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In an electrode potential with a salt bridge and high resistant voltmeter, does the emf change over time as the reactions occur?

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Yes. Remember that the standard electrode potentials are for 298K at 1 atm of pressure and 1N concentration of reagents. As the concentration of ions to be reduced at the cathode decreases the emf will fall as well and is reflected in the Nernst equation.$$E_{cell} = E^\circ_{cell} - \frac{RT}{nF}ln(Q)$$

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    $\begingroup$ what about the mercury button cells their emf is independent of concentration of ions so theoritically its constant 1.35V but varies 1 % over shelf life. $\endgroup$ Jun 13, 2017 at 4:41
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    $\begingroup$ @Physicsapproval The mercury button cells have solid products and reactants, therefore, Q is a constant 1 and emf does not change. $\endgroup$
    – A.K.
    Jun 13, 2017 at 21:45

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