| \[C{{u}^{+}}(aq)\] is unstable in solution and undergoes simultaneous oxidation and reduction according to the reaction: |
| \[2C{{u}^{+}}(aq)C{{u}^{2+}}(aq)+Cu(s)\] |
| choose correct \[{{E}^{o}}\] for above reaction if \[E_{C{{u}^{2+}}/Cu}^{0}=0.34\,V\] and \[E_{C{{u}^{2+}}/C{{u}^{+}}}^{0}=0.15\,V\] [AIPMT 2000] |
A) \[\,0.38\text{ }V\]
B) \[+\text{ }0.49\text{ }V\]
C) \[+\text{ }0.38\text{ }V\]
D) \[-\text{ }0.19\text{ }V\]
Correct Answer: C
Solution :
| [c] From given data \[(\text{From}\,\,\Delta {{G}^{o}}=-n{{E}^{o}}F)\] |
| (i) \[Cu(s)\xrightarrow[{}]{{}}C{{u}^{2+}}(aq)+2{{e}^{-}}\] |
| \[\Delta G_{1}^{o}=-2\times (-0.34)\times F\] |
| (ii) \[C{{u}^{2+}}(aq)+{{e}^{-}}\xrightarrow[{}]{{}}C{{u}^{+}}(aq)\]\[\Delta G_{2}^{o}=-1\times (0.15)\,\,F\] |
| On addition |
| \[Cu(s)\xrightarrow[{}]{{}}C{{u}^{2+}}(aq)+{{e}^{-}},\,\,\,\Delta G_{3}^{o}=-1\times {{E}^{o}}\times F\] |
| \[\Delta G_{3}^{o}=\Delta G_{1}^{o}+\Delta G_{2}^{o}\] |
| \[=(-2\times -0.34\times F)+(-1\times 0.15\times F)\] |
| \[=\,+\,0.68\,F-0.15\,F=0.53\,F\] |
| or \[{{E}^{o}}=-0.53\,V\] |
| Reaction \[2C{{u}^{+}}(aq)\rightleftharpoons C{{u}^{2+}}(aq)+Cu(s)\,{{E}^{o}}=?\] |
| So, \[C{{u}^{2+}}(aq)+{{e}^{-}}\rightleftharpoons Cu(s),\,{{E}^{o}}=+0.53\,V\] |
| \[\frac{C{{u}^{+}}(aq)C{{u}^{2+}}(aq)+{{e}^{-}};\,\,\,\,{{E}^{o}}=-0.15V}{2C{{u}^{+}}(aq)C{{u}^{2+}}(aq)+Cu(s),\,{{E}^{o}}=+0.38V}\] |
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