Calculate pH of a buffer solution contains 0.1M `RNH_(3)`Cl (aq) & 1 M `RNH_(2)`(aq) solution at `25^(@)C`. (Given : `K_(b)=10^(-7)`)

Correct Answer - 1
`H_(3)A(aq)iffH^(+)(aq)+H_(2)A^(1-)(aq)," "K_(a_(1))=10^(-5)`
`"0.1-x x+y+z x-y"`
`H_(2)A^(1-)(aq)iffH^(+)(aq)+HA^(2-)(aq)," "K_(a_(2))=10^(-9)`
`"x-y x-y-z y-z"`
`HA^(2-)(aq)iffH^(+)(aq)+A^(3-)(aq), " "K_(a_(3))=10^(-13)`
`"y-z x+z+y z"`
`K_(a_(1))=gtgtgtgtK_(a_(2))gtgtK_(a_(3))`
`K_(a_(1))=10^(-5)=(x^(2))/(0.1-x)" implies "x=sqrt(K_(a_(1))C)=10^(-3)`
`K_(a_(2))=y=10^(-9)`
`K_(a_(3))=((x)(z))/(y)=(10^(-3)xx(z))/(10^(-9))" implies "z=10^(-19)`
`X=([A^(3-)])/([HA^(2-)])=(10^(-19))/(10^(-9))=10^(-10)`
`pX=-log10^(-10)=10, (pX)/(10)=(10)/(10)=1`