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The standard enthalpies of formation of ions in aqueous solutions are obtained by arbitrarily assigning a value of zero to \(\mathrm{H}^{+}\) ions; that is, \(\Delta H_{\mathrm{f}}^{\mathrm{o}}\left[\mathrm{H}^{+}(a q)\right]=0 .\) (a) For the following reaction \(\begin{aligned} \mathrm{HCl}(g) \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{H}^{+}(a q)+\mathrm{Cl}^{-}(a q) & \Delta H^{\circ}=-74.9 \mathrm{~kJ} / \mathrm{mol} \end{aligned}\) calculate \(\Delta H_{\mathrm{f}}^{\circ}\) for the \(\mathrm{Cl}^{-}\) ions. \((\mathrm{b})\) Given that \(\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{OH}^{-}\) ions is \(-229.6 \mathrm{~kJ} / \mathrm{mol},\) calculate the enthalpy of neutralization when 1 mole of a strong monoprotic acid (such as \(\mathrm{HCl}\) ) is titrated by \(1 \mathrm{~mole}\) of a strong base \((\) such as \(\mathrm{KOH})\) at \(25^{\circ} \mathrm{C}\).

Short Answer

Expert verified
\(-167.2 \text{ kJ/mol}\) for \(\mathrm{Cl}^{-}\); neutralization: \(-56.2 \text{ kJ/mol}\).

Step by step solution

01

Write the Given Information

We know that \( \Delta H^{\circ} = -74.9 \text{ kJ/mol} \) for the reaction: \( \mathrm{HCl}(g) \rightarrow \mathrm{H}^{+}(aq) + \mathrm{Cl}^{-}(aq) \). Also, \( \Delta H_{\mathrm{f}}^{\circ} \left[ \mathrm{H}^{+}(aq) \right]=0 \).
02

Use Enthalpy of Formation Equation

The enthalpy change for a reaction is given by the sum of the enthalpies of formation of the products minus the sum of the enthalpies of formation of the reactants. For the reaction: \( \mathrm{HCl}(g) \rightarrow \mathrm{H}^{+}(aq) + \mathrm{Cl}^{-}(aq) \), we have:\[ \Delta H^{\circ} = \Delta H_{\mathrm{f}}^{\circ} \left[ \mathrm{H}^{+}(aq) \right] + \Delta H_{\mathrm{f}}^{\circ} \left[ \mathrm{Cl}^{-}(aq) \right] - \Delta H_{\mathrm{f}}^{\circ} \left[ \mathrm{HCl}(g) \right] \]
03

Solve for Enthalpy of Formation of Cl⁻

Rearrange the equation from Step 2 to solve for \( \Delta H_{\mathrm{f}}^{\circ} \left[ \mathrm{Cl}^{-}(aq) \right] \):\[ \Delta H_{\mathrm{f}}^{\circ} \left[ \mathrm{Cl}^{-}(aq) \right] = \Delta H^{\circ} + \Delta H_{\mathrm{f}}^{\circ} \left[ \mathrm{HCl}(g) \right] \] We need \( \Delta H_{\mathrm{f}}^{\circ} \left[ \mathrm{HCl}(g) \right] \), which is commonly \(-92.3 \text{ kJ/mol} \). Substitute the known values:\[ \Delta H_{\mathrm{f}}^{\circ} \left[ \mathrm{Cl}^{-}(aq) \right] = -74.9 \text{ kJ/mol} + (-92.3 \text{ kJ/mol}) \]\[ \Delta H_{\mathrm{f}}^{\circ} \left[ \mathrm{Cl}^{-}(aq) \right] = -167.2 \text{ kJ/mol} \]
04

Determine Enthalpy of Neutralization Reaction

The enthalpy of neutralization for the reaction between a strong acid and a strong base is calculated using: \( \mathrm{H}^{+}(aq) + \mathrm{OH}^{-}(aq) \rightarrow \mathrm{H}_2\mathrm{O}(l) \). The known value of this reaction is typically about \(-55.8 \text{ kJ/mol} \). To verify, using formation enthalpies: \[ \Delta H_{\mathrm{f}}^{\circ}[\mathrm{H}_2\mathrm{O}(l)] - \Delta H_{\mathrm{f}}^{\circ}[\mathrm{H}^{+}(aq)] - \Delta H_{\mathrm{f}}^{\circ}[\mathrm{OH}^{-}(aq)] = -285.8 \text{ kJ/mol} - 0 \text{ kJ/mol} - (-229.6 \text{ kJ/mol}) \]\[ = -285.8 + 229.6 \text{ kJ/mol} = -56.2 \text{ kJ/mol} \] \( \Delta H_{\text{neutralization}} = -56.2 \text{ kJ/mol} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Standard Enthalpy Change
Standard enthalpy change is a key concept in thermodynamics, often denoted by \( \Delta H^\circ \). It represents the heat change that occurs in a reaction at standard conditions, which are 1 bar pressure and a specified temperature, commonly \( 25^\circ \text{C} \). This measure helps standardize data so chemists and engineers can easily compare different reactions.
To fully understand this concept, remember:
  • The sign of \( \Delta H^\circ \) is important. If it's negative, the reaction releases heat and is exothermic. If positive, it absorbs heat and is endothermic.
  • Standard conditions ensure consistency, allowing for meaningful comparisons.
In essence, standard enthalpy change is like a common language for reactions, helping scientists accurately analyze and predict reaction behaviors under controlled circumstances.
Neutralization Reaction
Neutralization reactions are special types of chemical reactions where an acid and a base react to form water and a salt. During this process, the \( \text{H}^+ \) ions from the acid combine with the \( \text{OH}^- \) ions from the base to produce water \((\text{H}_2\text{O})\).
This type of reaction is incredibly significant in both practical and experimental chemistry. Here's why:
  • Neutralization is foundational in titration, which is a means of determining the concentration of an unknown acid or base.
  • These reactions are typically exothermic, releasing heat. This heat release is the enthalpy of neutralization.
  • Understanding this process helps explain everyday occurrences such as antacids neutralizing stomach acid.
By grasping the fundamentals of neutralization reactions, we gain insights into wider chemical processes and applications, both in the lab and in real-world scenarios.
Enthalpy Calculations
Enthalpy calculations are pivotal in determining the energy changes during chemical reactions. These calculations help us understand how energy is absorbed or released. The basic equation used in these calculations is:

\[ \Delta H = \sum \Delta H_f^\circ(\text{products}) - \sum \Delta H_f^\circ(\text{reactants}) \]
This formula is a powerful tool because:
  • It allows calculation of reaction enthalpies using known standard enthalpies of formation.
  • Gives insights into the energy efficiency of reactions, which has implications for industrial processes.
  • Provides a clear pathway to determining whether a reaction is feasible based on energy change.
Enthalpy calculations are not just about balancing equations; they are about unlocking the energy secrets of reactions, turning abstract chemistry into usable science.

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Most popular questions from this chapter

Producer gas (carbon monoxide) is prepared by passing air over red-hot coke: \(\mathrm{C}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}(g)\) Water gas (a mixture of carbon monoxide and hydrogen) is prepared by passing steam over red-hot coke: \(\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g)\) For many years, both producer gas and water gas were used as fuels in industry and for domestic cooking. The large-scale preparation of these gases was carried out alternately; that is, first producer gas, then water gas, and so on. Using thermochemical reasoning, explain why this procedure was chosen.

Determine the amount of heat (in kJ) given off when \(1.26 \times 10^{4} \mathrm{~g}\) of \(\mathrm{NO}_{2}\) are produced according to the equation $$ \begin{array}{l} 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \\ \qquad \Delta H=-114.6 \mathrm{~kJ} / \mathrm{mol} \end{array} $$

A student mixes \(88.6 \mathrm{~g}\) of water at \(74.3^{\circ} \mathrm{C}\) with \(57.9 \mathrm{~g}\) of water at \(24.8^{\circ} \mathrm{C}\) in an insulated flask. What is the final temperature of the combined water?

Define these terms: system, surroundings, thermal energy, chemical energy, potential energy, kinetic energy, law of conservation of energy.

A gas expands in volume from 26.7 to \(89.3 \mathrm{~mL}\) at constant temperature. Calculate the work done (in joules) if the gas expands (a) against a vacuum, (b) against a constant pressure of \(1.5 \mathrm{~atm},\) and \((\mathrm{c})\) against a constant pressure of \(2.8 \mathrm{~atm} .(1 \mathrm{~L} \cdot \mathrm{atm}=101.3 \mathrm{~J})\).

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