Two weak acid solutions `HA_(1)` and `HA_(2)` with the same concentration and having `pK_(a)` values 3 and 5 are placed in contact with hydrogen electrode `(1 atm ` and `25^(@)C)` and are interconnected through a salt bridge. Find the `EMF` of the cell.

Explanation

For hydrogen electrode at `1 atm` and `25^(@)C`
`E_(red)=-0.059pH`
Assuming the degree of dissociation to be small, `pH` of a weak acid,
`pH=((1)/(2)pK_(a)-(1)/(2)logc)`
`:. ` For electrode at acid `HA_(1)`,
`E_(redc)=-0.059pH=-0.0599((1)/(2)pK_(a_(1))-(1)/(2)logc)`
`E_(redc)=-(0.059)/(2)(pK_(a_(1))-logc)`
`=-(0.059)/(2)(3-logc)`
Similarly, for hydrogen electrode at acid `HA_(2)`,
`E_(reda)=-(0.059)/(2)(5-logc)`
`E_(cell)=E_(cathode)-E_(Anode)`
`=-[(0.059)/(2)(3-logc)]-[(0.059)/(2)(5-logc)]`
`=-0.0295xx3+0.0295xx5`
`=0.0295xx(5-3)=0.0295xx2=0.0295V`