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 (CCl \(_{4} ) ?\) Justify your answer.

Short answer

The solute that has the greatest effect on the boiling point of 1.00 kg of water is 150.0 g of carbon tetrachloride. This is because the molality (moles of solute per kilogram of solvent) of carbon tetrachloride is greater than that of strontium chloride. Specifically, the molality of strontium chloride is approximately 0.315 mol/kg, whereas the molality of carbon tetrachloride is roughly 0.975 mol/kg, which is higher. Therefore, the higher the molality of a solute, the greater its effect on the boiling point of a solvent, according to the boiling point elevation property.

Step-by-step solution

Calculate moles of strontium chloride

To find the moles of strontium chloride (\(\mathrm{SrCl}_{2}\)), we need to divide its mass by its molar mass. The molar mass of strontium chloride is the sum of the molar masses of strontium (87.62 g/mol), and two chloride atoms (2 × 35.45 g/mol): Molar mass of \(\mathrm{SrCl}_{2} = 87.62 + 2 × 35.45 = 158.52\,\mathrm{g/mol}\) Now divide 50.0 g of strontium chloride by its molar mass: Moles of \(\mathrm{SrCl}_{2} = \cfrac{50.0\,\mathrm{g}}{158.52\,\mathrm{g/mol}} \approx 0.315\,\mathrm{mol}\)

Calculate moles of carbon tetrachloride

To find the moles of carbon tetrachloride (\(\mathrm{CCl}_{4}\)), we need to divide its mass by its molar mass. The molar mass of carbon tetrachloride is the sum of the molar mass of carbon (12.01 g/mol) and four chloride atoms (4 × 35.45 g/mol): Molar mass of \(\mathrm{CCl}_{4} = 12.01 + 4 × 35.45 = 153.81\,\mathrm{g/mol}\) Now divide 150.0 g of carbon tetrachloride by its molar mass: Moles of \(\mathrm{CCl}_{4} = \cfrac{150.0\,\mathrm{g}}{153.81\,\mathrm{g/mol}} \approx 0.975\,\mathrm{mol}\)

Calculate molality of strontium chloride solution

Molality (m) is calculated by dividing the moles of solute by the mass of the solvent in kilograms: Molality of \(\mathrm{SrCl}_{2}\) = \(\cfrac{\mathrm{moles\, of\, SrCl}_{2}}{\mathrm{mass\, of\, solvent\, in\, kg}}= \cfrac{0.315\,\mathrm{mol}}{1.00\,\mathrm{kg}} = 0.315\,\mathrm{mol/kg}\)

Calculate molality of carbon tetrachloride solution

Molality (m) is calculated by dividing the moles of solute by the mass of the solvent in kilograms: Molality of \(\mathrm{CCl}_{4}\) = \(\cfrac{\mathrm{moles\, of\, CCl}_{4}}{\mathrm{mass\, of\, solvent\, in\, kg}}= \cfrac{0.975\,\mathrm{mol}}{1.00\,\mathrm{kg}} = 0.975\,\mathrm{mol/kg}\)

Comparison of molalities and conclusion

Now compare the molalities of the two solutions: Molality of \(\mathrm{SrCl}_{2} = 0.315\,\mathrm{mol/kg}\) Molality of \(\mathrm{CCl}_{4} = 0.975\,\mathrm{mol/kg}\) Since the molality of carbon tetrachloride (\(\mathrm{CCl}_{4}\)) is greater than the molality of strontium chloride (\(\mathrm{SrCl}_{2}\)), 150.0 g of carbon tetrachloride has a greater effect on the boiling point of 1.00 kg of water than 50.0 g of strontium chloride.

Key concepts

Boiling Point Elevation

Boiling point elevation is a colligative property, meaning it depends on the number of solute particles in a solvent, not the type of particles.
This phenomenon occurs because the solute particles disrupt the interactions between the solvent molecules. As a result, more energy (in the form of heat) is required to transition the solvent from a liquid state to a gaseous state.
The formula for calculating boiling point elevation is \[ \Delta T_b = i \cdot K_b \cdot m \] where:

• \( \Delta T_b \) = the change in boiling point
• \( i \) = the van 't Hoff factor (number of particles the solute splits into)
• \( K_b \) = ebullioscopic constant (unique to each solvent)
• \( m \) = molality of the solution

A higher molality means more solute particles in the solvent, leading to a greater boiling point elevation. In our exercise, the solution with the higher molality will have a larger effect on the boiling point.

Molar Mass Calculation

Molar mass calculation is essential for converting between mass and moles of a substance.
To find the molar mass of a compound, you sum the atomic masses of its constituent elements, which can be found on the periodic table.
The calculation involves identifying the type and number of atoms in the molecular formula.

For example:

• The molar mass of strontium chloride (\( \text{SrCl}_2 \)) is calculated by adding:
  • The atomic mass of strontium (\( \text{87.62 g/mol} \))
  • Two chlorine atoms (2 \( \times \) 35.45 g/mol = 70.90 g/mol)
  Resulting in a total molar mass of \( \text{158.52 g/mol} \).
• Similarly, for carbon tetrachloride (\( \text{CCl}_4 \)), add:
  • The atomic mass of carbon (\( \text{12.01 g/mol} \))
  • Four chlorine atoms (4 \( \times \) 35.45 g/mol = 141.80 g/mol)
  Arriving at a molar mass of \( \text{153.81 g/mol} \).

Understanding how to accurately calculate molar mass is fundamental in determining the number of moles a given mass of compound represents.

Molality

Molality is a concentration unit used in colligative properties, such as boiling point elevation.
It is defined as the ratio of the number of moles of solute to the mass of solvent in kilograms: \[ m = \cfrac{\text{moles of solute}}{\text{kg of solvent}} \] This unit is favored as it does not change with temperature, unlike molarity, which depends on the volume of the solution that can expand or contract with temperature variations.

To calculate molality:

• First, determine the number of moles of your solute.
• Then, divide that by the mass of the solvent in kilograms.

For instance, in the exercise:- Strontium chloride's molality is \( 0.315 \text{ mol/kg} \), as derived from \( 0.315 \text{ mol} \) over \( 1.00 \text{ kg} \) of solvent.- Carbon tetrachloride's molality is higher, calculated as \( 0.975 \text{ mol/kg} \). The difference in molality between the solutions directly influences their respective boiling point elevations.

Solute and Solvent Interactions

Understanding solute and solvent interactions is crucial in predicting colligative properties.
These interactions refer to how solute particles interact with solvent molecules, affecting the solution's physical properties.
When a solute dissolves, it disrupts the orderly arrangement of solvent molecules, affecting processes like boiling or freezing.
Two key interactions to consider are:

• Dissociation: Some compounds, like electrolytes (e.g., strontium chloride), dissociate into multiple ions in solution, which increases the effective number of solute particles.
• Non-Electrolytic Solutions: Non-electrolytes like carbon tetrachloride do not dissociate in solution, meaning they contribute fewer particles compared to ionic compounds.

In the boiling point elevation context, more particles from a dissociating solute generally mean a larger effect on boiling point, dictated by the van 't Hoff factor \( i \). Strontium chloride, with its dissociation into ions, typically has a van 't Hoff factor greater than one, impacting the boiling point elevation to a greater extent compared to a non-dissociative solute like carbon tetrachloride.