Understanding Gas Solubility in Water with Henry's Law

The solubility of a gas in a liquid is influenced by several factors, including temperature, pressure, and the nature of the gas and the liquid. For gases at a constant temperature, the relationship between the partial pressure of the gas above the liquid and its concentration (or mole fraction) in the liquid is described by Henry's Law.

Henry's Law is typically expressed as:

\(P_{gas} = K_H \cdot x_{gas}\)

Where:

• \(P_{gas}\) is the partial pressure of the gas above the solution.
• \(K_H\) is Henry's Law constant, which is specific to the gas, the solvent, and the temperature.
• \(x_{gas}\) is the mole fraction of the gas dissolved in the solution.

This equation can be rearranged to express the mole fraction of the dissolved gas:

\(x_{gas} = \frac{P_{gas}}{K_H}\)

At a constant temperature and pressure (which means a constant partial pressure for each gas above the solution, assuming ideal behavior and similar conditions), the mole fraction of the dissolved gas (representing its solubility) is inversely proportional to Henry's Law constant, \(K_H\).

This means:

• A lower value of \(K_H\) indicates higher solubility.
• A higher value of \(K_H\) indicates lower solubility.

Comparing Henry's Law Constants for Gas Solubility

We are given four different gases and their Henry's Law constants (\(K_H\)) at 298 K and 1 atm pressure. To find the gas with the maximum solubility in water, we need to identify the gas with the lowest \(K_H\) value.

Let's list the given gases and their \(K_H\) values:

Now, let's compare these \(K_H\) values to find the smallest one:

• Methanal: 0.000018
• Methane: 0.41
• CO₂: 1.6
• Argon: 40.3

Arranging the \(K_H\) values in ascending order:

0.000018 (Methanal) < 0.41 (Methane) < 1.6 (CO₂) < 40.3 (Argon)

The lowest \(K_H\) value is 0.000018, which corresponds to Methanal.

Identifying the Gas with Maximum Solubility

Since solubility is inversely proportional to the Henry's Law constant (\(K_H\)), the gas with the smallest \(K_H\) value will have the highest solubility in water under the given conditions.

Comparing the values, Methanal has the lowest \(K_H\) (0.000018) among the options provided. This indicates that Methanal is significantly more soluble in water than Methane, CO₂, or Argon.

Methanal (Formaldehyde, HCHO) is a polar molecule that can interact strongly with water through hydrogen bonding and can even undergo a reversible chemical reaction with water to form a hydrate (methylene glycol, H₂C(OH)₂), which further enhances its apparent solubility compared to non-polar or less reactive gases like Methane and Argon.

Therefore, based on the provided Henry's Law constants, Methanal exhibits the maximum solubility in water at 298 K and 1 atm pressure among the given choices.

Revision Table: Key Concepts for Gas Solubility

Additional Information on Gas Solubility and Henry's Law

Henry's Law is a useful approximation, especially for dilute solutions and gases that do not react extensively with the solvent. However, for gases like Methanal or Ammonia (NH₃) that react significantly with water, the "solubility" measured includes both the physically dissolved gas and the reaction products. The low \(K_H\) value for Methanal reflects this strong interaction/reaction with water.

Units of \(K_H\) can vary. In the form \(P = K_H \cdot x\), \(K_H\) has units of pressure (e.g., atm, bar, mmHg). Other common forms of Henry's Law use concentration (like molarity) instead of mole fraction, leading to different units for \(K_H\) (e.g., mol/(L·atm), M/atm). Regardless of the specific units used in the provided values, comparing them directly is valid if they are all in the same units and the relationship \(x_{gas} = P_{gas}/K_H\) holds.

The question specifies standard conditions (298 K and 1 atm), which implies a fixed temperature and pressure, making the direct comparison of the provided \(K_H\) values appropriate for determining relative solubility.