The heat of solution of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) in water was determined by measuring the amount of electrical work needed to compensate for the cooling which would otherwise óccur when the salt dissolves. After the \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) was added to the water, electrical energy was provided by passage of current through a resistance coil until the temperature of the solution reached the value it had prior to the addition of salt. In a typical experiment, \(4.4 \mathrm{~g}\) of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) was added to \(200 \mathrm{~g}\) water. A current of \(0.75\) ampere was provided through the heater coil, and the voltage across the terminals was \(6.0 \mathrm{~V}\). The current was applied for \(5.2\) minute. Calculate \(\Delta H\) for the solution of \(1.0\) mole \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) in enough water to give same concentration as was attained in the above experiment.

Heat of solution, in thermodynamics, refers to the total amount of heat energy that is either absorbed or released when a substance, such as a salt, is dissolved in a solvent like water. This process is crucial because it tells us whether the dissolving process is endothermic (absorbing heat) or exothermic (releasing heat). In the given exercise, the dissolution of ammonium nitrate (\( \text{NH}_4\text{NO}_3 \)) in water is endothermic; the solution gets cooler, which implies that it absorbs heat from the surroundings.

To counter this cooling effect and obtain a precise measurement of the heat of solution, electrical energy is used to heat the solution back up to its original temperature. This method ensures that the amount of heat absorbed by the solution is equal to the electrical energy supplied, allowing for an accurate calculation of the enthalpy change. The heat of solution for a particular substance can greatly influence practical applications, such as in pharmacology, where it can affect drug formulation and delivery.

Molar mass is a fundamental concept in chemistry that represents the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a critical factor in converting between the mass of a substance and the number of moles. For substances like \(\text{NH}_4\text{NO}_3 \), knowledge of molar mass allows chemists to determine how many moles are present in a certain mass of the substance.

In the context of our exercise, the student must first ascertain the molar mass of ammonium nitrate, which can be derived from the periodic table as the sum of the atomic masses of the constituent nitrogen, hydrogen, and oxygen atoms. Once the molar mass is known, the student is equipped to convert the mass of \(\text{NH}_4\text{NO}_3 \) used in the experiment to moles, which is a crucial step for the calculation of enthalpy change.

Electrical energy is a form of energy resulting from the flow of electric charge through a conductor. It's commonly used to perform work, such as heating an element in a resistive heater. This energy can be calculated by multiplying the power consumed (in watts) by the time (in seconds) during which the power is applied. Power itself is the product of the current (in amperes) and the potential difference (in volts).

In our exercise, the electrical energy was provided by passing a current through a resistance coil, supplying the necessary heat to maintain the solution's temperature. The accurate measurement of electrical energy applied is essential for determining the heat of solution of \(\text{NH}_4\text{NO}_3 \) when dissolved in water. Understanding the relationship between electrical energy and heat energy is not only important in chemistry but also in fields like physics and engineering where energy transformations are involved.

Enthalpy change per mole is a thermodynamic concept that indicates the amount of heat absorbed or released during a reaction or a process such as dissolving, per mole of a substance. It's a key measurement in understanding the energy changes associated with chemical reactions and is calculated by dividing the total energy change by the number of moles of the reactant or product involved.

In the exercise we've discussed, to find the enthalpy change per mole for the dissolution of \(\text{NH}_4\text{NO}_3 \), you start with the total electrical energy supplied (calculated from the voltage, current, and time). Then, using the molar mass and the mass of the salt used, you calculate the moles of \(\text{NH}_4\text{NO}_3 \). Dividing the total energy applied by the number of moles gives us the enthalpy change per mole. This value is crucial as it provides a standard way to express and compare the energetic changes for chemical processes independent of the quantity of the substances used.