Standard Hydrogen Electrode Potential Shift Calculator
Our electrochemistry calculator computes hydrogen electrode potential accurately. Enter measurements for results with formulas and error analysis.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
E = -(RT/2F) * ln(1 / ([H+]^2 * P_H2))
The hydrogen electrode potential shift from the SHE standard is calculated using the Nernst equation for the half-reaction 2H+ + 2e- = H2. R is the gas constant, T is temperature in Kelvin, F is Faraday's constant, [H+] is hydrogen ion concentration in mol/L, and P_H2 is hydrogen gas pressure in atmospheres.
Worked Examples
Example 1: SHE at pH 7 (Neutral Solution)
Problem:Calculate the potential shift of a hydrogen electrode in a neutral solution (pH 7, [H+] = 1e-7 M) at 1 atm H2 and 25 C.
Solution:E_shift = -(RT/2F) ln(1/([H+]^2 * P_H2))\nE_shift = -(0.01285) ln(1/(1e-14 * 1))\nE_shift = -(0.01285)(32.236) = -0.4142 V\nOr: E = -0.05916 * pH = -0.05916 * 7 = -0.4141 V
Result:E_shift = -0.414 V (SHE at pH 7)
Example 2: Non-Standard Pressure and Concentration
Problem:Find the potential of a hydrogen electrode with [H+] = 0.01 M (pH 2) and H2 pressure = 2 atm at 25 C.
Solution:Q = 1/([H+]^2 * P_H2) = 1/(0.0001 * 2) = 5000\nE = -(0.01285) ln(5000)\nE = -(0.01285)(8.517) = -0.1094 V
Result:E = -0.109 V (shifted from 0 V standard)
Frequently Asked Questions
What is the Standard Hydrogen Electrode (SHE)?
The Standard Hydrogen Electrode is the universally accepted reference electrode for electrochemical measurements, assigned a potential of exactly 0.000 V at all temperatures. It consists of a platinum electrode coated with platinum black, immersed in a solution with hydrogen ion activity of exactly 1 (effectively 1 M H+), with hydrogen gas bubbled over it at a pressure of exactly 1 atmosphere (101.325 kPa). Under these standard conditions, the half-reaction 2H+(aq) + 2e- goes to H2(g) has E0 = 0.000 V. All other standard reduction potentials are measured relative to the SHE, making it the foundation of the electrochemical series.
What causes a potential shift from the SHE standard?
A potential shift occurs whenever the actual conditions deviate from the standard conditions of 1 M H+ and 1 atm H2. According to the Nernst equation, the hydrogen electrode potential equals E0 minus (RT/2F) times ln(1/([H+]^2 times P_H2)). Decreasing H+ concentration (increasing pH) makes the potential more negative, while increasing H+ concentration makes it more positive. Similarly, changing the hydrogen gas pressure shifts the potential. At 25 degrees Celsius, each unit increase in pH shifts the potential by approximately -59.16 mV. Temperature also affects the Nernst factor RT/F, causing additional shifts at non-standard temperatures.
How do you correct for non-standard hydrogen electrode conditions?
To correct a measured potential for non-standard SHE conditions, calculate the shift using the Nernst equation and subtract it from the measured value. The shift is E_shift = -(RT/2F) times ln(1/([H+]^2 times P_H2)). For pH-only deviations with standard pressure, this simplifies to E_shift = -(RT/F) times 2.303 times pH. For example, if measuring at pH 7 instead of pH 0, the SHE potential shifts by about -0.414 V at 25 degrees Celsius. Any potential measured against this non-standard hydrogen electrode must be corrected by adding 0.414 V to convert to the standard SHE scale. This correction is essential for accurate electrochemical measurements in non-acidic solutions.
What are alternatives to the Standard Hydrogen Electrode?
While the SHE is the theoretical standard, it is impractical for daily laboratory use because it requires a continuous supply of pure hydrogen gas. Common alternative reference electrodes include the Saturated Calomel Electrode (SCE) at +0.241 V vs SHE, the Silver-Silver Chloride electrode (Ag/AgCl in saturated KCl) at +0.197 V vs SHE, and the Mercury-Mercurous Sulfate electrode at +0.640 V vs SHE. These secondary reference electrodes are more convenient and stable. Measurements made against these electrodes can be converted to the SHE scale by adding the appropriate reference potential. The choice of reference electrode depends on the solution composition and whether chloride or mercury interference is a concern.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy