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The concentration of potassium ions insi...

The concentration of potassium ions inside a biological cell is at least 20 times higher than outside. The resulting potential difference across the cell is important in several processes such as transmission of nerve impulses and maintaining the ion balance. A simplel model for a concentration cell involving a metal `M` is
`M(s)|M^(o+)(aq,0.05 ` molar`)||M^(o+)(aq,1` molar`)|M(s)`
For the abov electrolytic cell, the magnitude of the cell potential is `|E_(cell)|=70mV.`
For the above cell

A

`E_(cell) lt 0, DeltaG gt 0`

B

`E_(cell) gt 0, DeltaG lt 0`

C

`E_(cell) lt 0, DeltaG^(@) gt 0`

D

`E_(cell) gt 0, DeltaG^(@) lt 0`

Text Solution

Verified by Experts

The correct Answer is:
B
`M(s) rarr M_(L)^(+)(aq) +e^(-)` at anode
`M_(R)^(+)(aq) +e^(-) rarr M(s)-` at cathode
`bar("Net cell reaction" : M_(R)^(+)(aq) rarr M_(L)^(+)(aq))`
`Q_(cell) = ([M_(L)^(+)])/([M_(R)^(+)])`
From Nernst equation:
`E_(cell) = E_(cell)^(@) - (0.59)/(n) log Q_(Cell)`
`= 0 -(0.59)/(1) log.([M_(L)^(+)])/([M_(R)^(+)])`
`[ :' E_(cell)^(@) = 0` for concentration cell]
`= +0.059 log.([M_(L)^(+)])/([M_(R)^(+)])`
`= 0.059 log.(1)/(0.05)`
so, `E_(cell) = +ve` and `DeltaG =- nFE_(cell) =- ve`
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