Given the measured cell potential, E cell is -0.3603 V at 25°C in the following cell, calculate the H+ concentration
Pt(s)|H2(g,0.713 atm)|H+(aq, ? M)||Cd2+(aq 1.00 M)|Cd(s)
The balanced reduction half-reactions for the cell, and their respective standard reduction potential values, E o, are as follows.
2H+(aq) + 2e- —> H2(g).[Eo=0.00 V]
Cd2+(aq)+2e- —> Cd(s). [Eo=-0.403V]
To calculate the H+ concentration, we need to use the Nernst equation, which relates the concentration of reactants and products to the measured cell potential. The Nernst equation is given by:
Ecell = Eo - (0.0592/n) * log(Q)
Where:
- Ecell is the measured cell potential
- Eo is the standard cell potential
- n is the number of electrons transferred in the balanced half-reaction
- Q is the reaction quotient, which is the ratio of product concentrations to reactant concentrations
In this case, the balanced half-reaction for the reduction of H+ is:
2H+(aq) + 2e- -> H2(g)
The standard cell potential for this half-reaction (Eo) is 0.00 V.
Given that the measured cell potential (Ecell) is -0.3603 V, and the standard cell potential (Eo) is 0.00 V, we can calculate the value of Q using the Nernst equation:
Ecell = Eo - (0.0592/n) * log(Q)
-0.3603 V = 0.00 V - (0.0592/2) * log(Q)
Simplifying the equation:
-0.3603 V = -0.0296 * log(Q)
Now, we can solve for Q:
log(Q) = -0.3603 V / -0.0296
log(Q) = 12.177 %
Using logarithmic properties, we can rewrite the equation:
Q = 10^(12.177)
Q = 8.58 x 10^12
Since Q is the ratio of product concentrations to reactant concentrations, and in this case, it is the ratio of [H2(g)] to [H+(aq)], we can write:
[H2(g)] / [H+(aq)] = 8.58 x 10^12
Since the concentration of H2 is not given in the question, we need additional information to solve for [H+(aq)].