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

Dalton's Law of Partial Pressure states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases in the mixture. Let's evaluate the mathematical expressions provided:

• p = p₁ + p₂ + p₃

  This expression aligns with Dalton's Law, reflecting that the total pressure is the sum of individual partial pressures.

• p = n₁(\(\frac{RT}{V}\)) + n₂(\(\frac{RT}{V}\)) + n₃(\(\frac{RT}{V}\))

  This equation also adheres to Dalton's Law, as it calculates the total pressure via the ideal gas law for each gas.

• p_i = χ_ip, where p_i = partial pressure of i_th gas; χ_i = mole fraction of i_th gas in gaseous mixture

  This is correct as it relates the partial pressure of a gas to its mole fraction and the total pressure.

• 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

  This expression is incorrect for Dalton's Law. It wrongly relates the partial pressure in a mixture to the pressure in a pure state, which doesn't conform to Dalton's Law conditions.