Question

Which one is not correct mathematical equation for Dalton's Law of partial pressure? Here p = total pressure of gaseous mixture

• A. p = p₁ + p₂ + p₃
• B. p = n₁(\(\frac{RT}{V}\)) + n₂(\(\frac{RT}{V}\)) + n₃(\(\frac{RT}{V}\))
• C. p_i = χ_ip, where p_i = partial pressure of i_th gas; χ_i = mole fraction of ith gas in gaseous mixture
• D. p_i = χ_ip_io, where χ_i = mole fraction of i_th gas in gaseous mixture p_io = pressure of ith gas in pure state

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Dalton's Law of Partial Pressures states that the total pressure of a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases.
Step 2: Detailed Explanation:
Let's evaluate each mathematical expression:
1. Statement (1): \(p = p_1 + p_2 + p_3\)
This is the fundamental definition of Dalton's Law. Correct.

2. Statement (2): \(p = n_1 \frac{RT}{V} + n_2 \frac{RT}{V} + n_3 \frac{RT}{V}\)
Since \(p_i = \frac{n_i RT}{V}\) from the Ideal Gas Law, substituting this into the sum of partial pressures gives this equation. Correct.

3. Statement (3): \(p_i = \chi_i p\)
The partial pressure of a gas is the product of its mole fraction and the total pressure. Correct.

4. Statement (4): \(p_i = \chi_i p_i^\circ\)
This equation describes Raoult's Law, which applies to liquid solutions (vapor pressure), not to the partial pressure of a mixture of gases in a container. Incorrect for Dalton's Law.
Step 3: Final Answer:
The equation in option (D) is not a correct mathematical representation of Dalton's Law.