The pH of blood stream is maintained by a proper balance of `H_(2) CO_(3)` concentrations. What volume of `5M NaHCO_(3)` solution be mixed with 10 mL sample of blood which is `2M ` in `H _(2) CO _(3)` in order to maintain a pH of `7.4 K_(a)` for `H_(2) CO_(3)`in blood is `7.8 xx10^(-2)`?

Options

A. `41. 86 mL`
B. `83.2 mL`
C. `78.36 mL`
D. `52.43 mL`

Answer

C

Explanation

`[H _(2) CO _(3) ]` in blood =2 M, Volume of blood = 10 mL
`[ Na HCO _(3) ] = 5 M` let volume of `Na HCO _(3)` used = V mL
`[H _(2) CO _(3) ] ` in mixture `= ( 2 xx 10 )/( V + 10) , [Na HCO _(3) ] ` in mixture `= (5 xx V)/( V + 10)`
`pH = pKa + log "" (["Salt"])/(["Acid"]) , 7.4 = - log 7.8 xx 10 ^(-7) + log "" (( 5 xx V) (V + 10))/((2 xx 10 ) (V + 10)), V = 78. 36 mL`