Similarity between Ecell and equilibrium constant Kc

$$\ce{Cu^{2+} + Zn<=>Zn^{2+} + Cu}$$ 


$K\_c=1.9\*10^{37}$


$E\_{cell}=1.1V$


I know that they both suggest that the forward reaction is going to completion but can someone please tell me a bit more about what both these values are suggesting and how these two values concord with each other.


Also, many books quote such reactions in only one direction and gives a value for $E\_{cell}$. However, isn't $E\_{cell}$ just another way of illustrating the condition of an equilibrium (i.e. in which direction the reaction would occur if left alone)... so how can a one way reation be shown




$E^\circ\_{cell}$ and $K\_c$ are related. Both indicate which direction of the reaction is spontaneous. Both tell you something about the position of equilibrium.


However, $E^\circ\_{cell}$ is a directly measurable value. If you construct an [electrochemical cell](http://en.wikipedia.org/wiki/Electrochemical_cell) as using a zinc electrode immersed in a 1.0 M solution of say zinc chloride and a copper electrode immersed in a 1.0 M solution of copper (II) chloride with a salt bride of sodium chloride connecting the solutions, a voltmeter connected between the two electrodes will read the value of $E^\circ\_{cell}$, at least initially. The voltage will change as the reaction progresses, but the initial voltageis $E^\circ\_{cell}$ which is defined for standard conditions of 1.0 M concentration, 1 bar of pressure, and 25 $^\circ$C.


$$\ce{Zn|ZnCl2}(1.0 \text{ M})\parallel\ce{CuCl2}(1.0 \text{ M})|\ce{Cu} \ \ \ \ E^\circ\_{cell}=1.1\text{ V}$$


The relationship between $E^\circ\_{cell}$ and $K\_c$ is the [Nernst Equation](http://en.wikipedia.org/wiki/Nernst_equation). Note the use of both $E^\circ\_{cell}$, the **standard** cell potential and $E\_{cell}$, the **observed** cell potential under other conditions. The remainder of the alphabet soup is defined below.
$$E\_{cell}=E^\circ\_{cell}-\frac{RT}{zF}\ln{Q}$$


* $E^\circ\_{cell}$ - Standard cell potential
* $E\_{cell}$ - nonstandard cell potential at other conditions
* $R$ - the [ideal gas constant](http://en.wikipedia.org/wiki/Universal_gas_constant) (which appears here because it is equal to [Avogadro's number](http://en.wikipedia.org/wiki/Avogadro_constant) times [Boltzmann's constant](http://en.wikipedia.org/wiki/Boltzmann_constant)
* $T$ - the temperature in kelvins
* $z$ - the number of **moles** of electrons being transferred in this redox process. If we wanted to use the number of individual electrons, then we would need to replace $R$ with $k\_B$
* $F$ - [Faraday's constant](http://en.wikipedia.org/wiki/Faraday_constant)
* $Q$ - the [reaction quotient](http://en.wikipedia.org/wiki/Reaction_quotient)


We need to use $Q$ in the Nernst equation, because this equation can relate the cell potential to any range of conditions, not just equilibrium. 



> 
> At equilibrium $Q = K\_c$ and $E\_{cell} = 0 \text{ V}$ (there is no net change in the reaction composition, so there is no potential difference across the half-cells.
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Thus, the Nernst Equation becomes:


$$0=E^\circ\_{cell}-\frac{RT}{zF}\ln{K\_c}$$
$$E^\circ\_{cell} = \frac{RT}{zF}\ln{K\_c}$$



> 
> To determine the values of $E^\circ\_{cell}$ and $K\_c$ for the reverse reaction...
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For $E^\circ\_{cell}$:


$$E^\circ\_{cell} = -E^\circ\_{rev}$$


For $K\_c$


$$K\_{rev} = \frac{1}{K\_c}$$


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