A 0.218 M solution of the weak acid HX has pH 4.57 at 25^∘ C. What is ΔG^∘ for the dissociation

step 1 We are continuing on with thermodynamics and so we're looking to calculate the pH. That can be c

A 0.218 M solution of the weak acid HX has pH 4.57 at 25^∘...

A 0.218 M solution of the weak acid HX has $\mathrm{pH} 4.57 \mathrm{at} 25^{\circ} \mathrm{C}$. What is $\Delta G^{\circ}$ for the dissociation of the weak acid?

$$
\mathrm{RNH}_2(a q)+\mathrm{H}_2 \mathrm{O} \rightleftharpoons \mathrm{RNH}_3^{+}(a q)+\mathrm{OH}^{-}(a q)
$$

Key Concepts

Standard Free Energy Change and Equilibrium

The standard free energy change (?G°) is directly related to the equilibrium constant of a reaction via the equation ?G° = -RT ln K. This relationship allows one to quantify the spontaneity of a reaction under standard conditions based on the equilibrium constant, and it is fundamental in connecting thermodynamics with chemical equilibria.

pH and Hydrogen Ion Concentration

pH is a logarithmic measure of the hydrogen ion concentration in aqueous solutions, defined as the negative logarithm of [H+]. In the context of weak acid ionization, the measured pH provides a direct way to calculate the concentration of hydrogen ions, which is then used to determine the extent of the acid’s dissociation.

Acid Dissociation Constant (Ka)

Ka quantifies the equilibrium between the weak acid and its conjugate base in solution. It is defined as the ratio of the concentrations of the dissociated ions to the undissociated acid at equilibrium. A smaller Ka indicates a weaker acid with less ionization, and it is often related to the pH and the initial concentration of the acid.

Weak Acid Ionization

This concept describes the process by which a weak acid only partially donates its proton to water, establishing an equilibrium between the undissociated acid and its dissociated ions. It highlights how the acid does not completely ionize in solution, and the degree of ionization can be determined from measurements such as pH and the initial acid concentration.

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