Refer to the following standard reduction half-cell potentials at 25∘C:

VO2+(aq)+Ni2+(aq)2H+(aq)++2e−e−→ →Ni(s)VO2+(aq) +H2O(l)E∘=−0.23V E∘=0.99V

An electrochemical cell is based on these two half-reactions: Oxidation:Reduction:

Ni(s)VO2+(aq,0.083M)+2H+(aq,1.1M)+e −→→Ni2+(aq,2.5M)+2e−VO2+(aq,2.5M)+H 2O(l)

Calculate the cell potential under these nonstandard concentrations.

Express the cell potential to two decimal places and include the appropriate units.

Cell potential under non standard concentration is 4.09 v

Explanation:

To solve this problem we need to use Nernst Equation because concentrations of the components of the chemical reactions are differents to 1 M (normal conditions:  1 M , 1 atm).

Nernst equation at 25ºC is:

where

E: Cell potential (non standard conditions)

= Cell potential (standard conditions)

n: Number of electrons transfered in the redox reaction

Q: Reaction coefficient (we are going to get it from the balanced chemical reaction)

For example, consider the following general chemical reaction:

aA + bB --> cC + dD

where

a, b, c, d: coefficient of balanced chemical reaction

A,B,C,D: chemical compounds in the reaction.

Using the previous general reaction, expression of Q is:

Previous information is basic to solve this problem. Let´s see the Nernst equation, we need to know: , n and Q

Let´s  calcule potential in nomal conditions  ():

1. We need to know half-reactions (oxidation and reduction), we take them from the chemical reaction given in this exercise:

Half-reactions:                               Eo (v):

+ e- -->                -0.23

 + 2 e-                   +0.99    

Balancing each half-reaction, first we are going to balance mass and then we will balance charge in each half-reaction and then charge between half-reactions:

Half-reactions:                                                                Eo (v):

2 * [ + e- --> ]                                          -0.23

1 * [  + 2 e-     ]                                         +0.99  

-------------------------------------------------------------------         -------------

2 + 2e- + Ni  --> 2 + + 2e-              0.76 v  

Then global balanced chemical reaction is:

2 + Ni  --> 2 +      

 and the potential in nomal conditions is:

= 0.76 v

Also from the balanced reaction, we got number of electons transfered:

n = 2

2. Calculate Q:

Now using previous information, we can establish Q expression and we can calculate its value:

From the exercise we know:

3. Use Nernst equation:

Finally, we replace all these results in the Nernst equation:

Cell potential under non standard concentration is 4.09 v

93.2 ml + 3920 ml = 4013 ml total  

(93.2 ml) * (2.03 m) / (4013 ml) = 0.0471 m

the volume in in l of the diluted solution would be 0.0471 m.