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For the electrochemical cell, Mg(s)|Mg...

For the electrochemical cell,
`Mg(s)|Mg^(2+) (aq. 1M)||Cu^(2+) (aq. 1M)|Cu(s)`
the standard emf of the cell is 2.70 V at 300 K. When the concentration of `Mg^(2+)` is chaged to x M, the cell potential changes to 2.67 V at 300 K. The value of x is ________ .
(Given `F/R=11500 kV^(-1)`. where F is the Faraday constant and R is the gas constant, ln (10) = 2.30)

Text Solution

Verified by Experts

The correct Answer is:
3
`E = E^(@) - (0.059)/(2) "log" ([Mg^(2+)])/([Cu^(2+)])`
`2.651 = 2.71 - (0.059)/(2)"log" (0.1)/((1. 0 xx 10^(-x)))`
`2.651 - 2.71 = - (0.059)/(2) "log" (0.1)/((1.0 xx 10^(-x)))`
`2 = log 0.1 - log (1.0 xx 10^(-x))`
`2 = -1 - log (1.0 xx 10^(-x))`
`log (1.0 xx 10^(-x)) = -3`
`log 1.0 - x log 10 = - 3`
`therefore - x = - 3`
or x = 3
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