At \(25^{\circ} \mathrm{C},\) the standard enthalpy of formation of \(\mathrm{HF}(a q)\) is given by \(-320.1 \mathrm{~kJ} / \mathrm{mol} ;\) of \(\mathrm{OH}^{-}(a q),\) it is \(-229.6 \mathrm{~kJ} / \mathrm{mol} ;\) of \(\mathrm{F}^{-}(a q),\) it is \(-329.1 \mathrm{~kJ} / \mathrm{mol} ;\) and of \(\mathrm{H}_{2} \mathrm{O}(l),\) it is \(-285.8 \mathrm{~kJ} / \mathrm{mol} .\) (a) Calculate the standard enthalpy of neutralization of \(\mathrm{HF}(a q)\) $$ \mathrm{HF}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{F}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) $$ (b) Using the value of \(-56.2 \mathrm{~kJ}\) as the standard enthalpy change for the reaction $$\mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) $$calculate the standard enthalpy change for the reaction$$\mathrm{HF}(a q) \longrightarrow \mathrm{H}^{+}(a q)+\mathrm{F}^{-}(a q) $$

The enthalpy of formation, symbolized as \(\Delta H_f\), is the change in enthalpy when one mole of a substance is formed from its elements under standard conditions. This concept is a cornerstone of thermochemistry, enabling us to understand how much energy is absorbed or released when compounds are created. For instance, the values given for HF(aq), OH\(^-\)(aq), F\(^-\)(aq), and H\(_2\)O(l) in the exercise indicate the amount of energy involved in forming these substances from their constituent elements.

When substances react, the total enthalpy of the products can be compared with the total enthalpy of the reactants to determine the overall energy change. This comparison uses the principle that enthalpy, being a state function, depends only on the initial and final states of a system, not on the path taken. Therefore, careful tabulation of \(\Delta H_f\) values enables the calculation of energy changes for a wide array of chemical reactions.

Exothermic reactions are chemical processes that release energy to the surroundings, usually in the form of heat. The concept of exothermicity is fundamental in chemical energetics. When the bonds formed in the product molecules release more energy than the energy required to break the bonds in the reactants, the reaction is exothermic. This is reflected by a negative value for the enthalpy change \(\Delta H\), indicating that the system loses energy.

In the context of our exercise, the neutralization reaction where HF(aq) reacts with OH\(^-\)(aq) to form F\(^-\)(aq) and H\(_2\)O(l) is exothermic. The calculated enthalpy change of -65.2 kJ/mol confirms the exothermic nature—the reaction releases 65.2 kJ of energy per mole of HF neutralized. These types of reactions are often associated with an increase in temperature of the reaction mixture.

Thermochemistry calculations involve quantifying the heat exchange associated with chemical reactions. Understanding these calculations allows for the prediction of energy changes during reactions, which is essential in many areas of chemistry and industry. The steps outlined in the solution demonstrate a systematic approach to these calculations:

• Identify the chemical equation for the reaction.
• Observe standard enthalpy of formation values for reactants and products.
• Apply the enthalpy changes to Hess's Law or the principles of thermochemistry to find the net change in enthalpy for the reaction.

By using the given \(\Delta H_f\) values and applying the formula for enthalpy change, students can practice their calculation skills and gain a deeper understanding of how energy is processed and conserved in chemical reactions.

Chemical energetics refers to the study of energy flows and transformations in chemical processes. It is an integral part of understanding chemical reactions, as it allows us to determine whether a reaction is likely to occur spontaneously and what might be the driving force behind it. Enthalpy, along with entropy and free energy, is one of the key thermodynamic quantities in this field.

Learning about chemical energetics involves exploring the different types of reactions, such as exothermic and endothermic, and how they influence the energy of the system. It also involves understanding that the standard enthalpies of formation, reaction, and neutralization are all part of a bigger framework that helps us predict and measure energy changes. This makes it easier to design processes that are not only effective but also economical and safe.