Liquid Junction Potential Calculator

Find the liquid junction potential that develops between two concentrations of the same electrolyte.

🔀 Liquid Junction Potential Calculator
-
K
mol/L
mol/L
Junction potential (Ej)
—
Step-by-step working

🔀 What is the Liquid Junction Potential Calculator?

This liquid junction potential calculator finds the small voltage, Ej, that develops at the boundary between two concentrations of the same electrolyte, caused by the cation and anion diffusing across that boundary at different rates. Enter the cation's transference number and the two concentrations to see the resulting junction potential.

Liquid junction potentials matter in reference electrode design, pH meter calibration, and any precision electrochemical cell measurement, because they add an uncontrolled offset to the measured cell voltage. Analytical chemists selecting a salt bridge electrolyte, or instrument designers building a reference junction, need to know how large this effect will be for their chosen ions and concentrations.

A common misconception is that junction potentials are always negligible. While they are typically small (a few millivolts to a few tens of millivolts), for precision measurements like pH near the extremes of the scale, or for cells where the junction electrolyte differs significantly from the sample, this "small" voltage can be a meaningful source of error.

This calculator is useful for analytical and physical chemistry students, electrochemists, and instrument designers who need a fast, correct junction potential estimate without deriving the transference-number formula from the general Henderson equation by hand.

📐 Formula

Ej  =  −(RT/F) × (2t+ − 1) × ln(C2/C1)
R = 8.314 J/(mol·K), T = temperature, K
F = 96,485 C/mol (Faraday constant)
t+ = cation transference number (t− = 1 − t+)
C1, C2 = electrolyte concentrations on each side of the junction, mol/L
Simplified Henderson equation for two concentrations of the same 1:1 electrolyte (per standard electrochemistry references)
Example: t+=0.49, C1=0.1, C2=0.01 mol/L, T=298.15K: Ej ≈ −1.183 mV

📖 How to Use This Calculator

Steps

1
Enter the cation transference number - Enter t+, the fraction of current carried by the cation in this electrolyte, between 0 and 1.
2
Enter the two concentrations - Enter C1 and C2, the concentrations of the same electrolyte on each side of the junction.
3
Enter temperature - Enter the temperature in kelvin, or use the 298.15 K default for room temperature.
4
Read the junction potential - See the calculated junction potential in millivolts, along with the full step-by-step working.

💡 Example Calculations

Example 1 - KCl salt bridge junction (near-matched mobilities)

1
t+ = 0.49 (KCl), C1 = 0.1 mol/L, C2 = 0.01 mol/L, T = 298.15 K
2
Ej = −(8.314×298.15/96485) × (2×0.49−1) × ln(0.01/0.1) = −1.183 mV
3
Because t+ is close to 0.5, the junction potential stays very small
Ej = −1.183 mV
Try this example →

Example 2 - NaCl junction with the same tenfold dilution

1
t+ = 0.396 (NaCl), C1 = 0.1 mol/L, C2 = 0.01 mol/L, T = 298.15 K
2
Ej = −(8.314×298.15/96485) × (2×0.396−1) × ln(0.01/0.1) = −12.305 mV
3
The larger deviation of t+ from 0.5 produces a much bigger junction potential than KCl
Ej = −12.305 mV
Try this example →

Example 3 - HCl junction with reversed concentration gradient

1
t+ = 0.821 (HCl, highly mobile H+), C1 = 0.01 mol/L, C2 = 0.1 mol/L, T = 298.15 K
2
Ej = −(8.314×298.15/96485) × (2×0.821−1) × ln(0.1/0.01) = −37.978 mV
3
HCl's very unequal ion mobilities (H+ far more mobile than Cl-) produce the largest junction potential of the three examples
Ej = −37.978 mV
Try this example →

❓ Frequently Asked Questions

What is a liquid junction potential?+
A liquid junction potential is a small voltage that develops at the boundary between two electrolyte solutions of different concentration or composition, caused by the cation and anion diffusing across the boundary at different rates due to their different mobilities.
How do you calculate liquid junction potential?+
For two concentrations of the same 1:1 electrolyte, the junction potential is Ej = -(RT/F)(2t+ - 1)ln(C2/C1), where t+ is the cation transference number, R is the gas constant, T is temperature, and F is the Faraday constant.
Why does the junction potential depend on the transference number?+
The transference number measures what fraction of current is carried by the cation versus the anion. If t+ differs from 0.5, the cation and anion cross the concentration boundary at different rates, separating charge and creating a small electric field, which is the junction potential.
What is a salt bridge and why does it use KCl?+
A salt bridge is a tube of concentrated electrolyte solution connecting two half-cells to complete the circuit while minimizing liquid junction potential. Saturated KCl is the standard choice because K+ and Cl- have nearly equal ionic mobilities, keeping the junction potential very small.
Can the liquid junction potential be exactly zero?+
Yes, if the cation and anion transference numbers are exactly equal (t+ = t- = 0.5), the junction potential formula gives zero, since (2t+ - 1) becomes zero. This is why ions like K+ and Cl-, with nearly matched mobilities, are chosen for salt bridges.
Does the sign of the junction potential matter?+
Yes. The sign shows which solution the junction potential effectively favors, and it flips if you swap the concentrations C1 and C2, since ln(C2/C1) changes sign. Getting the concentration labeling consistent with your physical setup is essential for correct sign interpretation.
Why do junction potentials matter in pH measurement?+
A pH electrode's reference junction develops its own junction potential wherever it contacts the sample solution. Because this potential is included in the measured voltage along with the pH-dependent signal, an unstable or poorly controlled junction potential directly degrades pH measurement accuracy.
What is the Henderson equation?+
The Henderson equation is the general formula for liquid junction potential between two arbitrary electrolyte solutions, accounting for every ion's concentration and mobility on each side. The transference-number formula used here is the simplified special case for two concentrations of the same single 1:1 electrolyte.
How large is a typical liquid junction potential?+
Typical liquid junction potentials range from about 1 mV to a few tens of millivolts, depending on the transference number imbalance and the concentration ratio. This is small compared to a full cell voltage, but significant for precision electrochemical and pH measurements.
Does temperature affect liquid junction potential?+
Yes, the junction potential scales directly with absolute temperature through the RT/F prefactor, so a higher temperature produces a proportionally larger junction potential for the same transference number and concentration ratio.
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What is a liquid junction potential?

A liquid junction potential is a small voltage that develops at the boundary between two electrolyte solutions of different concentration or composition, caused by the cation and anion diffusing across the boundary at different rates due to their different mobilities.

How do you calculate liquid junction potential?

For two concentrations of the same 1:1 electrolyte, the junction potential is Ej = -(RT/F)(2t+ - 1)ln(C2/C1), where t+ is the cation transference number, R is the gas constant, T is temperature, and F is the Faraday constant.

Why does the junction potential depend on the transference number?

The transference number measures what fraction of current is carried by the cation versus the anion. If t+ differs from 0.5, the cation and anion cross the concentration boundary at different rates, separating charge and creating a small electric field, which is the junction potential.

What is a salt bridge and why does it use KCl?

A salt bridge is a tube of concentrated electrolyte solution connecting two half-cells to complete the circuit while minimizing liquid junction potential. Saturated KCl is the standard choice because K+ and Cl- have nearly equal ionic mobilities, keeping the junction potential very small.

Can the liquid junction potential be exactly zero?

Yes, if the cation and anion transference numbers are exactly equal (t+ = t- = 0.5), the junction potential formula gives zero, since (2t+ - 1) becomes zero. This is why ions like K+ and Cl-, with nearly matched mobilities, are chosen for salt bridges.

Does the sign of the junction potential matter?

Yes. The sign shows which solution the junction potential effectively favors, and it flips if you swap the concentrations C1 and C2, since ln(C2/C1) changes sign. Getting the concentration labeling consistent with your physical setup is essential for correct sign interpretation.

Why do junction potentials matter in pH measurement?

A pH electrode's reference junction develops its own junction potential wherever it contacts the sample solution. Because this potential is included in the measured voltage along with the pH-dependent signal, an unstable or poorly controlled junction potential directly degrades pH measurement accuracy.

What is the Henderson equation?

The Henderson equation is the general formula for liquid junction potential between two arbitrary electrolyte solutions, accounting for every ion's concentration and mobility on each side. The transference-number formula used here is the simplified special case for two concentrations of the same single 1:1 electrolyte.

How large is a typical liquid junction potential?

Typical liquid junction potentials range from about 1 mV to a few tens of millivolts, depending on the transference number imbalance and the concentration ratio. This is small compared to a full cell voltage, but significant for precision electrochemical and pH measurements.

Does temperature affect liquid junction potential?

Yes, the junction potential scales directly with absolute temperature through the RT/F prefactor, so a higher temperature produces a proportionally larger junction potential for the same transference number and concentration ratio.

📌 Quick Tips

💡A liquid junction potential arises whenever two electrolyte solutions of different composition or concentration touch, because the cation and anion diffuse across the boundary at different rates.
💡If the cation and anion have equal transference numbers (t+ = t- = 0.5), the junction potential is exactly zero, since neither ion outruns the other.
💡A saturated KCl salt bridge is the standard way to minimize junction potential in real electrochemical cells, because K+ and Cl- have nearly equal mobilities, keeping the junction potential small no matter what solutions it connects.
💡The sign of the junction potential flips if you swap which concentration is called C1 versus C2, since it depends on the direction of the concentration gradient.
💡Junction potentials are typically a few millivolts to a few tens of millivolts, small compared to typical cell voltages, but large enough to matter in precision pH and reference electrode measurements.