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Given the cell: Cd(s)|Cd(OH)2(s)|NaOH(aq...

Given the cell: `Cd(s)|Cd(OH)_2(s)|NaOH(aq,0.01M)|H_2(g,1"bar")|Pt(s)`
with `E_(cell)=0.0V."if"E_(Cd^(2+)|Cd)^(@)=-0.39V,"then"K_(sp)"of"Cd(OH_2)`is:

A

`0.1`

B

`10^(-13)`

C

`10^(-15)`

D

`10^(-18)`

Text Solution

Verified by Experts

The correct Answer is:
C
`E_(cell)=E_(H^(+)//H_(2))-E_(OH^(-)|Cd(OH)_(2)|Cd)`
`=E_(H^(+)|H_(2))-E_(OH^(-)|Cd(OH)_(2)|Cd)=E_(H^(+)|H_(2))-E_(OH_(Cd^(2+)|Cd))`
`E_(cell)=E^(@)-(0.06)/(2)log.([cd^(2+)])/([H^(+)]^(2))`
`E_(cell)="0 , E"_(cell)^(0)=0.31log.([cd^(2+)][OH^(-)]^(2))/(K_(w)^(2))`
`log.(K_(sp))/(K_(w)^(2))=(0.09)/(0.03)=13,K_(sp)=10^(13)xx(10^(-14))^(2)=10^(-15)`
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