To what pH should you adjust a standard hydrogen electrode to get an electrode potential of -0.122 V? (Assume that the partial pressure of hydrogen gas remains at 1 atm.)

Verified step by step guidance

1. Identify the Nernst equation for the hydrogen electrode, which is given by: \( E = E^0 - \frac{0.0592}{n} \log \frac{[H^+]}{P_{H_2}} \). Here, \( E^0 \) is the standard electrode potential of the hydrogen electrode, \( n \) is the number of electrons transferred in the half-reaction, \( [H^+] \) is the concentration of hydrogen ions, and \( P_{H_2} \) is the partial pressure of hydrogen gas.
2. Substitute the known values into the Nernst equation. Since the standard electrode potential (\( E^0 \)) for hydrogen is 0 V and the partial pressure of hydrogen gas (\( P_{H_2} \)) is given as 1 atm, the equation simplifies to: \( E = -0.0592 \log [H^+] \).
3. Set the electrode potential (\( E \)) to -0.122 V as given in the problem statement. Substitute this value into the simplified Nernst equation: \( -0.122 = -0.0592 \log [H^+] \).
4. Solve for \( [H^+] \) by isolating it on one side of the equation. This involves exponentiating both sides to remove the logarithm.
5. Convert the hydrogen ion concentration (\( [H^+] \)) to pH using the formula: \( pH = -\log [H^+] \).

Key Concepts

Nernst Equation

The Nernst Equation relates the electrode potential of a half-cell to the concentration of the reactants and products involved in the electrochemical reaction. It is expressed as E = E° - (RT/nF)ln(Q), where E is the electrode potential, E° is the standard electrode potential, R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, F is Faraday's constant, and Q is the reaction quotient. This equation is essential for calculating how changes in concentration or pH affect electrode potential.

Standard Hydrogen Electrode (SHE)

The Standard Hydrogen Electrode (SHE) is a reference electrode used in electrochemistry, defined as having a potential of 0 V at all temperatures. It consists of a platinum electrode in contact with 1 M H⁺ ions and hydrogen gas at 1 atm pressure. Understanding the SHE is crucial for determining the potential of other electrodes relative to this standard, particularly when adjusting conditions like pH.

pH and Hydrogen Ion Concentration

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration (pH = -log[H⁺]). In electrochemistry, the pH of a solution directly influences the concentration of H⁺ ions, which in turn affects the electrode potential. Adjusting the pH can therefore be a method to achieve a desired electrode potential, as seen in the context of the Nernst Equation.