The ΔH for the solution process when solid sodium hydroxide dissolves in water is -44.4 kJ/mol. When a 12.89-g sample of NaOH (MM= 40.0 g/mol) dissolves in 250.00 g of water in a coffee-cup calorimeter, the temperature increases from 24°C to what final temperature?

• A. 30.0°C
• B. 35.2°C
• C. 40.1°C
• D. 28.5°C

Answer: (B)

Verified step by step guidance

1. Calculate the number of moles of NaOH using its mass and molar mass. Use the formula: \( \text{moles of NaOH} = \frac{\text{mass of NaOH}}{\text{molar mass of NaOH}} \). Substitute the given values: mass = 12.89 g and molar mass = 40.0 g/mol.
2. Determine the total heat absorbed or released by the solution using the enthalpy change (ΔH) and the number of moles calculated. Use the formula: \( q = \Delta H \times \text{moles of NaOH} \). Remember that ΔH is given as -44.4 kJ/mol, indicating an exothermic process.
3. Convert the heat from kJ to J, since the specific heat capacity is usually given in J/g°C. Use the conversion: \( 1 \text{ kJ} = 1000 \text{ J} \).
4. Calculate the temperature change (ΔT) using the formula: \( q = m \times c \times \Delta T \), where \( m \) is the mass of the solution (mass of water + mass of NaOH), \( c \) is the specific heat capacity of water (4.18 J/g°C), and \( q \) is the heat calculated in the previous step.
5. Determine the final temperature by adding the temperature change (ΔT) to the initial temperature of the water (24°C).