The cell potential of the following electrochemical cell depends on the pH of the solution in the anode half-cell:
Pt(s)|H2(g,1atm)|H+(aq,?M)||Cu^2+(aq,1.0M)|Cu(s)
what is the pH of the solution if Ecell is 375 mV?
I first got .65 as my pH, but it said that it was wrong. Please explain how to solve this problem!
To solve this problem, you need to apply the Nernst equation, which relates the cell potential (Ecell) to the concentration of the species involved in the electrochemical reaction and the standard cell potential.
The Nernst equation is given as:
Ecell = E°cell - (RT/nF) * ln(Q)
Where:
- E°cell is the standard cell potential, which is the cell potential when all the species in the reaction are at standard conditions (1M concentration, 1 atm pressure, 25°C temperature, and pH = 0).
- R is the ideal gas constant (8.314 J/K*mol).
- T is the temperature in Kelvin.
- n is the number of moles of electrons transferred in the cell reaction.
- F is the Faraday constant (96,485 C/mol).
- Q is the reaction quotient, which is the ratio of the concentrations of the products to the concentrations of the reactants, each raised to the power of their stoichiometric coefficients.
In this specific electrochemical cell:
Pt(s)|H2(g, 1atm)|H+(aq, ?M)||Cu2+(aq, 1.0M)|Cu(s)
The cell reaction is:
H2(g) → 2H+(aq) + 2e- (at the anode)
Cu2+(aq) + 2e- → Cu(s) (at the cathode)
From the given information, the standard cell potential (E°cell) is not provided, but we can determine it from standard reduction potentials. The standard reduction potentials for Cu2+(aq)/Cu(s) and H+(aq)/H2(g) are commonly known as 0.34V and 0V, respectively.
The cell potential (Ecell) is given as 375 mV, which is 0.375V.
Hence, we have:
Ecell = E°cell - (RT/nF) * ln(Q)
Substituting the known values, we get:
0.375V = E°cell - (8.314 J/K*mol * T / (2 * 96,485 C/mol)) * ln(Q)
Simplifying the equation, we have:
E°cell = 0.375V + (8.314 J/K*mol * T / (2 * 96,485 C/mol)) * ln(Q)
Now, we need to find the value of Q, which is the reaction quotient.
Q = [H+]^2 / [Cu2+]
The concentration of Cu2+ is given as 1.0M.
To determine the concentration of H+, we need to know the pH.
The pH is related to the concentration of H+ ions by the following equation:
pH = -log[H+]
To convert the pH value to the concentration of H+ ions, we use the equation:
[H+] = 10^(-pH)
Let's calculate the concentration of H+ ions:
[H+] = 10^(-pH) = 10^(-0.65) ≈ 0.221 M
Now that we have the values of [H+] and [Cu2+], we can calculate Q:
Q = [H+]^2 / [Cu2+] ≈ (0.221)^2 / 1.0
Next, plug the value of Q into the equation to determine E°cell.
Finally, solve the equation for E°cell to find the standard cell potential.