For an electrochemical cell
`Sn(s)|Sn^(2+)(aq, 1M)||Pb^(2+)(aq, 1M)|Pb(s)` the ratio `([Sn^(2+)])/([Pb^(2+)])` when this cell attains equilibrium is _________________.
`("Given "E_(Sn^(2+)|Sn)^(@)=-0.14V, " "E_(Pb^(2+)|Pb)^(@)=-0.13V,(2.303RT)/(F)=0.06)`

Options

A. `2.15`
B. `3.16`
C. `1.14`
D. `2.82`

Answer

A

Explanation

Cell reaction is :
`Sn(s)+Pb^(+2)(aq)rarr Sn^(+2)(aq)+Pb(s)`
Apply Nernst equation :
`E_("cell")=E_("cell")^(@)-(0.06)/(2)log.([Sn^(+2)])/([Pb^(+2)])" …(1)"`
`E_("cell")^(@)=-0.13+0.14=0.01V`
`"At equilibrium : "E_("cell")=0`
`"Substituting in (1)"`
`0=0.01-(0.06)/(2)log.([Sn^(+2)])/([Pb^(+2)])`
`rArr" "(1)/(3)=log.([Sn^(+2)])/([Pb^(+2)])`
`rArr" "([Sn^(+2)])/([Pb^(+2)])=2.15`