Question

Mathematical form of Henry's law is (a) \(m=k_{p}\) (b) \(p=k_{m}\) (c) \(\mu \frac{k}{m}\) (d) \(m \frac{1}{k} p\)

Short answer

The correct mathematical form of Henry's law is (d) \(m =\frac{1}{k} p\)

Step-by-step solution

Understanding the variables

In Henry's law expression, \(m\) represents the amount of gas dissolved, \(k\) is Henry's Law constant, and \(p\) is the partial pressure of the gas. Therefore, we must choose an option that expresses \(m\) as being proportional to \(p\).

Selection of the right option

Based on the understanding of Henry's law and the variables involved, option (a) and option (d) represents Henry's law correctly. However, given that in the natural form of Henry's law, \(k\) is in the denominator, we can identify that (d) \(m =\frac{1}{k} p\) as the correct mathematical representation of Henry's law.

Key concepts

Gas Solubility

Gas solubility refers to the ability of a gas to dissolve in a liquid. This concept is vital in various scientific and industrial processes. For instance, the carbon dioxide dissolved in carbonated beverages or the oxygen dissolved in water that supports aquatic life are examples of gas solubility.
Gas solubility depends on many factors, including temperature and pressure. An important rule to remember is that gases generally become less soluble in liquids as temperature increases. This is why a cold soda keeps its fizz longer than a warm one.
Pressure also significantly affects solubility. According to Henry's Law, the solubility of a gas in a liquid is directly proportional to the pressure of that gas above the liquid. This means if you increase the pressure of the gas, more gas will dissolve. This principle is crucial in understanding how diving tanks or carbonated beverages work. Thus, a clear grasp of gas solubility can facilitate better understanding of both natural phenomena and industrial applications.

Partial Pressure

Partial pressure is a fundamental concept in understanding gas behavior in mixtures. It describes the pressure exerted by a single type of gas in a mixture of gases. For example, in the air we breathe, each gas (like oxygen or nitrogen) exerts its own partial pressure. The total pressure of the gas mixture is the sum of these individual partial pressures.
In practical applications, partial pressure is essential. It's used in scenarios such as calculating the behavior of gases in chemical reactions or the breathability of air in different altitudes. In relation to Henry's Law, the partial pressure of a gas is directly proportional to its concentration in a liquid. This means that the higher the partial pressure, the greater the amount of gas that will dissolve in the liquid.
Understanding partial pressure is also crucial in medicine, like in managing the oxygen levels for patients in hypoxic conditions. Knowledge of how different gases exert pressure helps in optimizing conditions for various medical treatments and procedures. Thus embracing the concept of partial pressure enables one to predict and control gas behavior effectively.

Henry's Law Constant

The Henry's Law constant is a crucial component in the application of Henry's Law. It is denoted by the symbol \(k\). This constant links the concentration of a gas in a liquid to its partial pressure above the liquid. Each gas-liquid pair has a unique Henry's Law constant, dictated by their chemical properties.
The units of the Henry’s Law constant depend on the choice of concentration units, often expressed in terms like mol/L/atm. A higher \(k\) value indicates that less gas is needed to achieve a certain concentration in the liquid under given pressure. Inversely, a lower \(k\) means you need more pressure to obtain the same concentration.
Analyzing the Henry's Law constant helps in industries where precise gas dissolution is necessary, such as in the production of soft drinks or oxygen equilibria in biological systems. By understanding how the Henry's Law constant operates, one can make informed predictions about how gases will behave under different pressures and temperatures, thus enhancing control over processes involving gas dissolution.