Calorimetry

Heat of Solution of Ammonium Nitrate

Calorimeters are designed to be well-insulated, so no heat is gained from or lost to the surroundings. If heat cannot enter or leave the calorimeter, than any heat released by a process or object within the calorimeter must be picked up by another object or process.

Imagine a reaction in which solid ammonium nitrate (NH₄NO₃ , a component in some fertilizers and an explosive) is dissolved in water to produce an aqueous ammonium nitrate solution.

NH₄NO₃ (s)   →   NH₄⁺ (aq)   +   NO₃^- (aq)

When this dissolution reaction occurs, the separation of the ammonium and nitrate ions from the crystal lattice and the solvation of each ion by water (the solvent) results in heat transfer, q_soln. Because this heat flow is a consequence of a solid dissolving to form a solution, q_soln is called the heat of solution. In this case, the heat flow is positive, because the reaction draws heat from the solution. Depending upon the compound, the heat of solution might be positive (endothermic) or negative (exothermic).

This reaction requires heat to occur. That heat cannot be supplied by the surroundings, because the calorimeter is perfectly insulated. Consequently, the heat must be supplied by the solution in the calorimeter or the calorimeter itself. This calorimetry experiment involves three distinct heat transfer.

The sum of these three heat transfers must equal zero, because no heat may enter or leave the calorimeter from the surroundings.

0   =   q_aq   +   q_cal   +   q_soln

The strategy in calorimetry is to use a temperature change and a heat capacity to determine a heat flow for an object (such as the solution or the calorimeter). In this experiment, both substances have the same initial and final temperatures, T_i and T_f , respectively.

q_cal   =   C_cal   ΔT   =   C_cal   ( T_f   -   T_i )

q_aq   =   C_aq   ΔT   =   m_aq   s_aq   ( T_f   -   T_i )

One typically determines the heat capacity of the aqueous solution (C_aq) from the mass of the solution (m_aq) and the specific heat capacity of the solution (s_aq). The mass of the aqueous solution is the sum of the masses of the water and ammonium nitrate originally placed in the calorimeter. The specific heat capacity of a dilute aqueous solution is usually close to that of pure water ( 4.184 J ^oC ^-1 g ^-1 ).

The objective of this experiment is to determine the heat of reaction (in this case, the heat of solution). The above equations can be combined and rearranged to yield a working equation:

q_soln   =   -   q_cal   -   q_aq   =   -   ( C_cal   +   m_aq   s_aq )   ( T_f   -   T_i )

Just as the heat capacity of a substance is an extensive property, so the heat of solution is also an extensive property. It is generally more convenient to report intensive properties, and for this reason the heat capacity of a substance is usually reported as a specific heat capacity, that is, the heat capacity per gram of substance. Similarly one can report a specific heat of solution, which is the heat of solution per gram of solute that dissolves. More commonly, though, the molar heat of solution is reported. The molar heat of solution ( ΔH_soln ) is the heat of solution ( q_soln ) per mole of solute ( n ).

Experiment

Objective

Determine the molar heat of solution of ammonium nitrate.

Approach:

Dissolve a known mass of ammonium nitrate solid in a known mass of water in a calorimeter. For the liquid in the calorimeter, observe the change in temperature that results for the dissolution of the ammonium nitrate. Use this temperature change with the heat capacities of the calorimeter and the water to calculate the heat flow that results when the ammonium nitrate dissolves.

The sample of solid ammonium nitrate is sealed in a glass ampule, which is placed in the water beneath a "hammer". The glass is thin and easily broken. To start the reaction, the hammer is lowered on the ampule to break the glass, exposing the solid ammonium nitrate to the water. The stirrer mixes the liquid while the solid dissolves.

Procedure

1. Select the mass (between 30 and 90 g) of water to be used in the experiment.
2. Select the mass (between 0.5 and 10 g) of the ammonium nitrate to be dissolved in the water.
3. After selecting the mass of each reactant, click on the Reset button to set up the experiment.
4. Record the initial temperature, T_i , of the water in the calorimeter.
5. Click on the Start button to initiate the experiment.
6. When the system has reached equilibrium and the temperature stabilizes, record the final temperature, T_f , for the solution in the calorimeter.
7. Calculate ΔH_soln and express the value in kJ mole ^-1

Information

Question: What is the experimental difficulty that results from performing the experiment with a very small amount of NH₄NO₃ and a large volume of water ?