• For nitrogen gas (\(\mathrm{N}_2\)), its molar mass is 28 g/mol, as each molecule consists of two nitrogen atoms, each with an atomic mass of 14 g/mol.

Knowing the molar mass allows us to calculate how many moles are present in a given mass of nitrogen. This conversion is used in the textbook problem to determine the moles of nitrogen that dissolve in blood at different pressures.
The number of moles is crucial for using the Ideal Gas Law and Henry's Law, both of which depend on the mole quantity of the gas.
In problems involving gases in solution, molar mass serves as a bridge between mass and moles, helping us apply relevant gas laws to understand behavior, particularly when calculating solubility and responding to pressure changes in scenarios like scuba diving.
Overall, grasping molar mass is essential for making accurate predictions about gas behavior and solubility as demonstrated in the exercise.