Sodium hydroxide (NaOH) has a lattice energy of -887 kJ/mol and a heat of hydration of -932 kJ/mol. How much solution could be heated to boiling by the heat evolved by the dissolution of 25.0 g of NaOH? (For the solution, assume a heat capacity of 4.0 J/g·°C, an initial temperature of 25.0 °C, a boiling point of 100.0 °C, and a density of 1.05 g/mL.)

Verified step by step guidance

1. Step 1: Calculate the number of moles of NaOH in 25.0 g. The molar mass of NaOH is approximately 40.0 g/mol. Use the formula: number of moles = mass (g) / molar mass (g/mol).
2. Step 2: Calculate the total heat evolved during the dissolution of NaOH. The heat evolved is the sum of the lattice energy and the heat of hydration. Remember that the lattice energy is given as a negative value, so when you add it, you're actually subtracting it.
3. Step 3: Convert the heat evolved from kJ to J by multiplying by 1000, because 1 kJ = 1000 J.
4. Step 4: Calculate the amount of heat required to heat the solution to boiling. Use the formula: q = mcΔT, where m is the mass of the solution, c is the specific heat capacity, and ΔT is the change in temperature (final temperature - initial temperature).
5. Step 5: Calculate the volume of the solution that can be heated to boiling by the heat evolved. Use the formula: volume = heat required / (density * heat capacity * ΔT). Remember to convert the volume from mL to L by dividing by 1000, because 1 L = 1000 mL.

Key Concepts

Lattice Energy

Lattice energy is the amount of energy released when one mole of an ionic compound forms from its gaseous ions. It is a measure of the strength of the forces between the ions in an ionic solid. In the case of sodium hydroxide (NaOH), the lattice energy of -887 kJ/mol indicates that a significant amount of energy is released when NaOH is formed from its constituent ions, which is crucial for understanding its dissolution process.

Heat of Hydration

The heat of hydration refers to the energy change that occurs when ions are surrounded by water molecules during the dissolution process. For NaOH, the heat of hydration is -932 kJ/mol, meaning that when NaOH dissolves in water, it releases energy, which contributes to the overall temperature change of the solution. This concept is essential for calculating how much water can be heated by the dissolution of a specific mass of NaOH.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. In this problem, the specific heat capacity of the solution is given as 4.0 J/g°C. This value is critical for determining how much energy is needed to raise the temperature of the water to its boiling point, allowing us to calculate the volume of water that can be heated by the energy released from dissolving NaOH.