For the calculation of the solubility c of a gas in a solvent, it is often convenient to use the expression \(\mathrm{c}=K p\), where \(\mathrm{K}\) is the Henry's law constant. Breathing air at high pressures, such as in scuba diving, results in an increased concentration of dissolved nitrogen. The Henry's law constant for the solubility of nitrogen is \(0.18 \mu \mathrm{g} /\left(\mathrm{g} \mathrm{H}_{2} \mathrm{O} \mathrm{atm}\right) .\) What mass of nitrogen is dissolved in \(100 \mathrm{~g}\) of water saturated with air at \(4.0 \mathrm{~atm}\) and \(20^{\circ} \mathrm{C}\) ? Compare your answer to that for \(100 \mathrm{~g}\) of water saturated with air at \(1.0 \mathrm{~atm}\). (Air is \(78.08\) mole per cent \(\mathrm{N}_{2}\).) If nitrogen is four times as soluble in fatty tissues as in water, what is the increase in nitrogen concentration in fatty tissue in going from I atm to 4 atm?

The solubility of gases in liquids is a fundamental concept in chemistry that describes how much of a gas can dissolve in a given amount of liquid. According to Henry's Law, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. This means that as the pressure of the gas increases, more of the gas will dissolve in the liquid until the solution becomes saturated.

When we talk about 'saturated,' it implies that the liquid has dissolved as much gas as it can at a given pressure and temperature. Solubility can vary widely depending on the type of gas and solvent, temperature, and the presence of other dissolved substances. This concept is particularly important in environmental science, where the solubility of gases in water bodies can affect aquatic life, and in industries like soft drink manufacturing, where carbonation is a key process.

Partial pressure is a measure of the pressure that a single gas component in a mixture of gases would exert if it occupied the entire volume alone at the same temperature. It's a crucial concept for understanding the behavior of gases. The total pressure exerted by a mixture of gases, such as air, is the sum of the partial pressures of the individual gases.

Hence, if air is 78.08% nitrogen by mole fraction, the partial pressure of nitrogen is 78.08% of the total pressure. This partial pressure plays a significant role in calculations of gas solubility in liquids, given that the solubility is proportional to the partial pressure, according to Henry's law.

Considering the solubility of nitrogen in water, we focus on how much nitrogen gas can be dissolved in water under different conditions, a vital concept in fields such as scuba diving and aquatic biology. At higher pressures, like those experienced during scuba diving, the amount of dissolved nitrogen in the body's tissues can significantly increase, potentially leading to conditions such as decompression sickness.

When water is saturated with air at standard atmospheric conditions (1 atm), the amount of dissolved nitrogen is relatively stable. However, as the pressure increases, the solubility of nitrogen in water also increases. It's also important to note that solubility decreases with increasing temperature and that gases are typically more soluble in cold water than in warm water.

Concentration calculation is the process of determining the amount of a substance dissolved in a specific volume of solution. In the context of Henry's Law, to calculate the concentration of a dissolved gas, we use the formula where the concentration (\(c\)) equals the Henry's Law constant (\(K\)) multiplied by the partial pressure (\(p\)) of the gas (\(c = Kp\)).

To convert to the mass of the dissolved gas, we multiply the concentration by the mass of the solvent. This calculation is commonly used in environmental science, medicine, and engineering to predict the behavior of gases in various scenarios, such as predicting the levels of a dissolved pollutant in a lake or calculating the amounts of anesthetic gases used during surgery.