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To determine the pH of the half-cell, we can use the Nernst equation, which relates the cell potential to the concentrations of the species involved. In this case, the half-cell reaction is: 2H+(aq) + 2e- → H2(g) with E° = 0.0 V Given that the hydrogen half-cell exhibits a potential of -0.02 V at a H2(g) pressure of 1.2 atm, we need to calculate the hydrogen ion concentration (H+) to find the pH of the half-cell. 1. Calculate the actual cell potential (Ecell) using the Nernst equation: Ecell = E° - (0.0592/n) * log(Q) where: - Ecell is the actual cell potential - E° is the standard cell potential (0.0 V in this case) - n is the number of electrons transferred (2 in this case) - Q is the reaction quotient, which can be expressed in terms of the hydrogen ion concentration (H+) 2. Plug in the values: - Ecell = -0.02 V - E° = 0.0 V - n = 2 - Q = [H2] / [H+]^2, where [H2] is determined by the given H2(g) pressure (1.2 atm) 3. Calculate [H2]: Using the ideal gas law: PV = nRT Given P = 1.2 atm, T = 298 K (standard temperature), R = 0.0821 L.atm/mol.K, and n = 1 mol (from the balanced half-cell reaction), we can find [H2] in mol/L. 4. Substitute [H2] into the expression for Q and solve for [H+]. 5. Calculate the pH from [H+]: pH = -log[H+] By following these steps, you can determine the pH of the half-cell based on the given information about the hydrogen half-cell potential and pressure of H2 gas.
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