Question

Using Henry's constant data for a gas dissolved in a liquid, explain how you would determine the mole fraction of the gas dissolved in the liquid at the interface at a specified temperature.

Short answer

Question: Using Henry's law, determine the mole fraction of a gas dissolved in a liquid at the interface at a specified temperature, given the value of Henry's constant (K_H), the partial pressure of the gas (P), and the molarities of the liquid (M_liquid) and gas (M_gas). Answer: To find the mole fraction of the dissolved gas (x_gas), use the formula: x_gas = (K_H * P) / (M_liquid/M_gas)

Step-by-step solution

Understand Henry's Law

Henry's law states that the concentration of a gas dissolved in a liquid is directly proportional to the partial pressure of the gas at a specified temperature. Mathematically, Henry's law can be represented as: C = K_H * P Where C is the concentration of the gas dissolved in the liquid, K_H is Henry's constant, and P is the partial pressure of the gas.

Define the mole fraction

The mole fraction (x) represents the ratio of the number of moles of a component in a mixture to the total number of moles of all components in the mixture. We are interested in calculating the mole fraction of the dissolved gas in the liquid at the interface.

Use Henry's law to determine the mole fraction

To find the mole fraction of the gas dissolved in the liquid at the interface, we'll need to express the concentration (C) in terms of the mole fraction and molarity (M) of the liquid. The relationship between concentration and mole fraction is: C = x_gas * (M_liquid/M_gas) Where x_gas is the mole fraction of the dissolved gas, M_liquid is the molarity of the liquid, and M_gas is the molarity of the gas. Now, using Henry's law, we can write: x_gas * (M_liquid/M_gas) = K_H * P

Solve for the mole fraction of the dissolved gas

To find the mole fraction of the dissolved gas (x_gas), we'll need to rearrange the equation in Step 3: x_gas = (K_H * P) / (M_liquid/M_gas) Given the value of Henry's constant (K_H), the partial pressure of the gas (P), and the molarities of the liquid (M_liquid) and gas (M_gas), we can now determine the mole fraction of the gas dissolved in the liquid at the interface at the specified temperature.