A certain weak acid has a p Ka of 5.83 . When 100.0 mL of a 0.00525 M solution of this weak aci

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A certain weak acid has a p Ka of 5.83 . When 100.0 mL of a...

A certain weak acid has a $\mathrm{p} K_{\mathrm{a}}$ of $5.83 .$ When $100.0 \mathrm{~mL}$ of a $0.00525 \mathrm{M}$ solution of this weak acid at $21.26^{\circ} \mathrm{C}$ is reacted with $45.6 \mathrm{~mL}$ of $0.00634 \mathrm{M}$ sodium hydroxide $\left(\mathrm{H} A+\mathrm{OH}^{-} \longrightarrow A^{-}+\mathrm{H}_{2} \mathrm{O}\right)$ at $22.18{ }^{\circ} \mathrm{C},$ the temperature of the mixture rises to $24.88^{\circ} \mathrm{C}$. What is the entropy change associated with the ionization $\left(\mathrm{H} A \longrightarrow A^{-}+\mathrm{H}^{+}\right)$ of this weak acid? (Assume that the volumes are additive and the densities of the two solutions are $1.000 \mathrm{~g} \mathrm{~cm}^{-3}$, with a specific heat that is the same as pure water.)

A certain weak acid has a $\mathrm{p} K_{\mathrm{a}}$ of $5.83 .$ When $100.0 \mathrm{~mL}$ of a $0.00525 \mathrm{M}$ solution of this weak acid at $21.26^{\circ} \mathrm{C}$ is reacted with $45.6 \mathrm{~mL}$ of $0.00634 \mathrm{M}$ sodium hydroxide $\left(\mathrm{H} A+\mathrm{OH}^{-} \longrightarrow A^{-}+\mathrm{H}_{2} \mathrm{O}\right)$ at $22.18{ }^{\circ} \mathrm{C},$ the
temperature of the mixture rises to $24.88^{\circ} \mathrm{C}$. What is the entropy change associated with the ionization $\left(\mathrm{H} A \longrightarrow A^{-}+\mathrm{H}^{+}\right)$ of this weak acid? (Assume that the volumes are additive and the densities of the two solutions are $1.000 \mathrm{~g} \mathrm{~cm}^{-3}$, with a specific heat that is the same as pure water.)

Key Concepts

Acid?Base Equilibria

This concept involves understanding the equilibrium established when a weak acid ionizes in water. The acid dissociation constant, expressed as pKa, quantifies the extent to which the acid donates a proton, indicating its relative strength and the balance between the undissociated acid and its ions.

Ionization Reactions

Ionization reactions describe the process by which molecules such as weak acids partially dissociate into their constituent ions. This concept is central to predicting the behavior of acids in solution and involves understanding how factors like pH and temperature shift the equilibrium between the acid (HA) and its ions (A– and H+).

Calorimetry

Calorimetry is the experimental technique used to measure the heat exchanged during chemical reactions. By monitoring temperature changes in a system with known mass and specific heat capacity, one can determine the enthalpy change associated with the reaction. This is particularly useful in quantifying reaction energetics for processes such as acid-base reactions.

Thermodynamic Relationships

This concept deals with the fundamental relation among free energy, enthalpy, and entropy in thermodynamics, encapsulated by the equation ?G = ?H - T?S. It provides a framework for understanding how changes in enthalpy (heat content) and entropy (degree of disorder) determine the spontaneity of a reaction, enabling the calculation of entropy changes from observed energy changes and equilibrium data.

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