Mole Fraction
Mole Fraction
Mole fraction is a way of expressing the concentration of a component in a mixture. It is a dimensionless quantity that represents the ratio of the number of moles of a particular substance to the total number of moles of all substances present in the mixture.
Definition
The mole fraction, denoted by the Greek letter chi (χ), of a component is defined as the number of moles of that component divided by the total number of moles of all components in the mixture.
Mathematically, the mole fraction of component A in a mixture can be expressed as:
$$ \chi_A = \frac{n_A}{n_{total}} $$
where:
- $\chi_A$ is the mole fraction of component A,
- $n_A$ is the number of moles of component A,
- $n_{total}$ is the total number of moles of all components in the mixture.
Properties of Mole Fraction
- It is a dimensionless quantity.
- The sum of the mole fractions of all components in a mixture is equal to 1.
$$ \sum_{i=1}^{n} \chi_i = 1 $$
where $n$ is the number of components in the mixture.
- Mole fraction does not change with temperature or pressure, as it is a ratio of moles and moles do not depend on temperature or pressure.
Differences and Important Points
Here is a table that summarizes the key differences and important points about mole fraction:
| Property | Description |
|---|---|
| Symbol | Represented by the Greek letter chi (χ). |
| Dimension | It is a dimensionless quantity. |
| Dependence | Independent of temperature and pressure. |
| Range | Ranges from 0 to 1 for each component. |
| Sum | The sum of mole fractions of all components equals 1. |
| Usage | Used in Raoult's law and Dalton's law of partial pressures. |
Formulas Involving Mole Fraction
Mole fraction is used in various chemical laws and equations, such as:
- Raoult's Law: For an ideal solution, the partial vapor pressure of each component is directly proportional to its mole fraction.
$$ P_A = \chi_A \cdot P_A^* $$
where:
- $P_A$ is the partial vapor pressure of component A,
- $\chi_A$ is the mole fraction of component A in the liquid phase,
$P_A^*$ is the vapor pressure of pure component A.
Dalton's Law of Partial Pressures: The total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases, each of which is proportional to its mole fraction.
$$ P_{total} = \sum_{i=1}^{n} P_i = \sum_{i=1}^{n} \chi_i \cdot P_{total} $$
where:
- $P_{total}$ is the total pressure of the mixture,
- $P_i$ is the partial pressure of component i,
- $\chi_i$ is the mole fraction of component i.
Examples
Example 1: Calculating Mole Fraction
Suppose we have a mixture of 2 moles of ethanol (C2H5OH) and 3 moles of water (H2O). What is the mole fraction of ethanol?
Using the formula for mole fraction:
$$ \chi_{ethanol} = \frac{n_{ethanol}}{n_{total}} = \frac{2}{2 + 3} = \frac{2}{5} $$
The mole fraction of ethanol is 0.4.
Example 2: Using Mole Fraction in Raoult's Law
If the vapor pressure of pure ethanol is 100 mmHg, what is the partial vapor pressure of ethanol in the mixture from Example 1?
Using Raoult's Law:
$$ P_{ethanol} = \chi_{ethanol} \cdot P_{ethanol}^* = 0.4 \cdot 100 \text{ mmHg} = 40 \text{ mmHg} $$
The partial vapor pressure of ethanol in the mixture is 40 mmHg.
Understanding mole fraction is crucial for solving problems in chemistry related to solutions, gas mixtures, and thermodynamics. It is a fundamental concept that is widely used in both theoretical and practical applications.