Q. how to calculate molality

Molality is a concentration unit defined as the number of moles of solute per kilogram of solvent. The symbol commonly used for molality is \(m\). The defining formula is

\[
m \;=\; \frac{n_{\text{solute}}}{m_{\text{solvent}}\;(\text{kg})}
\]

To calculate molality follow these steps exactly.

Step 1. Calculate the number of moles of solute. If you are given the mass of solute in grams, convert that mass to moles using the solute molar mass. Use the formula

\[
n_{\text{solute}} \;=\; \frac{w_{\text{solute}}\;(\text{g})}{M_{\text{solute}}\;(\text{g/mol})}
\]

Explanation. Here \(w_{\text{solute}}\) is the mass of solute in grams. Divide by the molar mass \(M_{\text{solute}}\) in grams per mole to obtain moles.

Step 2. Express the mass of the solvent in kilograms. If the solvent mass is given in grams, convert to kilograms by dividing by 1000:

\[
m_{\text{solvent}}\;(\text{kg}) \;=\; \frac{w_{\text{solvent}}\;(\text{g})}{1000\ \mathrm{g/kg}}
\]

Step 3. Divide the moles of solute by the kilograms of solvent to obtain molality:

\[
m \;=\; \frac{n_{\text{solute}}}{m_{\text{solvent}}\;(\text{kg})}
\]

Units. The units of molality are moles per kilogram, usually written as \(\mathrm{mol/kg}\) or simply as \(m\) (for example, 1.00 m).

Worked example. Calculate the molality of a solution made by dissolving 30.0 g of NaCl in 500.0 g of water.

Step A. Find the molar mass of NaCl:

\[
M_{\mathrm{NaCl}} \;=\; 22.99\ (\mathrm{Na}) \;+\; 35.45\ (\mathrm{Cl}) \;=\; 58.44\ \mathrm{g/mol}
\]

Step B. Convert the mass of NaCl to moles:

\[
n_{\mathrm{NaCl}} \;=\; \frac{30.0\ \mathrm{g}}{58.44\ \mathrm{g/mol}} \;=\; 0.513\ \mathrm{mol}
\]

Step C. Convert the mass of water to kilograms:

\[
m_{\text{solvent}} \;=\; \frac{500.0\ \mathrm{g}}{1000\ \mathrm{g/kg}} \;=\; 0.5000\ \mathrm{kg}
\]

Step D. Compute the molality:

\[
m \;=\; \frac{0.513\ \mathrm{mol}}{0.5000\ \mathrm{kg}} \;=\; 1.026\ \mathrm{mol/kg} \;=\; 1.03\ \mathrm{m}
\]

Summary. The procedure is: (1) convert solute mass to moles, (2) convert solvent mass to kilograms, (3) divide moles of solute by kilograms of solvent. The result is molality in \(\mathrm{mol/kg}\) (often written as \(m\)).