# A standard voltaic cell is constructed using Cu metal in 1.0 M Cu(NO3)2(aq) and an unknown metal in a 1.0 M solution of its nitrate salt. The cell voltage is 0.47 V when the Cu half-cell is the...

A standard voltaic cell is constructed using Cu metal in 1.0 M Cu(NO3)2(aq) and an unknown metal in a 1.0 M solution of its nitrate salt. The cell voltage is 0.47 V when the Cu half-cell is the cathode. What is the standard
reduction potential of the unknown metal? [E°Cu = 0.34 V]

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We can construct the electrochemical cell notation as:

`X_(s)|X^(2+) _(aq,1.0M) ||Cu^(2+) _(aq, 1.0M)|Cu_(s) `

`E^o _(cell) = E^o _(Cu^(2+) -> Cu) - E^o _(X -> X^(2+)) `

From the Nernst equation:

`E_(cell) = E^(o) _(cell) - (0.05196 V)/(n) log Q`

`E_(cell) = E^(o) _(cell) - (0.05196 V)/(n) * log [1.0]/[1.0]`

`0.47 = E^(o) _(cell) - (0.05196 V)/(2) (0)`

`0.47 =E^(o) _(cell) - 0 `

`E^(o) _(cell) = 0.47 `

Finally, the standard reduction potential of the unknown is:

`0.47 = 0.34 - E^o _(X -> X^(2+)) `

`E^o _(X -> X2+) = 0.47 - 0.34 `

`E^o _(X -> X2+) = -0.13 V -> answer`

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