Question: 55: Which one is not correct mathematical equation for Dalton’s Law of partial pressure? Here p= total pressure of gaseous mixture
(1) \mathrm{p}_{\mathrm{i}}=\mathrm{X}_{\mathrm{i}} \mathrm{p}, where
\mathrm{p}_{\mathrm{i}}= partial pressure of \mathrm{i}^{\text {th }} gas
X_{i}= mole fraction of i^{\text {th }} gas in gaseous mixture where
X_{i}= mole fraction of i^{\text {th }} gas in gaseous mixture
\mathrm{p}_{i}^{\circ}= pressure of \mathrm{i}^{\text {th }} gas in pure state
where X_{i}= mole fraction of i^{\text {th }} gas in gaseous mixture
(2) \mathrm{p}_{\mathrm{i}}=\mathrm{X}_{\mathrm{i}} \mathrm{p}_{i}^{\circ},
(3) p=p_{1}+p_{2}+p_{3}
(4) \mathrm{p}=\mathrm{n}_{1} \frac{\mathrm{RT}}{\mathrm{V}}+\mathrm{n}_{2} \frac{\mathrm{RT}}{\mathrm{V}}+\mathrm{n}_{3} \frac{\mathrm{RT}}{\mathrm{V}}
Answer: Option (2)
Explanation:
Dalton’s law of partial pressure states that the total pressure of a gaseous mixture is equal to the sum of the partial pressures of individual gases.
The partial pressure of a gas in a mixture is given by \mathrm{p}_{\mathrm{i}}=\mathrm{X}_{\mathrm{i}} \mathrm{p},
where \mathrm{X}_{\mathrm{i}} is the mole fraction of the gas and \mathrm{p} is the total pressure.
The total pressure can also be expressed as the sum of partial pressures,
as shown by p=p_{1}+p_{2}+p_{3}, which is correct.
Using the ideal gas equation, the total pressure of the mixture can be written as the sum of pressures due to individual gases, given by
\mathrm{p}=\mathrm{n}_{1} \frac{\mathrm{RT}}{\mathrm{V}}+\mathrm{n}_{2} \frac{\mathrm{RT}}{\mathrm{V}}+\mathrm{n}_{3} \frac{\mathrm{RT}}{\mathrm{V}},
which is also correct.
The equation \mathrm{p}_{\mathrm{i}}=\mathrm{X}_{\mathrm{i}} \mathrm{p}_{i}^{\circ}
is incorrect for Dalton’s law because \mathrm{p}_{i}^{\circ} represents the pressure of the pure gas, not the total pressure of the mixture.
Therefore, option (2) is not a correct mathematical expression of Dalton’s law of partial pressure.