The ionic equivalent conductivities of `K^(o+), Al^(3+)` , and `SO_(4)^(2-)` ions are `x,y,` and `z S cm^(2) Eq^(-1)`, respectively. Calculate `wedge_(m)^(@)` and `wedge_(eq)^(@)` for `(K_(2)SO_(4).Al_(2)(SO_(4))_(3).24H_(2)O)(` Potash alum `).`

Explanation

`wedge_(m)^(@)` for potash alum `=2lambda_(m(K^(o+)))^(@)+2lambda_(m(Al^(3+)))^(@)+4 lambda_(m(SO_(4)^(2-)))^(@)`
`=(2x+2y+4z)S cm^(2)Eq^(-1)`
Total charge on potash alum `=(+8 or -8)`
Number of equivalent of ion `=("Charge on the ions" )/("Tota charge")`
`K_(2)SO_(4).Al_(2)(SO_(4))_(3).24H_(2)O rarr 2K^(o+)+2Al^(3+)+4SO_(4)^(2-)+24H_(2)O`
`:.` Equivalent of `K^(o+)=(+1xx2)/(+8)=(1)/(4) Eq`
`:.` Equivalent of `Al^(3+)=(+3xx2)/(+8)=(3)/(4)Eq`
`:.` Equivalent of `SO_(4)^(2-)=(-2xx4)/(-8)=1 Eq`
`wedge_(eq(potash alum))^(@)=lambda_(Eq(K^(o+)))^(@)+lambda_(Eq(Al^(3+)))^(@)+lambda_(Eq(SO_(4)^(2-)))^(@)`
`=(1)/(4)xxx+(3)/(4)xxy+1xxz`
`((3)/(4)+(3y)/(4)+z)S cm^(2) Eq^(-1)`