The Henry's law constant for \(\mathrm{O}_{2}\) is \(1.3 \times 10^{-3} \mathrm{M} /\) atm at \(25^{\circ} \mathrm{C}\). Assuming ideal solution behavior, what mass of oxygen would be dissolved in a 40-L aquarium at \(25^{\circ} \mathrm{C}\), assuming an atmospheric pressure of \(1.00 \mathrm{atm}\), and that the partial pressure of \(\mathrm{O}_{2}\) is 0.21 atm?

Solubility is a measure of how much of a substance can dissolve in a liquid, and in the case of gases like oxygen, understanding how their solubility changes under different conditions is essential for many practical applications, from aquatic life support systems to carbonated beverages. Henry's Law provides a basis for understanding these changes by stating that the solubility of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid.

When the partial pressure of the gas increases, more gas will dissolve in the liquid until a new equilibrium is established. This principle applies to our example where we determine how much oxygen can dissolve in an aquarium. For gases, the solubility typically decreases with increased temperature, but we're considering a constant temperature of 25°C in this scenario. This means that the solubility rate will remain consistent according to the pressure and Henry's Law constant provided.

Partial pressure is the pressure that a single component of a gas mixture would exert if it were alone in the container. The atmosphere contains a mixture of different gases, each contributing to the total pressure in proportion to its concentration.

Understanding partial pressure is crucial because it allows us to predict and calculate how much of a particular gas will dissolve in a liquid under equilibrium conditions. In the context of the 40-L aquarium with atmospheric pressure at 1.00 atm, the partial pressure of oxygen is 0.21 atm, which is simply 21% of the atmospheric pressure owing to oxygen's approximate 21% presence in atmospheric composition. It is this pressure that defines the amount of oxygen that will dissolve into the water of the aquarium, following Henry's Law. This illustration proves useful in environmental sciences, respiratory physiology, and even brewing processes.

The molar mass of a substance, often quantified in grams per mole (g/mol), is a pivotal constant in chemistry that represents the mass of one mole of its particles, atoms for elements or molecules for compounds. This property is fundamental because it serves as a bridge between the microscopic particles that make up substances and measurable quantities we can manipulate in the lab or industry.

In our oxygen dissolution example, we use the molar mass of oxygen (\(O_2\)) to convert the calculated moles of dissolved oxygen into grams. Since oxygen is a diatomic molecule (\(O_2\)), we consider the mass of two oxygen atoms for its molar mass calculation. Recognizing and accurately using the molar mass allows us to move from the theoretical (moles) to the practical (grams), which, in terms of application, can mean figuring out how much of a substance we can physically add to a system or product.