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A button cell used in watches functions as following: Zn(s)+Ag2O(s)+H2O(l)2Ag(s)+Zn2+(aq)+2OH(aq)\text{Zn}(s) + \text{Ag}_2\text{O}(s) + \text{H}_2\text{O}(l) \rightleftharpoons 2\text{Ag}(s) + \text{Zn}^{2+}(aq) + 2\text{OH}^-(aq) If half-cell potentials are: Zn2+(aq)+2eZn(s)E=0.76 V\text{Zn}^{2+}(aq) + 2e^- \rightarrow \text{Zn}(s) \quad E^\circ = -0.76 \text{ V} Ag2O(s)+H2O(l)+2e2Ag(s)+2OH(aq)E=0.34 V\text{Ag}_2\text{O}(s) + \text{H}_2\text{O}(l) + 2e^- \rightarrow 2\text{Ag}(s) + 2\text{OH}^-(aq) \quad E^\circ = 0.34 \text{ V} The cell potential will be:

A

0.42 V

B

0.84 V

C

1.34 V

D

1.10 V

Step-by-Step Solution

In the given cell reaction, zinc (Zn\text{Zn}) is oxidized to Zn2+\text{Zn}^{2+} and acts as the anode, while silver oxide (Ag2O\text{Ag}_2\text{O}) is reduced to silver (Ag\text{Ag}) and acts as the cathode. The standard reduction potentials are given as: Ecathode(Ag2O/Ag)=0.34 VE^\circ_{\text{cathode}} (\text{Ag}_2\text{O}/\text{Ag}) = 0.34 \text{ V} Eanode(Zn2+/Zn)=0.76 VE^\circ_{\text{anode}} (\text{Zn}^{2+}/\text{Zn}) = -0.76 \text{ V}

The standard cell potential (EcellE^\circ_{\text{cell}}) is calculated using the formula: Ecell=EcathodeEanodeE^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} Ecell=0.34 V(0.76 V)E^\circ_{\text{cell}} = 0.34 \text{ V} - (-0.76 \text{ V}) Ecell=0.34 V+0.76 V=1.10 VE^\circ_{\text{cell}} = 0.34 \text{ V} + 0.76 \text{ V} = 1.10 \text{ V}

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