0.059156
V
100
4.60517
-11.415
kJ/mol
0.01284562
V
0.059156
V
100
4.60517
-11.415
kJ/mol
0.01284562
V
The Concentration Cell Calculator computes the potential generated by an electrochemical cell where both electrodes are identical but immersed in solutions of different concentrations. Since both half-reactions involve the same species, the standard cell potential is zero (E° = 0), and the entire driving force comes from the concentration difference as described by the Nernst equation. The cell operates to equalize concentrations: the metal dissolves from the electrode in the dilute solution while ions deposit on the electrode in the concentrated solution. Concentration cells demonstrate entropy-driven electrochemistry and are the principle behind many practical applications including ion-selective electrodes, pH meters, reference electrode bridges, and biological membrane potentials.
For a concentration cell with identical electrodes (E° = 0), the Nernst equation simplifies to:
$$E = \frac{RT}{nF} \ln \frac{C_1}{C_2}$$
where C₁ is the higher concentration, C₂ is the lower concentration, R = 8.314 J/(mol·K), T is the temperature in kelvin, n is the number of electrons transferred, and F = 96,485 C/mol.
At 25°C this becomes:
$$E = \frac{0.05916}{n} \log_{10} \frac{C_1}{C_2}$$
The Gibbs free energy is:
$$\Delta G = -nFE = -RT \ln \frac{C_1}{C_2}$$
The cell potential is always positive when C₁ > C₂ because the spontaneous direction equalizes concentrations (increasing entropy). For every 10-fold concentration ratio with n = 2, the potential is approximately 29.6 mV at 25°C.
A larger concentration ratio produces a higher cell potential. The potential is logarithmic — a 10-fold ratio gives the same voltage increment as going from 100-fold to 1000-fold. For n = 1 at 25°C, each tenfold change gives 59.2 mV (the basis of pH measurement). The negative ΔG confirms the spontaneous drive to equalize concentrations. In practice, the actual potential may be slightly lower due to activity coefficient differences and junction potentials. As the cell operates and concentrations equalize, the potential gradually drops to zero.
Inputs
Results
E = (8.314 × 298.15)/(2 × 96485) × ln(100) = 0.01285 × 4.605 = 0.0592 V (59.2 mV). The two-order-of-magnitude concentration difference generates a small but measurable voltage. ΔG = −11.42 kJ/mol.
Inputs
Results
E = (8.314 × 310.15)/(1 × 96485) × ln(100) = 0.02671 × 4.605 = 0.1231 V. With n = 1 (silver), the potential is doubled compared to n = 2 at the same ratio. The higher temperature (body temp) slightly increases the voltage.
A concentration cell is an electrochemical cell with identical electrodes immersed in solutions of the same electrolyte at different concentrations. The cell potential arises entirely from the concentration difference, not from different electrode materials.
Since both electrodes undergo the same half-reaction, E°cathode = E°anode, and E°cell = E°cathode − E°anode = 0. The driving force comes solely from the thermodynamic tendency to equalize concentrations (entropy increase).
The electrode in the dilute solution is the anode. Metal dissolves from it (oxidation) to increase the ion concentration in the dilute solution. The electrode in the concentrated solution is the cathode, where ions deposit (reduction) to decrease concentration.
A pH electrode is essentially a concentration cell for H⁺ ions. The glass electrode has a known internal H⁺ concentration, and the unknown external H⁺ concentration creates a measurable voltage: E = (0.05916/1) × log(C₁/C₂) = 59.16 mV per pH unit.
The logarithmic relationship means you need very large concentration ratios for significant voltage. A 10⁶:1 ratio with n = 2 gives only ~177 mV. Practical limits include electrolyte solubility, activity coefficient deviations, and junction potentials.
Higher temperature increases the cell potential proportionally (E ∝ T) since the RT/nF factor grows. At 100°C, the potential is about 25% higher than at 25°C for the same concentration ratio.
Nerve cells and muscle cells maintain ion concentration gradients (Na⁺, K⁺, Ca²⁺) across membranes. The resulting Nernst potential drives neural signaling. The resting membrane potential (~−70 mV) is essentially a concentration cell potential.
Yes, and for accurate results you should. Activities account for ion-ion interactions in non-ideal solutions. The equation becomes E = (RT/nF)ln(a₁/a₂). Activity coefficients approach 1 only in very dilute solutions.
When C₁ = C₂, the ratio equals 1, ln(1) = 0, and E = 0. The cell reaches equilibrium with no further net reaction. This is the expected endpoint of any concentration cell.
Yes, they are used in oxygen sensors (fuel cells), corrosion monitoring (differential aeration cells are a type of concentration cell), reference electrode calibration, and electroanalytical chemistry for trace metal detection.
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