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I've heard that cell potential is an intensive property. However, we know that an intensive property does not depend on number of moles, mass, or concentration of the substance involved. However, when we calculate cell potential using the Nernst equation, we definitely have to use the concentration of the substances. Therefore, how is cell potential categorized as an intensive property?

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    $\begingroup$ An intensive property does not depend on the total mass, or total volume. But it may change with the concentration. $\endgroup$
    – Maurice
    Jul 5 '20 at 10:24
  • $\begingroup$ Welcome to Chemistry! Please note that the proper term for "number of moles" is amount of substance. The former would be the same as referring to the mass as "number of kilograms". $\endgroup$ Jul 9 '20 at 14:45
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The simple mental test for the property being intensive or extensive is, what happens if you make the all the system twice as big.

If the property remains the same, like concentration, or the cell electromotoric force ( voltage ), it is intensive. If you use the double volume of the solution, its concentration is still the same. The open voltage of Li-ion cell does not change with the size. You can notice from the Nernst equation the potential depends on concentration, but not on the mass nor volume.

Intensive properties must not depend on extensive properties, unless they mutually cancel their extensiveness, forming an intermediate intensive property, like e.g. specific conductivity: $$\kappa_\mathrm{intensive} = const_\mathrm{intensive} \cdot \left( \frac{m_\mathrm{extensive} }{ V_\mathrm{extensive}}\right)_\mathrm{intensive} $$

If the property changes additively, like mass, energy, heat capacity, it is extensive. The cell capacity does change with the mass of the active material and electrolyte. Extensive properties may depend on any other properties.

If the property changes, but not additively with the system scaling, it is neither intensive neither extensive.

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