 # Dalton's Law of Partial Pressure

## What is Dalton’s Law of Partial Pressure?

Dalton’s law of partial pressure was observed by John Dalton in 1801. This law is related to ideal gas laws. It states that the sum of the partial pressures of individual gases is equal to the total pressure exerted by the mixture of non-reactive gases. Partial pressure can be understood as the pressure exerted by the individual gas of the mixture of gases. Mathematically, we can express Dalton’s law of partial pressure as:

Ptotal = p1 + p2 + p3 + p4 + … (at constant T, V)

Where ptotal = total pressure exerted by the mixture of gases.

p1, p2, p3 are the partial pressures of the gases.

Generally, gases are collected over water and therefore, are moist in nature. Hence, while calculating the pressure of a dry gas, we reduce the vapour pressure of water from the total pressure of the moist gas. The pressure exerted by the saturated water vapour is referred to as the aqueous tension. Aqueous tensions are different at different temperatures. The table given below shows the aqueous tension for different temperatures: ### Partial pressure in terms of mole fraction

Let us take three gases enclosed in volume V, at a temperature T, exerting partial pressure as p1, p2, and p3 respectively.  Then,

According to the ideal gas equation,

p1 = n1RT/V                       …… (i)

p2 = n2RT/V                       …… (ii)

p3 = n3RT/V                       …… (iii)

where n1, n2, and n3 are the numbers of moles of the three gases respectively.

Expression for the total pressure exerted will be

P total = p1 + p2 + p3

= n1(RT)/V + n2(RT)/V + n3(RT)/V

= (n1 + n2 + n3) (RT)/V

Dividing p1 by ptotal, we get

p1/ptotal  = (n1/(n1+n2+n3)) RTV/RTV

= (n1 / (n1+n2+n3)) = n1/n = x1

Where, x1 is the mole fraction of the gas.

n = n1 + n2 + n3

This implies that, p1 = x1 ptotal

p2 = x2 ptotal

p3 = x3 ptotal

Generalizing the above equations we can write,

pi = xi ptotal    ……………………………  (iv)

Where pi and xi are partial pressures and mole fractions for the i-th gas respectively.

From equation (iv), we can find the pressure exerted by individual gases.

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