Dalton’s Law of Partial Pressures

Dalton’s Law of Partial Pressures: 

The ideal gas law is:

$PV = \mu RT$

(P) = Pressure  

(V) = Volume  

(mu) = Number of moles of gas  

(R) = Universal gas constant  

(T) = Temperature  

Mixture of Gases : 

Suppose we have a mixture of gases: Gas 1, Gas 2, Gas 3, … each with mole numbers ($\mu_1, \mu_2, \mu_3, \dots$).

For the whole mixture:

$PV = (\mu1 + \mu2 + \mu_3 + \dots) RT \quad (1)$

Breaking It Down

Divide both sides by (V):

$P = \frac{\mu1 RT}{V} + \frac{\mu2 RT}{V} + \frac{\mu_3 RT}{V} + \dots \quad (2)$

Now, each term represents the pressure contribution of one gas.  

So we define:

$P_1 = \frac{\mu1 RT}{V}, \quad P2 = \frac{\mu2 RT}{V}, \quad \dots$

These are called partial pressures.

Dalton’s Law of Partial Pressures

Thus, the total pressure of the mixture is simply the sum of all partial pressures:

$P = P1 + P2 + P_3 + \dots \quad (3)$

Intuition : 

- Each gas in a mixture behaves independently, as if the others weren’t there.  

- The total pressure is just the sum of pressures each gas would exert if it occupied the container alone.  

- This principle is widely used in chemistry, physics, and even medicine (e.g., calculating oxygen pressure in air mixtures).