A voltaic cell consists of two \(\mathrm{H}_{2} / \mathrm{H}^{+}\) half-cells. Half-cell \(\mathrm{A}\) has \(\mathrm{H}_{2}\) at 0.95 atm bubbling into \(0.10 \mathrm{M} \mathrm{HCl}\). Half-cell \(\mathrm{B}\) has \(\mathrm{H}_{2}\) at 0.60 atm bubbling into \(2.0 \mathrm{M} \mathrm{HCl}\). Which half-cell houses the anode? What is the voltage of the cell?

The Nernst Equation is a key tool in electrochemistry for determining the cell potential under non-standard conditions. It is formulated as follows:
\[ E = E^0 - \frac{0.0592}{n} \,\log \, Q \]
Here, \( E \) represents the electrode potential, \( E^0 \) is the standard electrode potential, \( n \) is the moles of electrons transferred in the half-reaction, and \( Q \) is the reaction quotient.
The reaction quotient \( Q \) involves the concentrations of the reactants and products. For a hydrogen electrode, \( Q \) is calculated as follows:
\[ Q = \frac{[H^+]^2}{P(H_2)} \]
This relationship allows us to see how the cell potential changes with different hydrogen ion concentrations and gas pressures. Whether you're dealing with a voltaic or electrolytic cell, the Nernst Equation is instrumental in predicting cell behavior under various conditions.

Electrode potential refers to the voltage (potential) difference between an electrode and its surrounding solution. The standard electrode potential \( E^0 \) is measured under standard conditions (1 M concentration, 1 atm pressure, and 25°C).
In the given exercise, both half-cells use a standard hydrogen electrode, for which \( E^0 \) is universally 0 V. Real-world cells rarely operate under these standard conditions, which is why the Nernst Equation is so essential.
Changes in hydrogen ion concentration and pressure lead to different reaction quotients \( Q \), and we use these to calculate the electrode potential for each half-cell. These calculations provide insights into which half-cell will act as the anode and which will act as the cathode.

In any electrochemical cell, identifying the anode and cathode is critical. The anode is where oxidation occurs, and for voltaic cells, it is the electrode with the lower (more negative) electrode potential. Conversely, the cathode is where reduction occurs and has the higher (more positive) electrode potential.
For example, in the given problem, half-cell A has an electrode potential of 0.0888 V, while half-cell B has an electrode potential of -0.0729 V. Therefore, half-cell B, with the lower potential, is the anode, and half-cell A is the cathode.
The flow of electrons occurs from the anode to the cathode, and knowing the correct identification of these electrodes is essential for properly calculating the cell voltage.

Calculating the cell voltage is a straightforward but crucial part of understanding voltaic cells. The cell voltage (also known as electromotive force or EMF) is given by the difference in electrode potentials between the cathode and the anode:
\[ E_{cell} = E_{cathode} - E_{anode} \]
In the given exercise, we have already identified the potentials:
\[ E_A = 0.0888 \, V \ (cathode)\]
\[ E_B = -0.0729 \, V \ (anode)\]
We plug these values into our equation:
\[ E_{cell} = 0.0888 - (-0.0729) \, V = 0.1617 \, V \]
This calculation tells us that the voltaic cell, as assembled, will have a cell voltage of approximately 0.1617 V. This voltage is essentially the driving force that pushes electrons through the circuit from the anode to the cathode.

The standard hydrogen electrode (SHE) is a reference electrode that is universally recognized due to its stable and well-defined electrode potential of 0 V under standard conditions. It involves a half-cell where hydrogen gas is bubbled through a solution of hydrogen ions at 1 M concentration and 1 atm of pressure.
In practice settings, deviations from these conditions are common. As seen in the exercise, variations in hydrogen ion concentration and gas pressure impact the reaction quotient \( Q \), thus altering the electrode potential. This is why calculations with the Nernst Equation are necessary.
The reliance on the hydrogen electrode stems from its repeatability and predictability. For many cells, it serves as a baseline against which other electrodes are measured. Understanding the hydrogen electrode's role helps you better grasp why certain reactions occur and how those reactions drive a voltaic cell.