Question

Which of the following is not an expression of Dalton's law of partial pressures?

• A. \( P = P_1 + P_2 \)
• B. \( P = P^\circ x_1 \)
• C. \( P = P^\circ_1 + (P^\circ_2 - P^\circ_1) x_2 \)
• D. \( P_1 = P - P_2 \)

Hint:

Dalton’s law of partial pressures states that the total pressure of a mixture of gases is the sum of the partial pressures of the individual gases. For a gas mixture, the partial pressure of each gas is proportional to its mole fraction.

Answer 1

The Correct Option is D

Dalton's law of partial pressures states that the total pressure of a mixture of gases is the sum of the partial pressures of each individual gas in the mixture. Mathematically, this is expressed as: \[ P_{\text{total}} = P_1 + P_2 + \cdots \] where \( P_1, P_2, \cdots \) are the partial pressures of the individual gases. Now let's evaluate each option: - Option (1): \( P = P_1 + P_2 \) — This is the correct expression for Dalton's law when dealing with two gases. - Option (2): \( P = P^\circ x_1 \) — This expression is related to the partial pressure of a gas in terms of its mole fraction (\( x_1 \)) and the vapor pressure of the pure substance (\( P^\circ \)). This is a valid expression under Dalton's law for one gas in a mixture. - Option (3): \( P = P^\circ_1 + (P^\circ_2 - P^\circ_1) x_2 \) — This is another correct form of Dalton's law that includes partial pressures based on the mole fractions of the gases. It reflects the contributions of two gases to the total pressure. - Option (4): \( P_1 = P - P_2 \) — This is not a valid expression according to Dalton's law. This suggests that the partial pressure of gas 1 is the total pressure minus the partial pressure of gas 2, which does not accurately reflect Dalton's law.
Thus, the correct answer is Option (4), as it does not properly represent Dalton's law.