Ascorbic acid (vitamin C) is a diprotic acid, `H _(2) C _(6) H _(6) O _(6). [H^(+)] , pH and [C _(6)H _(6)O _(6) ]^(2-)` in a `0.10 M` solution of ascorbic acid will be respectively(Given `K _(a_1) = 6.8 xx 10 ^(-5) and K _(a_2) = 2. 7 xx 10 ^(-12)` for ascorbic acid).

Options

A. `3.6 xx 10 ^(-5) M, 2 . 58 , 2.7 xx 1 0 ^(-12) M`
B. `2.6 xx 10 ^(-3) M, 8.18 , 15 xx 10 ^(-10) M`
C. `2.6 xx 10 ^(-3) M, 2.58 ,2.7 xx 10 ^(-12) M`
D. `1.5 xx 10 ^(-4) M, 3.67, 1.7 xx 10 ^(-14) M`

Answer

C

Explanation

`[H^(+)] ` is determinded by the first protic equilibrium, `H _(2) C _(6) H _(6) O _(6) hArr H ^(+) + HC _(6) H _(6) O _(6) ^(-)`
The mass action expession is : `K _(a _(1)) = 6.8 xx 10 ^(-5) = (x ^(2))/( 0.10)`
So, `x = [H^(+)] = 2. 6 xx 10 ^(-3) M and pH =- log (2. 6 xx 10 ^(-3)) = 2. 58`
The concentration of the anion, `[HC _(6) H _(6) O _(6) ^(-)],` is given almost entirely by the second ionization equilibrium
`H C _(6) H _(6) O _(6) ^(-) hArr H ^(+) + C_(6) H _(6) O _(6) ^(2-) ,` for which the mass ation expression is
`K _(a_(2)) = ([ H ^(+)] [C _(6) H _(6) O _(6)^(2-)])/( [ HC _(6) H _(6)O _(6 ) ^(-)]) = 2.7 xx 10 ^(-12)`
Using the vaue of x from the first step above gives `2.7 xx 10 ^(-12) = (( 2. 6 xx 10 ^(-3)) [ C _(6) H_(6) O _(6) ^(2-)])/((2.6 xx 10 ^(-3)))`
So, `[C _(6) H _(6) O _(6) ^(2-) ]= 2. 7 xx 10 ^(-12) M.`