Question

(a) When a 3.88-g sample of solid ammonium nitrate dissolves in \(60.0 \mathrm{~g}\) of water in a coffee-cup calorimeter (Figure 5.17), the temperature drops from \(23.0^{\circ} \mathrm{C}\) to \(18.4^{\circ} \mathrm{C}\). Calculate \(\Delta H\left(\right.\) in \(\mathrm{kJ} / \mathrm{mol} \mathrm{NH}_{4} \mathrm{NO}_{3}\) ) for the solu- tion process $$ \mathrm{NH}_{4} \mathrm{NO}_{3}(s) \rightarrow \mathrm{NH}_{4}{ }^{+}(a q)+\mathrm{NO}_{3}^{-}(a q) $$ Assume that the specific heat of the solution is the same as that of pure water. (b) Is this process endothermic or exothermic?

Short answer

(a) The enthalpy change for the solvation process is approximately \(-23.738 \mathrm{kJ/mol}\) of NH4NO3. (b) Since the enthalpy change is negative, the process is exothermic, meaning that heat is released upon dissolution of NH4NO3 in water.

Step-by-step solution

Calculate the heat transferred

To find the heat transferred (q) by the solution we can use the formula: \(q = mcΔT \) where \(m = 60.0 g\) (mass of water), \(c = 4.184 J/(g· °C)\) (specific heat capacity of water) and \(\Delta T = T_{final} - T_{initial} = 18.4 °C - 23.0°C = -4.6 °C\)

Compute the heat transferred

Now, we can compute the amount of heat transferred by plugging the values into the formula: \(q = (60.0 g)(4.184 J/(g· °C))(-4.6 °C)\) \(q ≈ -1150.96 \mathrm{J}\)

Calculate moles of NH4NO3

The molar mass of NH4NO3 is (14.01 + 1.01 * 4) + (14.01 + 16.00 * 3) = 80.04 g/mol. Given that a 3.88-g sample of solid ammonium nitrate is used, we can now calculate the number of moles (n) of NH4NO3: \[n = \frac{3.88 \mathrm{g}}{80.04 \mathrm{g/mol}} \approx 0.0485 \mathrm{mol}\]

Calculate ΔH per mole

Finally, we determine the enthalpy change (∆H) per mole of NH4NO3 by dividing the heat transferred to the solution by the number of moles: \(\Delta H = \frac{-1150.96 \mathrm{J}}{0.0485 \mathrm{mol}}\) \(\Delta H ≈ -23738 \mathrm{J/mol}\) Since we need our answer in kJ/mol, we convert J/mol to kJ/mol: \(\Delta H ≈ -23.738 \mathrm{kJ/mol}\) (a) The enthalpy change for the solvation process is approximately \(-23.738 \mathrm{kJ/mol}\) of NH4NO3.

Determine endothermic or exothermic process

(b) Since the enthalpy change is negative (∆H < 0), it indicates that the process is exothermic, meaning that heat is released upon dissolution of NH4NO3 in water.

Key concepts

Thermochemistry

Thermochemistry is the study of the energy and heat associated with chemical reactions and physical transformations. It's a branch of thermodynamics that focuses on the calculation of energy changes, often expressed as the change in enthalpy (ΔH) of a reaction. An important principle of thermochemistry is the conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed.

• Enthalpy is a measure of the total energy of a thermodynamic system and includes the internal energy of the system plus the product of pressure and volume.
• To calculate the enthalpy change of a reaction, like the dissolution of ammonium nitrate in the example, we use the heat transferred and the amount of substance involved in the process.
• Enthalpy change values can tell us whether a reaction is endothermic (absorbs heat) or exothermic (releases heat), which are critical concepts for understanding chemical processes.

Calorimetry

Calorimetry is an experimental technique that measures the amount of heat involved in a chemical or physical process. This process is often performed with a device called a calorimeter. In the example given, a coffee-cup calorimeter was used to determine the heat change during the solvation process of ammonium nitrate.

• A coffee-cup calorimeter typically measures changes at constant pressure, which allows for the direct measurement of enthalpy changes.
• The formula used, q = mcΔT, is a fundamental calorimetry equation where q represents heat transferred, m is the mass of the solution, c is the specific heat capacity, and ΔT is the change in temperature.
• By accurately measuring these variables, calorimetry enables us to calculate the energy involved in endothermic and exothermic reactions.

Solvation Process

The solvation process involves the surrounding of solute particles by solvent molecules. It is a critical concept in chemistry, as it describes how substances dissolve. In the example exercise, solid ammonium nitrate dissolves in water, initiating a solvation process.

• Solvation can be either endothermic or exothermic. The nature of the reaction depends on the relative strengths of new solute-solvent interactions compared to the original intermolecular forces in the solute and solvent.
• For solid ammonium nitrate, solvation involves breaking ionic bonds between NH₄⁺ and NO₃⁻ ions and the formation of new hydrogen bonds between the ions and water molecules.
• The overall enthalpy change in solvation is calculated by taking into account all the energy changes occurring due to these bond breakages and formations.

Endothermic and Exothermic Reactions

Endothermic and exothermic reactions are two fundamental concepts that describe whether a process absorbs or releases heat, respectively. These terms directly relate to the sign of the enthalpy change (ΔH).

• In an endothermic reaction, the system absorbs heat from the surroundings, resulting in a positive ΔH.
• Conversely, in an exothermic reaction, the system releases heat to the surroundings, resulting in a negative ΔH.
• The ammonium nitrate dissolution example demonstrates an exothermic process with a negative ΔH of approximately -23.738 kJ/mol. This means that the process releases heat to the surroundings and, as the temperature of the solution drops, the heat is transferred to the solid ammonium nitrate, causing it to dissolve.