Question

According to Henry's law, the partial pressure of gas \(\left(P_{g}\right)\) is directly proportional to mole fraction of gas in liquid solution, \(P_{\text {gas }}=K_{H} \cdot X_{\text {gas }}\), where \(K_{H}\) is Henry's constant. Which is incorrect ? (a) \(K_{H}\) is characteristic constant for a given gas-solvent system (b) Higher is the value of \(K_{H}\), lower is solubility of gas for a given partial pressure of gas (c) \(K_{H}\) has temperature dependence (d) \(K_{H}\) decreases with increase of temperature

Short answer

Statement (d) is incorrect.

Step-by-step solution

Understand Henry's Law

Henry's law states that at a constant temperature, the amount of gas that dissolves in a type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid. The law is usually expressed as: \(P_{\text{gas}} = K_H \cdot X_{\text{gas}}\), where \(P_{\text{gas}}\) is the partial pressure of the gas, \(X_{\text{gas}}\) is the mole fraction of the gas, and \(K_H\) is Henry's law constant.

Analyze Statement (a)

Statement (a) says that \(K_H\) is characteristic constant for a given gas-solvent system. This is correct because Henry's law constant is specific to a particular gas-solvent combination at a fixed temperature.

Analyze Statement (b)

Statement (b) suggests that a higher value of \(K_H\) results in lower solubility of the gas for a given partial pressure. This is also correct, as the direct proportionality between the partial pressure and mole fraction indicates that for a fixed partial pressure, a larger \(K_H\) would lead to a smaller mole fraction (and thus lower solubility).

Analyze Statement (c)

Statement (c) states that \(K_H\) has temperature dependence. This is true because the solubility of gases typically changes with temperature, meaning that \(K_H\) also varies with temperature.

Analyze Statement (d)

Finally, statement (d) claims that \(K_H\) decreases with the increase of temperature. This statement is incorrect for many gases because usually, the solubility of gases decreases with an increase in temperature, which would mean that \(K_H\) increases as temperature increases, not decreases.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a foundational concept in physical chemistry that describes the balance between reactants and products in a chemical reaction. At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, resulting in no apparent change in the concentrations of reactants and products over time.

In the context of Henry's Law, chemical equilibrium refers to a particular state where the amount of gas dissolved in the liquid is constant, as the rate at which gas molecules enter the liquid is equal to the rate at which they leave. This principle is vital for understanding how gases behave when they come in contact with liquids and is crucial for various applications, such as carbonation in beverages and the uptake of oxygen in blood.

Gas Solubility

Gas solubility is the extent to which a gas can dissolve in a solvent at a given temperature and pressure. Solubility is critical for many environmental and industrial processes. As per Henry's Law, the solubility of the gas in a liquid is directly proportional to the partial pressure of that gas above the liquid.

Factors that affect gas solubility include the nature of the gas and the solvent, the temperature, and the partial pressure of the gas. In general, gases become less soluble as the temperature increases, which is related to increased molecular motion causing a lesser tendency for gas molecules to associate with the solvent molecules. This relationship ties in with the understanding that higher values of the Henry's law constant (\(K_H\)) correspond to a lower solubility.

Physical Chemistry

Physical chemistry explores the principles that govern the physical properties of chemical systems and the processes they undergo. It's a branch of chemistry that relies heavily on physics and mathematics to describe chemical phenomena.

Within this discipline, Henry's Law represents an intersection of chemical behavior and physical principles, by quantifying the relationship between the concentration of a gas in a liquid and the pressure of the gas. This law helps to elucidate the physicochemical processes involved in gas-liquid interactions and provides a predictive ability for understanding solubility changes with varying environmental conditions. Physical chemistry paves the way for a deeper comprehension of real-world systems, such as oceanic gas exchange and the effects of pressure changes in scuba diving.