Question

The EMF of the cell: \(\mathrm{Hg}(1) \mid \mathrm{Hg}_{2} \mathrm{Cl}_{2}(\mathrm{~s})\), \(\mathrm{KCl}\) sol. \((1.0 \mathrm{~N}) \mid\) Quinohydrone \(\mid \mathrm{Pt}\), is \(0.210 \mathrm{~V}\) at \(298 \mathrm{~K}\). What is the \(\mathrm{pH}\) of the quinohydrone solution, the potential of the normal calomel electrode is \(0.279 \mathrm{~V}\) and \(E^{\circ}\) for the quinohydrone electrode is \(0.699 \mathrm{~V}\), both at the same temperature. \([2.303 R T / F=0.06]\) (a) \(3.5\) (b) \(7.0\) (c) \(1.85\) (d) \(-3.5\)

Short answer

The pH of the quinhydrone solution is 7.0.

Step-by-step solution

Write down the Nernst equation for the cell

For the half-cell reactions involved, the Nernst equation can be used to relate the electrode potential to the ion concentrations. We will assume that the KCl solution is at unit activity, so its concentration effect is neutralized. We can write the Nernst equation for the cell as follows: \[E = E^\circ - \frac{2.303RT}{F} \times \text{pH}\] where:\(E\) is the cell potential, \(E^\circ\) is the standard electrode potential, \(R\) is the gas constant, \(T\) is the temperature in Kelvin, \(F\) is the Faraday constant, and the pH term comes from the quinhydrone electrode involving hydrogen ions.

Calculate the overall cell potential

The overall cell potential can be calculated by taking the difference between the potentials of the quinhydrone electrode and the calomel electrode: \[E_\text{cell} = E_{\text{quinone}} - E_{\text{calomel}}\] Given that the EMF of the cell is 0.210 V, we can plug in the values. We know that \(E_{\text{calomel}} = 0.279 V\), thus: \[E_{\text{quinone}} = E_\text{cell} + E_{\text{calomel}}\] and substitute the given values.

Determine the pH of the quinhydrone solution

Substitute the calculated potential for the quinhydrone electrode and the given standard potential into the modified Nernst equation to solve for the pH:\[E_{\text{quinone}} = E^\circ_{\text{quinone}} - \frac{2.303RT}{F} \times \text{pH}\] Solve this equation for the pH of the quinhydrone solution.

Key concepts

Nernst Equation

Understanding the Nernst equation is central to solving problems that involve electrode potentials in electrochemical cells. It describes the relationship between the electrode potential and the concentration of ions around the electrode. Specifically, it gives us a way to calculate the potential of an electrochemical cell under non-standard conditions.

The equation is typically written in the form: \[E = E^\circ - \frac{2.303RT}{nF} \log Q\]where:

• \(E\) is the cell potential under non-standard conditions,
• \(E^\circ\) is the standard electrode potential,
• \(R\) stands for the universal gas constant,
• \(T\) is the temperature in Kelvin,
• \(n\) is the number of moles of electrons exchanged in the electrochemical reaction,
• \(F\) is the Faraday constant, which represents the charge of one mole of electrons,
• \(Q\) is the reaction quotient, given by the concentration of products over reactants, raised to the power of their stoichiometric coefficients.

For pH calculations involving hydrogen ions, the Nernst equation often includes the pH term as the logarithmic ratio of hydrogen ion concentration, simplifying the calculations.

Cell Potential

Cell potential, also known as electromotive force (EMF), is a measure of the driving force behind the movement of electrons in an electrochemical cell. It is a key factor in determining how electrical energy is produced or required for a chemical reaction.

The cell potential can be calculated by adding up the electrode potentials for the anode and cathode within the cell. However, because the anode potential is typically a negative value (due to oxidation), we usually find the cell potential by subtracting the anode potential from the cathode potential, as showcased in the exercise provided. This resulting value tells us the voltage that the cell can produce and it also indicates the spontaneity of the electrochemical reaction; a positive cell potential means a spontaneous reaction.

Standard Electrode Potential

The standard electrode potential is a chemical property that provides the measure of the individual potential of a reversible electrode at standard state, which is a concentration of 1 molar, a pressure of 1 atmosphere, and a temperature of 25°C (298 K).

Presented as \(E^\circ\) in electrochemical equations, these values are crucial for determining the direction and magnitude of electron flow in electrochemical cells. It represents the tendency of a chemical species to gain electrons (be reduced) and is expressed in volts.

In the given exercise, the standard electrode potential of the quinhydrone electrode is a known value used to calculate the pH of the solution. Since these values are determined under specific conditions, any deviations from these conditions require adjustments to the potential using the Nernst equation.

Quinhydrone Electrode

The quinhydrone electrode is a type of redox electrode that is used in pH measurement. It's based on the redox system involving quinone and hydroquinone in solution, which are in equilibrium with the hydronium ions. The electrode potential of the quinhydrone electrode is sensitive to changes in the pH of the solution, which makes it useful for this purpose.

Following the Nernst equation, the pH can be determined by the observed potential of the quinhydrone electrode. In practice, the potential of the quinhydrone electrode is influenced by hydrogen ion concentration, among other factors. The calculated pH value is what links our understanding of electrode potential to the acidity of the solution, making it a practical application of electrochemical principles in analytical chemistry.