Law of Partial Pressures
Law of Partial Pressures
The Law of Partial Pressures, also known as Dalton's Law, is a principle in chemistry that describes the behavior of gas mixtures. It states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases in the mixture.
Understanding Partial Pressure
Before diving into Dalton's Law, it's important to understand what partial pressure means. The partial pressure of a gas is the pressure that the gas would exert if it alone occupied the entire volume of the mixture at the same temperature.
Dalton's Law of Partial Pressures
Mathematically, Dalton's Law can be expressed as:
$$ P_{total} = P_1 + P_2 + P_3 + \ldots + P_n $$
Where:
- ( P_{total} ) is the total pressure of the gas mixture.
- ( P_1, P_2, P_3, \ldots, P_n ) are the partial pressures of the individual gases in the mixture.
Important Points
- Dalton's Law applies to ideal gases, which are gases that follow the ideal gas law without any deviations.
- The partial pressure of a gas is directly proportional to its mole fraction in the gas mixture.
- The mole fraction is the ratio of the number of moles of a particular gas to the total number of moles of all gases in the mixture.
The partial pressure of a gas can also be calculated using its mole fraction (( X_i )) and the total pressure:
$$ P_i = X_i \cdot P_{total} $$
Where:
- ( P_i ) is the partial pressure of gas ( i ).
- ( X_i ) is the mole fraction of gas ( i ).
- ( P_{total} ) is the total pressure of the gas mixture.
Table of Differences and Important Points
| Feature | Description |
|---|---|
| Definition | The pressure exerted by a single gas in a mixture of gases. |
| Calculation | ( P_i = X_i \cdot P_{total} ) |
| Dependency | Directly proportional to the mole fraction of the gas in the mixture. |
| Applicability | Applies to ideal gases and non-reacting gas mixtures. |
Examples
Example 1: Calculating Partial Pressure
A container holds a mixture of oxygen and nitrogen at a total pressure of 1 atm. If the mole fraction of oxygen is 0.21 and nitrogen is 0.79, calculate the partial pressures of oxygen and nitrogen.
Solution:
For oxygen: $$ P_{O_2} = X_{O_2} \cdot P_{total} = 0.21 \times 1 \text{ atm} = 0.21 \text{ atm} $$
For nitrogen: $$ P_{N_2} = X_{N_2} \cdot P_{total} = 0.79 \times 1 \text{ atm} = 0.79 \text{ atm} $$
Example 2: Using Dalton's Law in a Reaction
Hydrogen and iodine react to form hydrogen iodide in a closed container:
$$ H_2(g) + I_2(g) \rightarrow 2HI(g) $$
If the partial pressures of ( H_2 ) and ( I_2 ) are 0.3 atm and 0.2 atm, respectively, and no other gases are present, what is the total pressure in the container before the reaction starts?
Solution:
Using Dalton's Law: $$ P_{total} = P_{H_2} + P_{I_2} = 0.3 \text{ atm} + 0.2 \text{ atm} = 0.5 \text{ atm} $$
The total pressure before the reaction is 0.5 atm.
Conclusion
The Law of Partial Pressures is a fundamental concept in the study of gas mixtures. It is essential for understanding how gases behave when mixed together and is widely used in various applications, including chemical reactions, gas collection experiments, and respiratory physiology. By understanding Dalton's Law and how to calculate partial pressures, students can solve a wide range of problems related to gas mixtures and their behaviors.