Problem 106 - Chemistry Matter and Change

Question

Which solute has the greatest effect on the boiling point of \(1.00 \mathrm{~kg}\) of water: \(50.0 \mathrm{~g}\) of strontium chloride \(\left(\mathrm{Sr} \mathrm{Cl}_{2}\right)\) or \(150.0 \mathrm{~g}\) of carbon tetrachloride \(\left(\mathrm{CCl}_{4}\right)\) ? Justify your answer.

Step-by-Step Solution

Answer

\( \text{CCl}_4 \) has a slightly greater effect on boiling point elevation than \( \text{SrCl}_2 \).

Step 1: Calculate Molality of Each Solution

First, convert the mass of each substance into moles. The molar mass of \( \text{SrCl}_2 \) is approximately \( 158.53 \text{ g/mol} \) and the molar mass of \( \text{CCl}_4 \) is approximately \( 153.82 \text{ g/mol} \). For \( \text{SrCl}_2 \):\[ \text{Moles of SrCl}_2 = \frac{50.0 \text{ g}}{158.53 \text{ g/mol}} \approx 0.315 \text{ moles} \]For \( \text{CCl}_4 \):\[ \text{Moles of CCl}_4 = \frac{150.0 \text{ g}}{153.82 \text{ g/mol}} \approx 0.975 \text{ moles} \]Now, determine the molality since we're dissolving the substances into \( 1 \text{ kg} \) of water:\[ \text{Molality of SrCl}_2 = \frac{0.315}{1} \text{ mol/kg} = 0.315 \text{ m}\]\[ \text{Molality of CCl}_4 = \frac{0.975}{1} \text{ mol/kg} = 0.975 \text{ m}\]

Step 2: Determine Van't Hoff Factor

The Van't Hoff factor \( i \) for \( \text{SrCl}_2 \) is 3 because it dissociates into three ions: one \( \text{Sr}^{2+} \) and two \( \text{Cl}^- \) ions. For \( \text{CCl}_4 \), it does not dissociate in solution, so \( i = 1 \).

Step 3: Calculate Boiling Point Elevation for Each Solute

The boiling point elevation \( \Delta T_b \) can be calculated using the formula:\[ \Delta T_b = i \cdot m \cdot K_b \]Where \( K_b \), the ebullioscopic constant for water, is approximately \( 0.512 \text{ °C/m} \).For \( \text{SrCl}_2 \):\[ \Delta T_b = 3 \cdot 0.315 \cdot 0.512 = 0.48456 \text{ °C} \]For \( \text{CCl}_4 \):\[ \Delta T_b = 1 \cdot 0.975 \cdot 0.512 = 0.4992 \text{ °C} \]

Step 4: Compare the Boiling Point Elevations

Both calculated boiling point elevations are very close, but \( \Delta T_b \) for \( \text{CCl}_4 \) is slightly greater than that for \( \text{SrCl}_2\). Therefore, based on calculated values, \( \text{CCl}_4 \) has a greater effect on the boiling point elevation.

Key Concepts

Molality

Molality is a way of expressing the concentration of a solute in a solution. It measures the number of moles of solute per kilogram of solvent. This method is often preferred in boiling point elevation calculations because it does not change with temperature, unlike molarity.
To compute molality:

• Determine the moles of solute by dividing the mass of the solute by its molar mass.
• Divide the moles of solute by the mass of the solvent in kilograms to find molality.

For example, if you dissolve 0.315 moles of strontium chloride in 1 kg of water, the molality will be 0.315 m. Likewise, dissolving 0.975 moles of carbon tetrachloride in 1 kg of water results in a molality of 0.975 m.

Van't Hoff Factor

The Van't Hoff factor ( \( i \) ) is essential in determining the effect of solutes on boiling point elevation and other colligative properties. The factor indicates the number of particles a compound splits into or dissociates in a solution. Some substances like ionic compounds (e.g., \( ext{SrCl}_2 \) ) dissociate in water.
To calculate the Van't Hoff factor:

• Count the total ions produced from the dissociation of a compound. For \( ext{SrCl}_2 \), the dissociation results in one \( ext{Sr}^{2+} \) and two \( ext{Cl}^- \) ions, so \( i = 3 \).
• For non-electrolytes like \( ext{CCl}_4 \), which do not dissociate, \( i = 1 \).

Understanding the Van't Hoff factor helps predict how a solute will affect physical properties like boiling point.

Ebullioscopic Constant

The ebullioscopic constant ( \( K_b \) ) is a property of the solvent that is used to calculate boiling point elevation. It represents how much the boiling point of a solvent is raised per molal concentration of a solute. For water, \( K_b \) is approximately 0.512 °C/m.
Boiling point elevation ( \( T_b \) ) can be calculated using the formula: \[ T_b = i  m  K_b \]To perform the calculation:

• Utilize the Van't Hoff factor and the molality of the solution.
• Multiply them together along with \( K_b \) .

For instance, in the exercise, \( ext{SrCl}_2 \) with \( i = 3 \) and molality of 0.315 m leads to a boiling point elevation of 0.48456 °C, while \( ext{CCl}_4 \) with \( i = 1 \) and molality of 0.975 m results in a slightly greater 0.4992 °C elevation.