Molality, Composition, and Crystallization

Definition of Molality and its Difference from Molarity

Molality is defined as the number of moles of solute per kilogram of solvent. It is a measure of the concentration of a solute in a solution. Molality is different from molarity in that molality is defined based on the mass of the solvent, whereas molarity is defined based on the volume of the solution. The unit used to measure molality is $\frac{mol}{kg}$, which is often abbreviated as 'm'.

The equation for molality is:
$\text{Molality (m)} = \frac{\text{Moles of solute}}{\text{Kilograms of solvent}}$

Example Problem

Problem: What is the molality of a solution made by dissolving 14.7 g of $H<em>2SO</em>4$ in 125 g of water?

1. Convert grams of solute to moles:
   • The molar mass of $H<em>2SO</em>4$ is approximately 98.08 g/mol.
     $\text{Moles of } H<em>2SO</em>4 = \frac{14.7 \text{ g}}{98.08 \text{ g/mol}} = 0.15 \text{ mol}$
2. Convert grams of solvent to kilograms:
   $\text{Kilograms of water} = \frac{125 \text{ g}}{1000 \text{ g/kg}} = 0.125 \text{ kg}$
3. Calculate molality:
   $\text{Molality} = \frac{0.15 \text{ mol}}{0.125 \text{ kg}} = 1.2 \text{ m}$

Percent Composition

Percent composition refers to the percentage by mass of each element in a compound. To find the percent composition of different compounds:

1. Determine the molar mass of each element in the compound.
2. Calculate the total molar mass of the compound.
3. Divide the molar mass of each element by the total molar mass of the compound, and then multiply by 100% to get the percent composition of that element.

For example, consider a compound with the formula $A<em>xB</em>y$. The percent composition of element A is given by:
$\% \text{ of A} = \frac{x \times \text{molar mass of A}}{\text{molar mass of } A<em>xB</em>y} \times 100$
Similarly, the percent composition of element B is:
$\% \text{ of B} = \frac{y \times \text{molar mass of B}}{\text{molar mass of } A<em>xB</em>y} \times 100$

Practice Problem

Problem: Determine the percent composition of each element in $Fe<em>2O</em>3$ (Iron(III) oxide).

1. Determine the molar mass of each element:
   • Iron (Fe): 55.845 g/mol
   • Oxygen (O): 16.00 g/mol
2. Calculate the total molar mass of $Fe<em>2O</em>3$:
   $\text{Molar mass of } Fe<em>2O</em>3 = (2 \times 55.845) + (3 \times 16.00) = 111.69 + 48.00 = 159.69 \text{ g/mol}$
3. Calculate the percent composition of each element:
   • Percent Iron (Fe):
     $\% \text{ of Fe} = \frac{2 \times 55.845}{159.69} \times 100 = \frac{111.69}{159.69} \times 100 = 69.95 \%$
   • Percent Oxygen (O):
     $\% \text{ of O} = \frac{3 \times 16.00}{159.69} \times 100 = \frac{48.00}{159.69} \times 100 = 30.05 \%$

Thus, the percent composition of $Fe<em>2O</em>3$ is 69.95% Iron and 30.05% Oxygen.

Crystallization

Crystallization is a process by which