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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:
A
`underset(E_(cell)^(o)=2.70)((10)Mg(s)+)Cu^(2+)underset(E_(cell)=2.67)((aq)to)Mg^(2+)undersetunderset(Cu^(2+)=1M)(Mg^(2+)=xM)((aq)+Cu(s))`
`E_(cell)=E_(cell)^(o)-(RT)/(nF)ln" "x`
`2.67=2.70-(RT)/(2F)ln" "x`
`-0.03=-(Rxx300)/(2F)xxln" "x`
ln `x=(0.03xx2)/(300)xx(F)/(R)=(0.03xx2xx11500)/(300xx1)`
ln `x=2.30=ln(10)impliesx=10`
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Knowledge Check

  • For the cell reaction Zn_((s)) + Cu_("0.1 M")^(2+) to Zn_(0.1 M)^(2+) + Cu_((s)) if the standard EMF of the cell is E^(@) , then

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    C
    `E = E^(@)`
    D
    `E le E^(@)`

  • For the given cell, Mg | Mg^(2+) || Cu^(2+) | Cu

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    C
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    D
    Cu is the oxidising agent.

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