Step 1: Understanding the Tafel Equation
The Tafel equation is an empirical relationship that describes how the rate of an electrochemical reaction (expressed as current density) is related to the overpotential (extra voltage required beyond the equilibrium potential) at the electrode. It is especially used for reactions involving hydrogen evolution.
Tafel equation:
\begin{equation}
\eta = a + b \log i
\end{equation}
where: \quad
\( \eta \) = overpotential (in volts),
\( i \) = current density (in A/m\(^2\)),
\( a \) and \( b \) = Tafel constants specific to the system and electrode.
Step 2: Relevance to Hydrogen Overvoltage
Tafel equation is most commonly applied to describe the kinetics of the hydrogen evolution reaction at the cathode, where hydrogen gas is generated. The equation links hydrogen overvoltage (extra potential required for hydrogen gas evolution) with the current density.
Step 3: Evaluating the Options
- (A) Oxygen overvoltage: While similar in concept, Tafel equation is not specifically defined for it.
- (B) Correct: Hydrogen overvoltage and current density are directly related using the Tafel equation.
- (C) Decomposition voltage: This is unrelated to Tafel analysis.
- (D) Cell voltage includes multiple contributions; Tafel specifically relates overpotential to current density.
Conclusion: Tafel equation specifically correlates hydrogen overvoltage with current density.