What is the `pH` of `0.01 M` glycine solution? For glycine, `K_(a_(1))=4.5xx10^(-3)` and `K_(a_(2))=1.7xx10^(-10)` at `298 K`

Options

A. `3.0`
B. `10.0`
C. `6.1`
D. `7.2`

Answer

C

Explanation

`pK_(a_(1))= -log(4.5xx10^(-3))`
`=3-log4.5`
`pK_(a_(2))= -log(1.7xx10^(-10))`
`=10-log 1.7`
We have
`pH=(1)/(2)(pK_(a_(1))+pK_(a_(2)))`
`=(1)/(2)[3-log(4.5)+10-log(1.7)]`
`=(1)/(2)[3-log(4.5xx1.7)]`
`=(1)/(2)[13-log(7.65)]`
`=6.1`
Alternatively, overall ionization constant (K) is given as
`K= K_(a_(1))xxK_(a_(2))`
`=(4.5xx10^(-3))(1.7xx10^(-10))`
we have
`C_(H^(+))=sqrt(KC)=sqrt((7.65xx10^(-13))(0.01))`
`=sqrt(0.765xx10^(-14))`
`=0.875xx10^(-7)M`
`pH= -log(0.875xx10^(-7))=7-0.9=6.1`