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Yes, Ecell is the voltage created by the difference in cell potentials. For instance, in a concentration cell, the higher the difference in concentrations between the cathode and anode, the more work can be done by the voltage that is created across the electrodes.
In redox reactions (ie. Zn + 2H+ → Zn2+ + H2), the ion from the oxidation half-reaction (the anode) is a product (Zn2+), and the ion from the reduction half-reaction (the cathode) is a reactant (H+). In Le Chateliers principle, when you increase the concentration of reactants or decrease the concentration of products, the forward reaction is favored to balance out the change. So when you lower the amount of ion in the anode (lower the amount of product) and you increase the amount of ion in the cathode (increase the amount of reactant), the forward reaction is favored, and Ecell becomes more positive since the forward reaction is more likely to happen.
You can also see this mathematically with the Nernst equation. Q is the ratio of products to reactants in a concentration cell. When you increase the concentration of the products, lnQ consequently decreases and Ecell becomes a more positive value. When you increase the concentration of the reactants, lnQ increases and Ecell becomes a more negative value. A higher Ecell results in a more favorable reaction, while a lower Ecell results in a less favorable reaction. This inversely applies when you lower the concentration as well.
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