Zinc metal reacts with hydrochloric acid according to the balanced equation: When 0.103 g of Zn(s) is combined with enough HCl to make 50.0 mL of solution in a coffee-cup calorimeter, all of the zinc reacts, raising the temperature of the solution from 22.5 C to 23.7 C. Find Hrxn for this reaction as written. (Use 1.0 g/mL for the density of the solution and 4.18 J/g # C as the specific heat capacity.)

The heat capacity of a substance is a measure of the amount of heat energy required to raise the temperature of a given quantity of the substance by one degree Celsius. It is an extensive property, meaning it depends on the amount of substance present. For example, water has a high heat capacity, which means it can absorb a lot of heat before it starts getting significantly hotter. In calculations, we often use a related concept called specific heat capacity, which is the heat capacity per unit mass of a substance.

Understanding heat capacity is crucial for solving thermodynamic problems because it allows us to determine how much heat has been absorbed or released during a temperature change. The formula used is \(q = mc\Delta T\), where \(q\) represents the heat absorbed or released, \(m\) is the mass of the substance, \(c\) is the specific heat capacity, and \(\Delta T\) is the change in temperature. To enhance your understanding, remember that different substances have different capacities for storing heat, which is why specific heat capacities are a necessary part of these calculations.

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. A device called a calorimeter is often used to measure this heat. In our exercise, we use a simple coffee-cup calorimeter, which is essentially a polystyrene cup that provides insulation and helps in assuming that the heat transfer occurs only between the reaction and the solution, not the surroundings.

To calculate heat using calorimetric data, we use the principle that heat lost by one part of the system is gained by another. Essentially, if the solution heats up, it means it has absorbed the heat released by the chemical reaction happening inside it. Applying this concept, we can use the specific heat capacity of the solution and the change in temperature to calculate the heat of the reaction (\(q\)). Precise measurements and attention to thermal equilibrium are critical for this method to be effective.

Stoichiometry is the area of chemistry that pertains to the quantitative relationships between the substances involved in a chemical reaction. It is derived from the Greek words \(\text{stoicheion}\) meaning 'element' and \(\text{metron}\) meaning 'measure.' Stoichiometry allows us to predict the amounts of products and reactants that are consumed or produced in a given reaction.

The stoichiometric coefficients from the balanced chemical equation provide the ratio of moles of each substance involved. This ratio is the key to linking the mass of reactants used to the amount of heat released or absorbed during a reaction, as seen in the original exercise. Also, when normalizing enthalpy change in a reaction, we account for the stoichiometry to express it per mole of reactant, as is often customary in reporting standard enthalpy changes for reactions.

The enthalpy of reaction, also known as heat of reaction (\(\Delta H_{\text{rxn}}\)), is the change in enthalpy that occurs when a reaction takes place under constant pressure. Enthalpy, represented by \(H\), is a thermodynamic potential that reflects the heat content of a system. The change in enthalpy (\(\Delta H\)) for a reaction is related to the heat absorbed or released during the reaction.

In an exothermic reaction, like the one involving zinc and hydrochloric acid, the enthalpy of the products is lower than that of the reactants, and \(\Delta H_{\text{rxn}}\) is negative, indicating that heat is released to the surroundings. In contrast, for endothermic reactions, \(\Delta H_{\text{rxn}}\) is positive, as heat is absorbed from the surroundings. The calculation of \(\Delta H_{\text{rxn}}\) often involves the use of calorimetry, stoichiometry, and the concept of heat capacity to ascertain the heat change per mole of reactant or product to better understand and quantify the thermodynamics of a chemical reaction.