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Dalton's Law of Partial Pressure - Practice Questions & MCQ

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

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Dalton’s Law of Partial Pressure is considered one the most difficult concept.
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Dalton’s Law of Partial Pressure

According to Dalton's law, "Total pressure of a mixture of non-reacting gases is equal to the sum of partial pressure of these gases at constant temperature and constant volume."

$\\\mathrm{P_{\operatorname{mix}}=P_{1}+P_{2}+P_{3}}\\\\\mathrm{Here \: P_{mix }= pressure\: of\: the\: gaseous\: mixture}\\\\\mathrm{P_{1}, P_{2}, P_{3}= partial \: pressure \: of \: gases}\\\\\mathrm{Partial\: pressure \: of \: any\: gas\: =\: \frac{\%\: of\: that\: gas\: }{100} \times P_{mix}}\\\\\mathrm{\%\: of\: a\: gas\: in\: a\: mixture\: =\: \frac{Partial \: pressure\: of\: the\: gas}{Total \: pressure\: of\: gaseous \: mixture} \times 100}$

$\\\mathrm{Partial\: pressure \: of \: any \: component\: A \: is\: given\: as}\\\\\mathrm{P_{A}=\frac{moles \: of\: A}{Total \: moles} \times P_{Total }}\\\\\mathrm{Total\: pressure\: of\: a\: mixture\: having\: different\: components \: is\: given \: as}\\\\\mathrm{P_{mix}\: =\: \left(n_{1}+n_{2}+n_{3} \ldots . .\right) \frac{R T}{V}}\\\\\mathrm{P_{mix}\: =\: \left(\frac{w_{1}}{m_{1}}+\frac{w_{2}}{m_{2}}+\frac{w_{3}}{m_{3}}\right) \ldots . \frac{R T}{V}}\\\\\mathrm{Here\: w_{1}, \: w_{2},\: w_{3}\: =\: weight \: of\: components\: or\: non-reacting \: gases}\\\mathrm{ and \: m_{1},\: m_{2},\: m_{3}\: are \: their\: molar\: masses.}$

$\\\mathrm{T\: =\: Temperature \: in \: Kelvin.}\\\mathrm{V\: =\: Volume in litre.}$

When a gas is collected over water it mixes with water vapours so the correct pressure of moist gas is given as
P(moist gas) = P(dry gas) + P(VP of water)
P(dry gas) = P(moist gas) - P(V.P of water)
Aqueous tension = Partial pressure of water vapour in moist gas.
Vapour pressure of water varies with temperature. For example, Aa 0^oC, it is 4.6 torr while at 25^oC it is 23.8 torr.

NOTE: Dalton's law is not applicable for a mixture of reacting gases like N₂and O₂, SO₂ and O₂.

Partial pressure in terms of mole fraction
According to ideal gas equation, if n₁ is the number of molecules of one constituent gas of the gaseous mixture then P₁ is the pressure exerted by the gas at temperature(T) enclosed in the volume (V).

$\mathrm{P_{1}=\frac{n_{1} R T}{V}}\quad \quad \quad ..........(i)$
Similarly for the other two constituting gases of the gaseous mixture

$\\\mathrm{P_{2}\: =\: \frac{n_{2}RT}{V}}\\\\\mathrm{P_{3}\: =\: \frac{n_{3}RT}{V}}$

According to Dalton's Law of partial pressures

$\\\mathrm{P_{Total}\: =\: P_{1}\: +\: P_{2}\: +\: P_{3}\: +\ldots}\\\\\mathrm{=\: \frac{n_{1} R T}{V}\: +\: \frac{n_{2} R T}{V}\: +\: \frac{n_{3} R T}{V}\: +\: \ldots}\\\\\mathrm{P_{total}\: =\:(n_{1}\: +\: n_{2}\: +\: n_{3}) \frac{RT}{V}}\quad \quad \quad ........(ii)$

That means the total partial pressure of the mixture is determined by the total number of moles present.
Dividing equation (i) by (ii) we get.

$\\\mathrm{\frac{P_{1}}{P_{total}}\: =\: \left(\frac{n_{1}}{n_{1}+n_{2}+n_{3}}\right) \frac{R T V}{R T V}}\\\\\mathrm{=\: \frac{n_{1}}{n_{1}+n_{2}+n_{3}}\: =\: \frac{n_{1}}{n}}\\\\\mathrm{where n=n_{1}+n_{2}+n_{3}}$

$\mathrm{Now,\: \frac{n_{1}(moles \: of\: 1^{st}\: gas)}{n(Total\: number\: of\: moles)}= Mole\: fraction\: of\: first\: gas \: x_{1}}$

Mole fraction:
It is the ratio of the number of moles of an individual gas to the total number of moles of all gases present in the container.

$\\\mathrm{\frac{P_{1}}{P_{total}}\: =\: x_{1}}\\\\\mathrm{Thus,\: P_{1}\: =\: x_{1} P_{total}}\\\\\mathrm{Similarly P_{2}\: =\: x_{2}P_{total}}\\\\\mathrm{Therefore\: the \: generalised \: equation \: becomes}\\\\\mathrm{P_{i}\: =\: x_{i}P_{Total}}$

Where, P_i = partial pressure of the i^th gas
x_i = mole fraction of the i^th gas
Thus, the partial pressure of a gas in the mixture of gases is the product of its mole fraction and the total pressure of the mixture.

Applications

Jet aeroplane flying at high altitude need pressurization of cabins so as to make partial pressure of oxygen sufficient for breathing, as the air pressure decreases with increase in altitude.
Calculation of the pressure of dry gas collected over water: When the gas is collected over water it is moist because of the water vapours. Saturated water vapour exerts its own partial pressure called aqueous tension. So, in order to calculate the partial pressure of dry gas, aqueous tension is subtracted from the pressure of moist gas (P_moist _gas or P_Total)
P_{dry gas} = P_total - Aqueous tension