When a 6.50 -g sample of solid sodium hydroxide dissolves in 100.0 g of water in a coffee-cup calorimeter (Figure 5.18\()\) the temperature rises from 21.6 to to \(37.8^{\circ} \mathrm{C}\) . (a) Calculate the quantity of heat (in kJ) released in the reaction. (b) Using your result from part (a), calculate \(\Delta H\) (in \(\mathrm{kJ} / \mathrm{mol} \mathrm{NaOH} )\) for the solution process. Assume that the specific heat of the solution is the same as that of pure water.

Understanding the heat of solution is crucial when studying how substances interact with solvents. Simply put, it's the total amount of heat energy that is either absorbed or released when a substance, such as sodium hydroxide (NaOH), dissolves in a solvent like water. This process is highly dependent on the nature of both the solute and the solvent. During dissolution, bonds between solute molecules break and new interactions between solute and solvent molecules form. If the energy required to break the solute bonds is less than the energy released when the new interactions form, the dissolution is exothermic, meaning heat will be released.

In the exercise provided, a 6.50g sample of NaOH dissolves in water, resulting in an increase in the water's temperature—a clear indicator of an exothermic process. To ensure clarity for students, it could be helpful to emphasize the connection between the temperature increase and the exothermic nature of the dissolution process, as this conceptual link can often enhance understanding.

At the heart of this problem lies a concept known as specific heat capacity. This fundamental property is defined as the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. It is crucial when calculating the heat energy change in a system. The specific heat capacity of water is famously high—approximately 4.18 J/g·°C—which means water can absorb a lot of heat without a large change in temperature.

Within the context of the exercise, when the solid NaOH dissolves and the solution's temperature rises from 21.6°C to 37.8°C, the specific heat capacity allows us to calculate the actual heat absorbed by the solution. A suggestion to improve the student's understandings would be to explain how the specific heat capacity relates to everyday experiences such as why water in a lake doesn't rapidly fluctuate in temperature.

Calorimetry is the technique used to measure the heat of chemical reactions or physical changes as well as heat capacity. The coffee-cup calorimeter mentioned in the exercise is a simple, yet effective tool often used in introductory chemistry labs. It assumes that no heat is lost to the surroundings, functioning as an isolated system. The calorimeter enables the determination of the heat involved in the dissolving process of the NaOH. It's important to emphasize to students that while this is an idealized situation, in practice, some heat loss occurs, but the coffee-cup calorimeter is still a valuable learning instrument.

In further detailing this concept, one might explore how the construction of a coffee-cup calorimeter—often with styrofoam cups—helps in minimizing the heat exchange with the environment, thereby making the experiment more accurate.

Stoichiometry is a section of chemistry involving the calculation of reactants and products in chemical reactions. It is based on the principle that matter cannot be created or destroyed. The goal of stoichiometry is to predict the amounts of substances consumed and created in a given chemical reaction. In the exercise provided, stoichiometry comes into play as we convert the mass of NaOH into moles using its molar mass. These moles are then used to calculate the enthalpy change per mole of NaOH when it dissolves, providing a molar view of the heat of solution.

For better comprehension, students should be encouraged to understand the significance of stoichiometry in ensuring the balance of equations and predicting the outcomes of reactions, reinforcing the concept that each calculation is a step towards comprehending the broader picture of how reactions proceed quantitatively.