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Question: Calculate the emf of the following cell at \[{{25}^{\circ }}C\]. \[Ag\left( s \right)|A{{g}^{+}}\l...

Calculate the emf of the following cell at 25∘C{{25}^{\circ }}C.

\right)|Cu\left( s \right)$$ $$\left[ E_{cell}^{0}=+0.46Vand\log {{10}^{n}}=n \right]$$
Explanation

Solution

The voltage or electric likely distinction over the terminals of a cell when no flow is drawn from it. The electromotive power (emf) is the whole of the electric potential contrasts created by a detachment of charges (electrons or particles) that can happen at each stage limit (or interface) in the cell.

Step by step answer: The most extreme potential contrast which can be estimated for a given cell is known as the electromotive power, curtailed emf and spoke to by the image E. By show, when a cell is written in shorthand documentation, its emf is given a positive worth if the cell reaction is unconstrained.
Here silver goes through oxidation by loss of electrons, consequently going about as anode. Copper goes through decreases by increase of electrons and subsequently goes about as cathode.
Cathode: −CCl2++2e−→CCl-CC{{l}^{2+}}+2{{e}^{-}}\to CCl
Anode: −2Ag→2Ag++2e−-2Ag\to 2A{{g}^{+}}+2{{e}^{-}}

Cell reaction- Cu2++2Ag→2Ag++CuC{{u}^{2+}}+2Ag\to 2A{{g}^{+}}+Cu
Ecell=Ecell0−0.0591nlog⁡[Ag+]2[Cu2+]{{E}_{cell}}=E_{cell}^{0}-\frac{0.0591}{n}\log \frac{{{\left[ A{{g}^{+}} \right]}^{2}}}{\left[ C{{u}^{2+}} \right]}
Ecell0=E_{cell}^{0}=standard electrode potential =+0.46V=+0.46V

Ecell0=+0.46V ⇒Ecell=0.46V−0.05912log⁡[Ag+]2[Cu2+] ⇒Ecell=0.46V−0.05912log⁡[10−3]2[10−1] ⇒Ecell=+0.61V E_{cell}^{0}=+0.46V \\\ \Rightarrow {{E}_{cell}}=0.46V-\frac{0.0591}{2}\log \frac{{{\left[ A{{g}^{+}} \right]}^{2}}}{\left[ C{{u}^{2+}} \right]} \\\ \Rightarrow {{E}_{cell}}=0.46V-\frac{0.0591}{2}\log \frac{{{\left[ {{10}^{-3}} \right]}^{2}}}{\left[ {{10}^{-1}} \right]} \\\ \Rightarrow {{E}_{cell}}=+0.61V \\\

Additional Information: A positive worth shows the oxidation-decrease response is an unconstrained response. That implies without the assistance of an outside office. On the off chance that it is a negative worth, it implies just the opposite response is unconstrained. It implies oxidation at the cathode and decreases at the anode.

Note: Emf is regularly estimated in units of volts, equal in the meter–kilogram–second framework to one joule for each coulomb of electric charge. In the electrostatic units of the centimeter–gram–second framework, the unit of electromotive power is the statvolt, or one erg for each electrostatic unit of charge.