Cell Voltage (Non-Standard)
Electrochemistry context
This page focuses on a practical question: What cell voltage is expected under real operating conditions? It applies Nernst directly to either the overall cell reaction or both half-cells.
\[ E_{\mathrm{cell}} = E^\circ_{\mathrm{cell}} - \frac{RT}{nF}\ln Q \]
Typical use cases: galvanic cells, battery operating-point estimation, concentration cells, and measured-vs-theoretical voltage checks.
Note: This is a contextual entry page built on top of Nernst methodology with explicit cell-voltage focus.
General calculator: Nernst Equation
Formulas (MathJax)
\[ E_{\mathrm{cell}} = E^\circ_{\mathrm{cell}} - \frac{RT}{nF}\ln Q \]
\[ E_{\mathrm{cell}} = E_{\mathrm{cathode}} - E_{\mathrm{anode}} \]
\[ E_{\mathrm{cell}} = \left(E^\circ_{\mathrm{C}} - \frac{RT}{n_{\mathrm{C}}F}\ln Q_{\mathrm{C}}\right) - \left(E^\circ_{\mathrm{A}} - \frac{RT}{n_{\mathrm{A}}F}\ln Q_{\mathrm{A}}\right) \]
Legend
- \(E_{\mathrm{cell}}\): cell voltage [V]
- \(E^\circ_{\mathrm{cell}}\): standard cell voltage [V]
- \(E_{\mathrm{cathode}}, E_{\mathrm{anode}}\): half-cell potentials [V]
- \(R\): gas constant \(8.314\,\mathrm{J\,mol^{-1}\,K^{-1}}\)
- \(T\): temperature [K]
- \(n\): number of transferred electrons
- \(F\): Faraday constant \(96485\,\mathrm{C\,mol^{-1}}\)
- \(Q\): reaction quotient
Worked examples
Example 1 (overall reaction):
\(E^\circ_{\mathrm{cell}}=1.10\,V\), \(n=2\), \(T=298.15\,K\), \(Q=10\)
\(E_{\mathrm{cell}}\approx1.070\,V\)
\(E^\circ_{\mathrm{cell}}=1.10\,V\), \(n=2\), \(T=298.15\,K\), \(Q=10\)
\(E_{\mathrm{cell}}\approx1.070\,V\)
Example 2 (half-cell model):
\(E^\circ_C=0.34\,V\), \(E^\circ_A=-0.76\,V\), \(Q_C=Q_A=1\)
\(E_{\mathrm{cell}}\approx1.10\,V\)
\(E^\circ_C=0.34\,V\), \(E^\circ_A=-0.76\,V\), \(Q_C=Q_A=1\)
\(E_{\mathrm{cell}}\approx1.10\,V\)
Deeper insight
Why does voltage drop at high Q?
As reaction quotient increases, the correction term \(\frac{RT}{nF}\ln Q\) grows, reducing \(E_{\mathrm{cell}}\) relative to \(E^\circ_{\mathrm{cell}}\).
Practical interpretation
In real systems, concentration drift, temperature changes, and polarization influence delivered voltage. This page gives the thermodynamic baseline for evaluating measurements.
Crosslink: For full Nernst workflows including back-calculation of \(Q\), use the Nernst Equation Calculator.
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