The reduction potential of hydrogen half cell will be negative if \((T=298 \mathrm{~K})\) (1) \(\mathrm{P}_{\mathrm{H}_{2}}=1 \mathrm{~atm}\) and \(\left[\mathrm{H}^{+}\right]=1.0 \mathrm{M}\) (2) \(\mathrm{P}_{\mathrm{H}_{2}}=2 \mathrm{~atm}\) and \(\left[\mathrm{H}^{*}\right]=2.0 \mathrm{M}\) (3) \(\mathrm{P}_{\mathrm{H}_{2}}=2 \mathrm{~atm}\) and \(\left[\mathrm{H}^{+}\right]=1.0 \mathrm{M}\) (4) \(\mathrm{P}_{\mathrm{H}_{2}}=1 \mathrm{~atm}\) and \(\left[\mathrm{H}^{+}\right]=2.0 \mathrm{M}\) (5) \(\mathrm{P}_{\mathrm{H}_{2}}=1 \mathrm{~atm}\) and \(\left[\mathrm{H}^{+}\right]=1.5 \mathrm{M}\)

Electrochemistry is the branch of chemistry that deals with the relationship between electrical energy and chemical changes. It involves studying how electrons move through a solution and how they cause chemical reactions. Understanding this process is key to grasping concepts like electrode potentials and galvanic cells. One of the fundamental tools in electrochemistry is the Nernst equation, which helps predict the potential of a cell under non-standard conditions. By measuring potentials, we can understand the energy changes that occur during reactions. Electrochemistry has many practical applications such as batteries, electroplating, and sensors.

Reduction potential represents a substance's tendency to gain electrons and be reduced. It's a vital concept in electrochemistry. The more positive the reduction potential, the greater the substance's ability to be reduced. In the context of the Nernst equation, the reduction potential under standard conditions \(E^\theta\) is impacted by temperature, ion concentration, and gas pressure. The equation is:
\[ E = E^\theta - \frac{0.0591}{n} \log \left( \frac{P_{H_2}}{[H^+]^2} \right) \]
Here, \(E^\theta\) is the standard electrode potential, \(n\) is the number of electrons involved, \(P_{H_2}\) is the pressure of hydrogen gas, and \[H^+\] is the concentration of hydrogen ions. By adjusting these variables, the potential changes, guiding us to understand whether a reaction is more or less favorable under specific conditions.

The hydrogen half-cell is an essential reference in electrochemistry. It is often chosen as a standard for measuring and comparing electrode potentials. It consists of a platinum electrode in contact with \(1 \text{atm}\) hydrogen gas and an aqueous solution with \(1 \text{M}\) \[H^+\] ions. This setup is given a standard electrode potential of 0 V. The hydrogen half-cell can either act as an anode (oxidation) or cathode (reduction) depending on the other half-cell it is paired with. For any non-standard condition, the Nernst equation helps calculate its potential. This concept plays a crucial role in understanding and predicting the behavior of other electrochemical cells.