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 \(\mathrm{J} / \mathrm{C} \cdot \mathrm{g}\) 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 kJ/mol.

Short answer

The enthalpy change for the dissolution of \(\mathrm{NH}_{4}\mathrm{NO}_{3}\) in the given coffee-cup calorimeter experiment is \(-26.02 \ \mathrm{kJ/mol}\).

Step-by-step solution

Calculate the heat change (q) of the solution

To calculate the heat change, we will use the formula: q = mcΔT where q represents the heat change or transferred energy, m is the mass of the solution, c is the heat capacity of the solution, and ΔT is the change in temperature. Given: Mass of water (m): 75.0 g Heat capacity of the solution (c): 4.18 J/g·°C Initial temperature (Ti): 25.00 °C Final temperature (Tf): 23.34 °C First, let's find the change in temperature (ΔT): ΔT = Tf - Ti = 23.34 °C - 25.00 °C = -1.66 °C Now, plug in the values into the formula: q = (75.0 g)(4.18 J/g·°C)(-1.66 °C) = -520.47 J The heat change is -520.47 J, which means the heat is released by the system (exothermic reaction) during the dissolution process.

Calculate the moles of NH4NO3 dissolved

We can find the moles of NH4NO3 dissolved (n) using the molar mass and given mass: Mass of NH4NO3: 1.60 g Molar mass of NH4NO3: N(14.01 g/mol) + H(4 x 1.01 g/mol) + N(14.01 g/mol) + O(3 x 16.00 g/mol) = 80.05 g/mol To find the moles of NH4NO3 dissolved, we can use the formula: n = (mass of NH4NO3) / (molar mass of NH4NO3) n = (1.60 g) / (80.05 g/mol) = 0.02 mol

Calculate the enthalpy change (ΔH) per mole of NH4NO3

Now that we have the heat change and the number of moles of NH4NO3 dissolved, we can calculate the enthalpy change (ΔH) in kJ/mol. To find the enthalpy change, we simply divide the heat change (q) by the moles of NH4NO3 (n), and convert J to kJ: ΔH = (q / n) / 1000 = (-520.47 J) / (0.02 mol) / 1000 = -26.02 kJ/mol The enthalpy change for the dissolution of NH4NO3 is -26.02 kJ/mol.

Key concepts

Enthalpy Change

Enthalpy change is a crucial concept when analyzing how energy changes during a chemical process. It represents the total heat content in a system under constant pressure. When a reaction occurs, the enthalpy change (\( \Delta H \)) can tell us whether the process is exothermic or endothermic.

In the context of this experiment, the dissolution of ammonium nitrate in water results in a temperature drop, which is indicative of an exothermic reaction. The calculated enthalpy change of \(-26.02 \: \text{kJ/mol}\) signifies that energy is released as the salt dissolves. Understanding this helps in recognizing how matter and energy interact during chemical reactions, which is a foundational piece of thermodynamics.

Dissolution Process

The dissolution process involves the breaking down of a solute, in this case, ammonium nitrate (\(\text{NH}_4\text{NO}_3\)), into its constituent ions in a solvent, like water.

This specific dissolution is characterized by a decrease in temperature, indicating the absorption of heat from the surroundings. During this process, ions of \(\text{NH}_4^+\) and \(\text{NO}_3^-\) get uniformly distributed throughout the water, forming a homogeneous mixture. It’s helpful to recognize that not all dissolutions are exothermic; some result in a heat absorption, making them endothermic.

Observing these heat exchanges helps chemists understand and predict the energy needs or releases of similar reactions.

Heat Capacity

Heat capacity is the amount of energy required to change the temperature of a substance by one degree Celsius. In this exercise, the given heat capacity is \(4.18 \: \text{J/g} \cdot \text{°C}\), which is typically the specific heat for water.

This value implies that for every gram of water, 4.18 joules are needed to raise the temperature by one degree Celsius. Understanding this concept is fundamental, as it allows us to calculate the heat change in a system, like our coffee-cup calorimeter setup, where no heat is assumed to be lost to the environment.

By using heat capacity in conjunction with mass and temperature change, you gain insights into the energetics of the dissolution process or other reactions.

Ammonium Nitrate (NH4NO3)

Ammonium nitrate is a common chemical compound with a variety of uses, from fertilizers to cold packs. Its ability to readily dissolve in water and change its temperature is why it’s often involved in thermochemistry studies.

The dissolution of \(\text{NH}_4\text{NO}_3\) is a useful example for studying enthalpy changes because it is relatively straightforward to measure the temperature change when this compound interacts with a solvent.

Furthermore, by analyzing the dissolution of ammonium nitrate, students can gain practical insights into the importance of thermodynamics and chemical energy transformations.