Consider the following cell:
Pt(s)|H2(g, p1)|H+(aq, pHA)||H+(aq, pHC)|H2(g, p2)|Pt(s)
If the partial pressure of hydrogen gas is the same for both half-cells, what is E for the cell?
a) 0.0296 log(pHA/PhC)
b) 0.0296 log(pHC/PhA)
c) 0.0592 (pHA - pHC)
d) 0.0592 (pHC - pHA)
I know its not A because I got it wrong on my hw....
To determine the value of E for the cell, you need to use the Nernst equation. The Nernst equation relates the cell potential (E) to concentrations (or partial pressures) of the species involved in the half-reactions in the cell.
The Nernst equation for a cell with two half-cells can be written as:
E = E° - (0.0592/n) log(Q)
Where:
- E is the cell potential
- E° is the standard cell potential (given for the specific reaction)
- n is the number of electrons involved in the reaction
- Q is the reaction quotient, which is the ratio of the concentrations (or partial pressures) of the reactants and products.
In this given cell, the half-reactions are:
Half-reaction 1: Pt(s) | H2(g, p1) | H+(aq, pHA)
Half-reaction 2: H+(aq, pHC) | H2(g, p2) | Pt(s)
Since the partial pressure of hydrogen gas (H2) is the same in both half-cells, we can simplify the Nernst equation by removing it from the equation. Thus, we only need to consider the concentrations (or partial pressures) of the hydrogen ions (H+) in both half-reactions.
Therefore, the Nernst equation for this cell becomes:
E = E° - (0.0592/n) log(Q)
Substituting the values for the half-reactions:
E = E° - (0.0592/2) log((pHA)/(pHC))
Comparing this equation with the options provided, we can see that the correct answer is (b) 0.0296 log(pHC/PhA).