Question

In a coffee-cup calorimeter, \(1.60 \mathrm{~g} \mathrm{NH}_{4} \mathrm{NO}_{3}\) is mixed with \(75.0 \mathrm{~g}\) water at an initial temperature of \(25.00^{\circ} \mathrm{C}\). After dissolution of the salt, the final temperature of the calorimeter contents is \(23.34^{\circ} \mathrm{C}\). Assuming the solution has a heat capacity of \(4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\) and assuming no heat loss to the calorimeter, calculate the enthalpy change for the dissolution of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) in units of \(\mathrm{kJ} / \mathrm{mol}\).

Short answer

The enthalpy change for the dissolution of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) is -26.16 kJ/mol.

Step-by-step solution

Calculate the total heat change in the calorimeter (q)

First, we need to determine the change in temperature (∆T) of the solution, which is the final temperature (Tf) minus the initial temperature (Ti). ∆T = Tf - Ti = 23.34°C - 25.00°C = -1.66°C Next, we will use the formula q = mc∆T to calculate the total heat change (q). The mass (m) of the solution is the sum of the masses of NH4NO3 (1.60 g) and water (75.0 g), and the heat capacity (c) of the solution is given as 4.18 J/°C·g. m = 1.60 g + 75.0 g = 76.6 g q = mc∆T = (76.6 g) × (4.18 J/°C·g) × (-1.66°C) = -523.2 J

Convert grams of NH4NO3 to moles

To convert grams of NH4NO3 to moles, we must first calculate the molar mass of NH4NO3. Molar mass of NH4NO3 = 14 (N) + 4 (H) + 14 (N) + 16 (O) × 3 = 80 g/mol Now we can calculate the number of moles (n) of NH4NO3 by dividing the mass (1.60 g) by the molar mass (80 g/mol). n = 1.60 g / 80 g/mol = 0.0200 mol

Calculate the enthalpy change (ΔH) per mole

We can now calculate the enthalpy change (ΔH) per mole of NH4NO3 by dividing the total heat change (q) by the number of moles (n) of NH4NO3. ΔH = q / n = -523.2 J / 0.0200 mol = -26160 J/mol

Convert ΔH to kJ/mol

Finally, we will convert the enthalpy change (ΔH) to kJ/mol by dividing by 1000. ΔH = -26160 J/mol / 1000 = -26.16 kJ/mol So, the enthalpy change for the dissolution of NH4NO3 is -26.16 kJ/mol.