Question

When 1 g-equivalent of strong acid reacts with strong base, heat released is \(13.5 \mathrm{kcal}\). When 1 g-equivalent \(\mathrm{H}_{2} \mathrm{~A}\) is completely neutralized against strong base, \(13 \mathrm{kcal}\) is released. When 1 g-equivalent \(\mathrm{B}(\mathrm{OH})_{2}\) is completely neutralized against strong acid, 10 kcal heat is released. What is the enthalpy change when 1 mole of \(\mathrm{H}_{2} \mathrm{~A}\) is completely neutralized by \(\mathrm{B}(\mathrm{OH})_{2}\). (a) \(-27 \mathrm{kcal}\) (b) \(-10 \mathrm{kcal}\) (c) \(-20 \mathrm{kcal}\) (d) \(-19 \mathrm{kcal}\)

Short answer

-36 kcal

Step-by-step solution

Understand the reactions

We know that when an acid reacts with a base, the process is called neutralization and it results in the formation of water and a salt. For each of these reactions, we are given the amount of heat released per gram-equivalent. Note that 1 g-equivalent of an acid or base is the amount that will release or accept 1 mole of \(H^+\) or \(OH^-\) ions respectively.

Calculate enthalpy change for \(H_2A\) reaction

Given that 1 g-equivalent of \(H_2A\) releases 13 kcal when neutralized, and 1 mole of \(H_2A\) contains 2 g-equivalents because it can release two moles of \(H^+\) ions, the total heat released when 1 mole of \(H_2A\) is neutralized will be double that for 1 g-equivalent.

Calculate enthalpy change for \(B(OH)_2\) reaction

Since 1 g-equivalent of \(B(OH)_2\) releases 10 kcal upon neutralization and \(B(OH)_2\) contains 2 g-equivalents per mole (because it can accept two moles of \(H^+\) ions), the total heat released will be the same for 1 g-equivalent and 1 mole, as we are concerned with the neutralization of 1 equivalent only.

Combine the enthalpy changes

When 1 mole of \(H_2A\) reacts with 1 mole of \(B(OH)_2\), the total enthalpy change will be the sum of the enthalpy changes of both reactants. Since \(H_2A\) releases 26 kcal (13 kcal \times 2) and \(B(OH)_2\) releases 10 kcal for complete neutralization, the enthalpy change for the reaction will be the sum of these two amounts.

Calculate the overall enthalpy change

The overall enthalpy change for the neutralization of 1 mole of \(H_2A\) by \(B(OH)_2\) is simply the addition of 26 kcal and 10 kcal, which gives a total of 36 kcal released. However, because the question is asking for heat consumed, we need to consider the direction of heat flow. The enthalpy change will be negative, as the reaction is exothermic.

Key concepts

Neutralization Reactions

Neutralization reactions are a specific type of chemical reaction where an acid and a base react with each other to form water and a salt. This process can be generalized by the reaction:

\( \text{Acid} + \text{Base} \rightarrow \text{Water} + \text{Salt} \).

These reactions are significant because they represent a key mechanism for regulating the pH levels within various environments including industrial processes, biological systems, and environmental contexts. The concept of gram-equivalent, which figures prominently in understanding these reactions, refers to the amount of a substance that will either donate or accept an Avogadro's number of protons (\(H^+\)) or hydroxide ions (\(OH^-\)). In the provided exercise, the heat released during the reaction is quantified per gram-equivalent, illustrating the exothermic nature of neutralization reactions where energy is released, often in the form of heat, making the surroundings warmer.

Enthalpy of Reaction

Enthalpy of reaction, also known as heat of reaction or enthalpy change, is the difference in enthalpy, or heat content, of the reactants and products during a chemical reaction. For exothermic reactions, like neutralization, the enthalpy change is negative, indicating that heat is released to the surroundings. Conversely, endothermic reactions absorb heat, resulting in a positive enthalpy change.

In the context of the given problem, we determine the enthalpy change by calculating the heat released when one mole of a substance is completely neutralized. The enthalpy change for the neutralization of 1 mole of \(H_2A\) and 1 mole of \(B(OH)_2\) is a critical factor in understanding the energy dynamics of the reaction. Since enthalpy is an extensive property, it is directly proportional to the quantity of reacting substances, which means the enthalpy change must be adjusted for the specific amounts of reactants involved in the neutralization.

Acid-Base Reactions

Acid-base reactions are a subset of chemical reactions involving the transfer of protons (\(H^+\)) between reactants. Acids are defined as proton donors, while bases are proton acceptors, according to the Brønsted-Lowry theory. The strength of an acid or a base often dictates the extent of the reaction and thus the amount of energy or heat released.

Strong acids and bases dissociate completely in solution, yielding a greater degree of reaction and energy release. The problem provided refers to strong acids and bases, which is why the values given for heat release per gram-equivalent are high. It's important to note that in the enthalpy calculations for neutralization, the concept of gram-equivalents ensures comparability across different acids and bases, as they account for the number of \(H^+\) or \(OH^-\) ions that each can donate or accept, respectively. Understanding this allows students to predict products and calculate the energy changes associated with these acid-base reactions.