Engineering & Science
Randles-Sevcik Equation: Cyclic Voltammetry Peak Current (ip) & Reversible Peak Split
Calculate Nernstian cyclic voltammetry peak current ip = 2.686e5 * n^1.5 * A * SQRT(D) * C0 * SQRT(v) at 25 °C in microamps and reversible peak-to-peak separation Delta_Ep = 59.2 / n mV.
Distinguish diffusion-controlled redox couples from surface-adsorbed species!
In Cyclic Voltammetry (CV), sweeping electrode potential linearly at scan rate v (V/s) produces a characteristic duck-shaped voltammogram with peak current ip! At 25 °C (298.15 K), the Randles-Sevcik equation for a freely diffusing, electrochemically reversible redox couple in CGS units is ip = 2.686e5 * (n^1.5) * A * SQRT(D) * C0 * SQRT(v) Amperes, where A is in cm^2, D is in cm^2/s, C0 is bulk concentration in mol/cm^3 (= M / 1,000), and v is in V/s!
Notice the diagnostic SQRT(v) scaling: quadrupling scan rate from v = 0.10 V/s to v = 0.40 V/s DOUBLES peak current ip (81.96 uA -> 163.91 uA) for freely diffusing species, whereas surface-adsorbed monolayers scale linearly with v! Simultaneously, a reversible Nernstian couple exhibits scan-rate-independent anodic-to-cathodic peak separation Delta_Ep = |Epa - Epc| = 59.2 / n mV at 25 °C.
| Scan Rate v (5 mM, n=1, A=0.07 cm^2) | Peak Current ip (uA) | Reversible Peak Split Delta_Ep | Mechanistic Signature |
|---|---|---|---|
| v = 0.10 V/s (100 mV/s) | 81.96 uA | 59.2 mV (for n = 1) | Baseline Nernstian diffusion |
| v = 0.40 V/s (4x faster scan) | 163.91 uA (2.0x higher!) | 59.2 mV (Invariant if reversible!) | Linear ip vs SQRT(v) confirms diffusion |
| Two-Electron Couple (n = 2) | 2.828x higher (2^1.5) | 29.6 mV (59.2 / 2) | n^1.5 sensitivity in Randles-Sevcik |
Randles-Sevcik Reversible CV Peak Current ip at 25 °C (Microamperes, uA)
Evaluates 1e6 * 268600 * (n^1.5) * A_cm2 * SQRT(D_cm2_s) * C0_mol_cm3 * SQRT(v_V_s).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 < 0, B6 <= 0), "Invalid CV Parameters", ROUND(1000000 * 268600 * (B2 ^ 1.5) * B3 * SQRT(B4) * B5 * SQRT(B6), 2))Theoretical Reversible Peak-to-Peak Separation Delta_Ep at 25 °C (mV)
Computes 59.2 / n mV for an uncompensated-resistance-free Nernstian electron transfer.
=IF(B2 <= 0, "Invalid CV Parameters", ROUND(59.2 / B2, 1))Try the example
Use the original values or change them to test your understanding.