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Select the parameter from the list and provide all other required ones to calculate the results through this calculator using Nernst equation.
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An online Nernst equation calculator can calculate the equilibrium potential for an ion based on its concentration and charge. The standard cell potential for an electrochemical cell is determined by the difference between the two half-cell reduction potentials. A positive cell potential indicates a spontaneous reaction. This calculator provides detailed information on the Nernst equation, reduction potential, and equilibrium potential calculations.
The Nernst equation relates the electrochemical cell potential to temperature, standard cell potential, and the reaction quotient. It allows calculation of cell potentials under non-standard conditions such as specific pressures, concentrations, and temperatures.
$$ E_\text{cell} = E^0 - \frac{RT}{nF} \ln Q $$
Where:
For a reduction reaction \( ne^- + M^{n+} \rightarrow nM \), the electrode potential is:
$$ E_\text{red} = E^0_{M^{n+}/M} - \frac{2.303 RT}{nF} \log \frac{1}{[M^{n+}]} $$
Examples of equilibrium potential calculations for common ions:
Potassium \(K^+\):
$$ V_K = \frac{RT}{(+1)F} \ln \frac{[K^+]_\text{outside}}{[K^+]_\text{inside}} $$
Chloride \(Cl^-\):
$$ V_{Cl} = \frac{RT}{(-1)F} \ln \frac{[Cl^-]_\text{outside}}{[Cl^-]_\text{inside}} $$
Calcium \(Ca^{2+}\):
$$ V_{Ca} = \frac{RT}{(2)F} \ln \frac{[Ca^{2+}]_\text{outside}}{[Ca^{2+}]_\text{inside}} $$
| Ionic Species | Intracellular Concentration | Extracellular Concentration | Equilibrium Potential |
|---|---|---|---|
| Sodium (Na+) | 15 mM | 145 mM | VNa = +60.60 mV |
| Potassium (K+) | 150 mM | 4 mM | VK = −96.81 mV |
| Calcium (Ca2+) | 70 nM | 2 mM | VCa = +137.04 mV |
| Hydrogen (H+) | 63 nM (pH 7.2) | 40 nM (pH 7.4) | VH = −12.13 mV |
| Magnesium (Mg2+) | 0.5 mM | 1 mM | VMg = +9.26 mV |
| Chloride (Cl−) | 10 mM | 110 mM | VCl = −64.05 mV |
| Bicarbonate (HCO3−) | 15 mM | 24 mM | VHCO3- = −12.55 mV |
Example: Calculate the electrode potential of a 2 M solution at 300 K, with a standard electrode potential of 0.76 V for zinc:
$$ E_{Zn^{2+}/Zn} = 0.76 - \frac{2.303 \times 8.314 \times 300}{2 \times 96500} \log \frac{1}{2} \approx 0.769 \, V $$
At equilibrium, \( \Delta G = 0 \), and the Nernst equation becomes:
$$ 0 = E^0_\text{cell} - \frac{RT}{nF} \ln K_c $$
For standard temperature (298 K) and base 10 logarithms:
$$ E^0_\text{cell} = \frac{0.059 \, \text{V}}{n} \log K_c $$
Given: \(E^0(Cu^{2+}/Cu) = 0.34 V\), \(E^0(Ag^+/Ag) = 0.8 V\), measured cell potential 0.422 V, [Cu2+] = 0.1 M.
Using the Nernst equation:
$$ 0.422 = 0.46 - 0.0295 \log \frac{0.1}{[Ag^+]^2} \implies [Ag^+] \approx 0.072 \, M $$
Given standard electrode potentials:
Decreasing order of reducing power: Ca > Mg > Zn > Ni
Increasing temperature generally decreases the cell potential if other parameters remain constant.
At 298 K, simplified form:
$$ E = E^0 - \frac{0.0592}{n} \log_{10} Q $$
This online Nernst equation calculator allows quick calculation of reduction potentials, EMF, and equilibrium potentials for electrochemical cells, aiding scientists and engineers in battery design and energy optimization.
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