What is the boiling point of a 0.10 M solution of NaHSO4 if the solution has a density of 1.002 g>mL?

Verified step by step guidance

1. insert step 1> Calculate the molality (m) of the solution using the formula: \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \). First, find the mass of the solution using its density and volume, then determine the mass of the solvent (water) by subtracting the mass of the solute.
2. insert step 2> Determine the van't Hoff factor (i) for NaHSO4. Since NaHSO4 dissociates into Na^+ and HSO4^- ions, the van't Hoff factor is approximately 2.
3. insert step 3> Use the boiling point elevation formula: \( \Delta T_b = i \cdot K_b \cdot m \), where \( \Delta T_b \) is the boiling point elevation, \( K_b \) is the ebullioscopic constant for water (0.512 °C/m), and m is the molality calculated in step 1.
4. insert step 4> Calculate the boiling point elevation (\( \Delta T_b \)) using the values from the previous steps.
5. insert step 5> Add the boiling point elevation (\( \Delta T_b \)) to the normal boiling point of water (100 °C) to find the boiling point of the solution.

Key Concepts

Boiling Point Elevation

Boiling point elevation is a colligative property that describes how the boiling point of a solvent increases when a solute is dissolved in it. The extent of this elevation depends on the number of solute particles in the solution, not their identity. The formula used to calculate the change in boiling point is ΔT_b = i * K_b * m, where 'i' is the van 't Hoff factor, 'K_b' is the ebullioscopic constant of the solvent, and 'm' is the molality of the solution.

Van 't Hoff Factor (i)

The van 't Hoff factor (i) indicates the number of particles into which a solute dissociates in solution. For NaHSO4, which dissociates into Na⁺ and HSO4⁻ ions, the value of 'i' is 2. This factor is crucial for calculating colligative properties, as it directly affects the number of solute particles contributing to boiling point elevation.

Molality vs. Molarity

Molality (m) is a measure of concentration defined as the number of moles of solute per kilogram of solvent, while molarity (M) is defined as the number of moles of solute per liter of solution. In this question, the solution's molarity is given (0.10 M), but to calculate boiling point elevation, molality may be needed, which requires knowing the density of the solution to convert volume to mass.