Dalton's Law of Partial Pressures
Understanding Gas Mixtures, Mole Fractions, and Aqueous Tension.
In the real world, we rarely deal with single, pure gases. The air we breathe is a mixture of Nitrogen, Oxygen, Argon, and Carbon Dioxide. How do we determine the total pressure of a mixture? In 1801, John Dalton formulated a simple yet powerful law to answer this.
1. Statement of Dalton's Law
Dalton's Law states: The total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases present in the mixture.
The partial pressure of a gas is the pressure that the gas would exert if it occupied the entire volume of the mixture all by itself, at the same temperature.
2. Partial Pressure & Mole Fraction ($\chi$)
How do we calculate the partial pressure of just one gas in a mixture? We use its Mole Fraction ($\chi$). The mole fraction is simply the ratio of the moles of that specific gas to the total moles of all gases in the container.
According to the Ideal Gas Equation, pressure is directly proportional to the number of moles ($P \propto n$). Therefore, a gas's partial pressure is equal to its mole fraction multiplied by the total pressure.
Example:
A container holds 1 mole of $He$ and 3 moles of $Ne$ at a total pressure of $4 \text{ atm}$. Find the partial pressure of $He$.
- Total Moles ($n_{total}$) = $1 + 3 = 4$.
- Mole fraction of $He$ ($\chi_{He}$) = $\frac{1}{4} = 0.25$.
- Partial Pressure of $He$ ($p_{He}$) = $0.25 \times 4 \text{ atm} = \mathbf{1 \text{ atm}}$.
3. Application: Collection of Gas Over Water
In laboratory experiments, gases (like $O_2$ or $H_2$) are often collected by displacing water in an inverted tube. However, this method introduces an error: the collected gas is not pure. It is mixed with water vapor (steam).
Aqueous Tension
The partial pressure exerted by water vapor mixed with the gas is called Aqueous Tension. It depends solely on the temperature of the water.
To find the pressure of the dry gas, we must use Dalton's Law and subtract the aqueous tension from the total measured pressure:
4. Exceptions: When Dalton's Law Fails
Dalton's Law has one absolute prerequisite: The gases must be non-reacting.
If gases react with each other to form a new compound (especially a solid or liquid), the total number of moles decreases drastically, and the total pressure will drop. Dalton's law becomes completely invalid.
Famous Non-Obeying Mixtures (Highly Tested):
- $NH_3(g) + HCl(g) \rightarrow NH_4Cl(s)$ (Forms a solid white smoke)
- $NO(g) + O_2(g) \rightarrow NO_2(g)$ (Reacts immediately at room temp)
- $CO(g) + Cl_2(g) \rightarrow COCl_2(g)$ (Phosgene gas formation)
- $H_2(g) + F_2(g) \rightarrow 2HF(g)$
Conversely, mixtures like ($He + Ne$), ($N_2 + O_2$), or ($H_2 + N_2$ at room temp) DO obey Dalton's Law because they are inert towards each other under normal conditions.
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