Question

The freezing point depression constants of the solvents cyclohexane and naphthalene are \(20.1^{\circ} \mathrm{C} / \mathrm{m}\) and \(6.94^{\circ} \mathrm{C} / \mathrm{m},\) respectively. Which solvent will give a more accurate result if you are using freezing point depression to determine the molar mass of a substance that is soluble in either one? Why?

Short answer

Cyclohexane will give a more accurate result because it has a higher freezing point depression constant.

Step-by-step solution

- Understand Freezing Point Depression

Freezing point depression refers to the lowering of the freezing point of a solvent when a solute is dissolved in it. The extent of the freezing point depression is given by the formula: \[\triangle T_f = K_f \times m \] where \(\triangle T_f\) is the freezing point depression, \(K_f\) is the freezing point depression constant, and \(m\) is the molality of the solution.

- Compare Freezing Point Depression Constants

Given \(K_f\) for cyclohexane = 20.1°C/m, and \(K_f\) for naphthalene = 6.94°C/m. Larger \(K_f\) means a larger change in temperature per unit molality for a given amount of solute, making the changes easier to measure accurately.

- Evaluate Measurement Sensitivity

Since cyclohexane has a larger \(K_f\), the same molality will result in a larger freezing point depression. This larger change is easier to measure accurately, reducing experimental error.

- Conclusion

Cyclohexane, with a higher freezing point depression constant, will give a more accurate result in determining the molar mass of a dissolved substance because the resulting temperature change is more pronounced and easier to measure accurately.

Key concepts

Freezing Point Depression Constant

Freezing point depression is when the freezing point of a solvent lowers after a solute is added. The extent of this depression depends on several factors. One of the most critical ones is the freezing point depression constant, denoted as \( K_f \). \( K_f \) indicates how much the freezing point of the solvent will drop per molal concentration of solute. A higher \( K_f \) means a more significant change in temperature per molal unit, making measurements more noticeable. In our example, cyclohexane has a \( K_f \) of 20.1°C/m, and naphthalene has \( K_f \) of 6.94°C/m. This means cyclohexane will show a greater temperature drop for the same amount of solute dissolved compared to naphthalene.

Molality

Molality is different from molarity. It measures the concentration of a solute in a solution based on the mass of the solvent, not the volume of the solution. Molality is defined as the number of moles of solute per kilogram of solvent and is denoted as 'm'. When using the formula for freezing point depression, \[ \triangle T_f = K_f \times m \], 'm' represents molality. This value helps in determining how much the freezing point has dropped. Since molality is mass-based, it is not affected by temperature changes, making it a reliable concentration measure, especially for experiments involving temperature variations like freezing point depression.
\[ m = \frac{n_{\text{solute}}}{kg_{\text{solvent}}} \] where \( n_{\text{solute}} \) is the moles of solute and \( kg_{\text{solvent}} \) is the mass of the solvent in kilograms.

Experimental Accuracy

Accuracy in experiments is all about how close the measured value is to the true value. When measuring freezing point depression, higher accuracy is often achieved with a solvent having a larger freezing point depression constant. This leads to a larger temperature change for the same solute amount, making it easier to detect and measure. For example, with cyclohexane having a \( K_f \) of 20.1°C/m, the temperature drop will be more significant compared to naphthalene's \( K_f \) of 6.94°C/m. This larger change reduces possible errors in measurement, ensuring the results are more accurate. It makes cyclohexane a better solvent for determining molar mass when using freezing point depression.