A \(0.05 \mathrm{~L}\) sample of \(0.2 \mathrm{M}\) aqueous hydrochloric acid is added to \(0.05 \mathrm{~L}\) of \(0.2 \mathrm{M}\) aqueous ammonia in a calorimeter. Heat capacity of entire calorimeter system is \(480 \mathrm{~J} / \mathrm{K}\). The temperature increase is \(1.09 \mathrm{~K}\). Calculate \(\Delta_{r} H^{\circ}\) in \(\mathrm{kJ} / \mathrm{mol}\) for the following reaction: $$ \mathrm{HCl}(a q .)+\mathrm{NH}_{3}(a q) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(a q) $$ (a) \(-52.32\) (b) \(-61.1\) (c) \(-55.8\) (d) \(-58.2\)

Calorimetry is an experimental technique used to measure the amount of heat released or absorbed during a chemical reaction, physical change, or phase transition. Inside a calorimeter, the reaction takes place in a controlled environment, and the temperature change recorded is directly related to the thermal energy exchanged during the process.

To calculate the heat (\text{Q}) involved in a reaction, calorimetry typically involves using the equation: \( Q = C \times \Delta T \), where \(C\) is the total heat capacity of the calorimeter system and \(\Delta T\) is the observed change in temperature. It's essential to have a proper understanding of this concept in order to accurately interpret enthalpy changes in chemical reactions.

Chemical thermodynamics is the branch of thermodynamics that deals with the relationship between heat, work, and chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. One of the fundamental quantities measured in chemical thermodynamics is the change in enthalpy (\(\Delta H\)), defined as the total heat content of a system.

An enthalpy change can be a negative or positive value, indicating whether the process is exothermic (releases heat to the surroundings) or endothermic (absorbs heat from the surroundings), respectively. This distinction helps to understand whether a reaction is likely to occur spontaneously or if it requires energy input.

Stoichiometry is a section of chemistry that involves calculating the quantities of reactants and products in a chemical reaction. It is based on the conservation of mass and the concept that matter is neither created nor destroyed during a chemical reaction.

Using stoichiometry in the context of calorimetry helps to determine the amount of a reactant required to fully react with a given quantity of another reactant. For example, when equimolar solutions of an acid and a base are mixed, stoichiometry can be used to ensure a complete reaction, providing a clear connection to the enthalpy change of the reaction through the equation \(\Delta_{r} H^\text{^{\text{\circ}}}= \frac{Q}{n}\), where \(n\) is the moles of the limiting reactant.

Acid-base reactions are a type of chemical reactions which involve the transfer of protons (H+) between a pair of compounds. The reactions are fundamental to chemistry and involve an acid (proton donor) and a base (proton acceptor), resulting in the formation of water, in the case of strong acid-strong base reactions, or a generally less reactive acid-base conjugate pair.

In the calorimetry experiment focused on an acid-base reaction, such as the neutralization of hydrochloric acid (\(HCl\)) by ammonia (\(NH_{3}\)), the enthalpy change (\(\Delta_{r} H^\text{^{\text{\circ}}}\)) reflects the heat evolved or absorbed during the formation of the salt product, ammonium chloride in this example. Understanding these reactions allows for the prediction and calculation of the heat changes accompanying such reactions, which is crucial for energy management in industrial processes.