A galvanic cell is based on the following half-reactions: Fe^2++2 e^-⟶Fe(s) ℰ^∘=-0.440

A galvanic cell is based on the following half-reactions: ...

A galvanic cell is based on the following half-reactions: $$\begin{array}{ll}\mathrm{Fe}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Fe}(s) & \mathscr{E}^{\circ}=-0.440 \mathrm{~V} \\ 2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_{2}(g) & \mathscr{E}^{\circ}=0.000 \mathrm{~V} \end{array}$$ where the iron compartment contains an iron electrode and $\left[\mathrm{Fe}^{2+}\right]=1.00 \times 10^{-3} M$ and the hydrogen compartment contains a platinum electrode, $P_{\mathrm{H}_{2}}=1.00 \mathrm{~atm}$, and a weak acid, $\mathrm{HA}$, at an initial concentration of $1.00 M .$ If the observed cell potential is $0.333 \mathrm{~V}$ at $25^{\circ} \mathrm{C}$, calculate the $K_{\mathrm{a}}$ value for the weak acid HA.

A galvanic cell is based on the following half-reactions:
$$\begin{array}{ll}\mathrm{Fe}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Fe}(s) & \mathscr{E}^{\circ}=-0.440 \mathrm{~V} \\
2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_{2}(g) & \mathscr{E}^{\circ}=0.000 \mathrm{~V}
\end{array}$$
where the iron compartment contains an iron electrode and $\left[\mathrm{Fe}^{2+}\right]=1.00 \times 10^{-3} M$ and the hydrogen compartment contains a platinum electrode, $P_{\mathrm{H}_{2}}=1.00 \mathrm{~atm}$, and a weak acid, $\mathrm{HA}$, at an initial concentration of $1.00 M .$ If the observed cell potential is $0.333 \mathrm{~V}$ at $25^{\circ} \mathrm{C}$, calculate the $K_{\mathrm{a}}$ value for the weak acid HA.

Key Concepts

Acid Dissociation Constant (Ka)

The acid dissociation constant, Ka, is a measure of the strength of an acid in water. It quantifies the extent to which a weak acid dissociates into its constituent ions. A higher Ka value indicates a stronger acid that ionizes more completely, whereas a lower Ka indicates a weaker acid with less ionization.

Nernst Equation

The Nernst equation is a fundamental relation in electrochemistry that accounts for the effect of concentration (or pressure) changes on the cell potential. It adjusts the standard electrode potential to non?standard conditions by incorporating the reaction quotient, enabling the calculation of actual potentials within a galvanic cell.

Chemical Equilibrium

Chemical equilibrium in the context of acid dissociation involves the balance between the undissociated acid and its dissociated ions. Understanding equilibrium is essential for connecting the measured cell potential in a galvanic cell to the intrinsic Ka of an acid, as the potential reflects the relative concentrations of the species involved.

Galvanic Cell

A galvanic cell is an electrochemical cell that converts chemical energy from spontaneous redox reactions into electrical energy. It comprises two half-cells where oxidation occurs at one electrode and reduction at the other, with the overall potential difference determined by the difference in the electrode potentials of the two half-reactions.

Standard Electrode Potentials

Standard electrode potentials (E° values) represent the inherent tendency of a chemical species to be reduced under standard conditions (1 M concentration, 1 atm pressure, and 25°C). They serve as reference points in electrochemistry to predict the direction of electron flow and to calculate the cell potential for a given redox reaction.

Transcript

00:01 We are given these two half -reactions that occur within a galvanic cell, and we ultimately want to determine what the value is for a weak acid, ha, that has been dissociated to produce h -plus ions.

00:15 And when we talk about k -a, then we are dissociating the weak acid, h -a., reversibly, into aqueous h -plus ions, plus aqueous.

00:32 Aqueous a minus ions.

00:36 And these are all equious species.

00:38 So the value for the equilibrium of this dissociation is equal to the concentration of h plus times a concentration of a minus divided by the concentration of h .a.

00:54 So once we have these three species concentrations, we can plug them into this ratio in order to determine ka.

01:01 We can use the inerts equation in order to to find the concentration of h plus ions that we have.

01:09 And based on the fact that this is a one to one stoichiometry, that would also equal the concentration of a minus ions that we have.

01:18 So we would square the concentration of h plus ions for the numerator.

01:22 And for the denominator, we are told that we initially have 1 .00 molars of this weak acid.

01:30 So the first thing that we need to do is find the concentration of h plus ions.

01:35 And we need to use a nerts equation to do that, and part of the nerts equation is solving for the standard cell potential.

01:42 We know that this is a galvanic cell, so we have to rearrange the two half reactions in such a way that gives us a positive value for the cell potential.

01:50 And we also know that one of these reactions has to be reversed to undergo oxidation so that we can cancel out the electrons.

01:57 When we compare the two given values for the standard reduction potentials, we see that zero is greater than negative, 0 .440.

02:06 So that means h -plus will be reduced to form hydrogen gas while we reverse the first reaction so that iron will be oxidized to fe2 plus.

02:17 And when we do that, we also have to reverse the sign of the standard reduction potential to be 0 .440.

02:25 When we rearrange the equations that way, we see that two electrons cancel out on either side...

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