The formula to calculate the molarity (M) from the mole fraction is:
\[ M = \frac{X \cdot \rho \cdot 1000}{X \cdot M_s + (1 - X) \cdot M_t} \]
Where:
Let's say the mole fraction (\( X \)) is 0.2, the density (\( \rho \)) is 1.2 g/L, the molar mass of the solvent (\( M_s \)) is 18 g/mol, and the molar mass of the solute (\( M_t \)) is 58.5 g/mol. Using the formula:
\[ M = \frac{0.2 \cdot 1.2 \cdot 1000}{0.2 \cdot 18 + (1 - 0.2) \cdot 58.5} \]
We get:
\[ M = \frac{240}{3.6 + 46.8} = \frac{240}{50.4} \approx 4.76 \text{ mol/L} \]
So, the molarity (\( M \)) is approximately 4.76 mol/L.
Suppose the mole fraction (\( X \)) is 0.1, the density (\( \rho \)) is 1.0 g/L, the molar mass of the solvent (\( M_s \)) is 18 g/mol, and the molar mass of the solute (\( M_t \)) is 58.5 g/mol. Using the formula:
\[ M = \frac{0.1 \cdot 1.0 \cdot 1000}{0.1 \cdot 18 + (1 - 0.1) \cdot 58.5} \]
We get:
\[ M = \frac{100}{1.8 + 52.65} = \frac{100}{54.45} \approx 1.84 \text{ mol/L} \]
So, the molarity (\( M \)) is approximately 1.84 mol/L.
Mole fraction is a way of expressing the concentration of a component in a mixture. It is the ratio of the number of moles of a particular component to the total number of moles of all components in the mixture. Mole fraction is a dimensionless quantity and is often used in chemistry to describe the composition of mixtures, especially in solutions and gas mixtures. It is particularly useful because it does not depend on temperature or pressure, unlike other concentration measures such as molarity or molality.
