Freshly precipitated aluminium and magnesium hydroxides are stirred vigorously in a buffer solution containing 0.25 `mol L^(-1)` of `NH_4Cl` and 0.05(M) of ammonium hydroxide. Calculate the concentration of aluminium and magnesium ions in solution. `K_b(NH_4OH)=1.8xx10^(-5),K_(sp)[Al(OH)_3]=6xx10^(-32)`
`K_(sp)[Mg(OH)_2)]=8.9xx10^(-12)`

Explanation

For a buffer solution containing `NH_4Cl` and `NH_4OH`
`pOH=pK_b+log([NH_4Cl])/([NH_4OH])`
`pK_b=-log_(10)K_b=-log_(10)(1.8xx10^(-5))=4.74`
`[NH_4Cl]=0.25mol*L^(-1)` and `[NH_4OH]=0.05mol*L^(-1)`
`:.pOH=4.74+log(0.25)/(0.05)=5.44`
or `-log_(10)[OH^-]=5.44:.[OH^-]=3.63xx10^(-6)(M)`
For `Mg(OH)_2,K_(sp)[Mg(OH)_2]=[Mg^(2+)][OH^-)^2`
`=8.9xx10^(-12)`
`:.[Mg^(2+)]=(8.9xx10^(-12))/([OH^-]^2)=(8.9xx10^(-12))/((3.63xx10^(-6))^2)`
`=0.6754(M)`
For `Al(OH)_3,K_(sp)[Al(OH)_3]=[Al^(3+)][OH^-]^3`
`=6xx10^(-32)`
`:.[Al^(3+)]=(6xx10^(-32))/([OH^-]^3)=(6xx10^(-32))/((3.63xx10^(-6))^3)`
`=1.25xx15^(-15)(M)`
So, the concentrations of `Mg^(2+)` and `Al^(3+)` ions in solution are 0.6754(M) and `1.25xx10^(-15)(M)` respectively.