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Chapter 12: Problem 186

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

Expert verified
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

01

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.
02

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.
03

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.
04

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.

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