Question

Henry's law tells us that the solubility \(s\) of a gas in a liquid increases as the pressure \(P\) of the gas increases. Which of the following mathematical expressions of Henry's law is correct? Explain your choice and explain why the other two expressions are incorrect. (Hint: The \(k\) is just a constant of proportionality and can be ignored.) (a) \(s=k P\) (b) \(s=k / P\) (c) \(s=k P / P\)

Short answer

The correct expression for Henry's Law is \(s = kP\), as it directly links solubility with pressure. The other two expressions are incorrect because they contradict Henry's Law: (b) \(s = \frac{k}{P}\) implies that solubility decreases with increasing pressure, and (c) \(s = \frac{kP}{P}\) simplifies to \(s = k\), implying that solubility is independent of pressure.

Step-by-step solution

Understand Henry's Law

Henry's Law states that the solubility (s) of a gas in a liquid is directly proportional to the partial pressure of the gas (P) above the liquid. The constant of proportionality (k) depends on the specific gas and the temperature.

Analyze each expression

We will analyze each of the given expressions to see if they match the description of Henry's Law. (a) \(s = kP\): This expression states that solubility (s) is directly proportional to pressure (P) as required by Henry's Law. (b) \(s = \frac{k}{P}\): This expression states that solubility (s) is inversely proportional to pressure (P) which contradicts what we know about the behavior of the gas's solubility from Henry's Law. (c) \(s = \frac{kP}{P}\): This expression can be simplified to \(s = k\), which states that solubility (s) is independent of pressure (P). This contradicts the pressure dependence of gas solubility according to Henry's Law.

Identify the correct expression

Based on our analysis, we can conclude that the correct expression for Henry's Law is: \(s = kP\). This is because this expression directly links solubility with pressure, as stated in Henry's Law.

Explain why other expressions are incorrect

The other expressions are incorrect because they do not correctly convey the relationship between solubility and pressure according to Henry's Law: - Expression (b): \(s = \frac{k}{P}\) implies that solubility would decrease with increasing pressure, which contradicts Henry's Law. - Expression (c): \(s = \frac{kP}{P}\) simplifies to \(s = k\), which implies that solubility is independent of pressure, also contradicting Henry's Law.

Key concepts

Gas Solubility

The solubility of a gas refers to how well a gas dissolves in a liquid. This concept is crucial because it helps explain phenomena like the behavior of carbonated beverages, where gases are dissolved under pressure. Solubility can vary widely depending on different factors such as temperature, the nature of the gas, and the solvent. In general, gases with higher solubility in a given liquid will dissolve more readily at a specific pressure and temperature.

Solubility is essential in various fields, including chemistry, environmental science, and engineering, as it influences reactions, processes, and biological systems. Understanding gas solubility helps in optimizing industrial processes and even in everyday activities like cooking and fermentation.

Pressure Dependence

Pressure significantly impacts how gases dissolve in liquids, which is where Henry's Law comes into play. According to this law, the solubility of a gas is directly proportional to the pressure of that gas above the liquid. As pressure increases, more gas molecules are "pushed" into the liquid, enhancing solubility. This phenomenon can be seen in carbonation, where drinks are infused with carbon dioxide under high pressure.

Conversely, reducing pressure allows gas to escape from the liquid, leading to a decrease in solubility. This process is why a carbonated drink fizzes when opened, as the pressure above the liquid decreases rapidly.

Proportionality Constant

In Henry's Law, the proportionality constant, denoted as \(k\), is specific to each gas-liquid pair and represents how much gas will dissolve at a by the standard pressure (atmospheric pressure). The value of \(k\) depends on factors such as temperature and the nature of both the gas and the solvent.

It's important to note that while \(k\) is constant for a given gas and solvent at a specific temperature, it can change if these conditions are altered. Understanding the role of the proportionality constant helps in predicting the behavior of gases under different pressure conditions.

Solubility Expressions

Solubility expressions, like those given in textbook problems, help to conceptualize how gas solubility can be mathematically described. For Henry's Law, the expression \(s = kP\) accurately conveys that solubility \(s\) is directly proportional to pressure \(P\). This formula is a straightforward representation of how gas solubility works according to Henry's Law.

Other expressions like \(s = \frac{k}{P}\) and \(s = \frac{kP}{P}\) are incorrect for describing Henry's Law because they suggest a wrong relationship with pressure. The correct formula, \(s = kP\), helps students and scientists alike to comprehend the pressure-solubility relationship in a clear and precise manner.

Introductory Chemistry

Introductory Chemistry is the foundational course that often introduces students to important principles like Henry's Law. In these courses, students learn to connect theoretical knowledge with practical applications. Understanding fundamental laws like Henry's Law helps to explain everyday phenomena, from why soda cans are pressurized to how gases behave in different environments.

Studying Introductory Chemistry provides a basis for later chemistry courses and scientific inquiry, where students can explore more complex reactions and environmental considerations. Mastering these basic concepts fosters a deeper appreciation and understanding of the chemical world.