About This Visualization

This interactive tool demonstrates the Butler-Volmer equation for hydrogen reactions on a platinum catalyst. The same equation describes both hydrogen evolution (HER) and hydrogen oxidation (HOR):

i = i₀ [exp(α_anFη/RT) - exp(-α_cnFη/RT)]

The reactions:

• Hydrogen Evolution (η < 0): 2H⁺ + 2e⁻ → H₂ (reduction, cathodic)
• Equilibrium (η = 0): No net current flow
• Hydrogen Oxidation (η > 0): H₂ → 2H⁺ + 2e⁻ (oxidation, anodic)

Parameters: Platinum catalyst with i₀ = 1×10⁻³ A/cm², α_a = α_c = 0.5, T = 298 K

Watch the graph and schematic update in real-time as you adjust the overpotential!

Understanding the Visualization

H₂ volume rate calculation: Using Faraday's law and the molar volume at STP (22.4 L/mol):

H₂ rate = (i / 2F) × 22.4 L/mol

Why Platinum? Pt has one of the highest exchange current densities (i₀ = 10⁻³ A/cm²) for hydrogen reactions, meaning high current with minimal overpotential - ideal for both electrolyzers and fuel cells.

Real-World Applications

Water Electrolysis (Negative Overpotential):

• Process: Apply a negative overpotential to drive the hydrogen evolution reaction (2H⁺ + 2e⁻ → H₂) at the cathode.
• Purpose: Produce hydrogen gas for fuel or chemical processes by splitting water (H₂O → H₂ + ½O₂).
• Scale-up: For a 100 cm² electrode at η = -0.2 V producing ~2.4 A/cm², you'd generate approximately 2.8 liters per hour of H₂ gas at STP!
• Industrial use: Green hydrogen production using renewable electricity, ammonia synthesis, petroleum refining.
• Challenge: Minimizing overpotential reduces energy waste. Platinum's high i₀ means less overpotential needed for a given production rate.

Hydrogen Fuel Cells (Positive Overpotential):

• Process: H₂ gas is oxidized at the anode (H₂ → 2H⁺ + 2e⁻), generating electrical current with only water as a byproduct.
• Purpose: Convert chemical energy in hydrogen directly to electricity with high efficiency (~60% vs ~40% for combustion engines).
• Power output: At η = +0.1 V delivering 0.05 A/cm², a 100 cm² electrode produces 5 A of current, which at typical cell voltages (~0.7 V) gives about 3.5 watts of power.
• Applications: Vehicle propulsion (buses, cars, forklifts), backup power systems, portable electronics, spacecraft.
• Advantage: Platinum's high catalytic activity means the fuel cell can operate efficiently with minimal voltage loss (overpotential), maximizing power output.

The Exchange Current Density (i₀) is Key: A high i₀ means the catalyst can achieve large currents with small overpotentials. This is why platinum, despite being expensive, remains the gold standard - it minimizes energy waste in electrolysis and maximizes power output in fuel cells.