The `ph` of blood stream is maintained by a proper balance of `H_(2)CO_(3)` and `NaHCO_(3)` concentrations. What volume of `5M NaHCO_(3)` solution, should be mixed with `10mL` 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 `4.0 xx 10^(-7)`?

Explanation

`[H_(2)CO_(3)]` in blood `=2M [NaHCO_(3)] = 5M`
Volume of blood `= 10mL`
Let volume of `NaHCO_(3)` used `= VmL`
`[H_(2)CO_(3)]` in mixture =` (2xx10)/((V +10))`
`[NaHCO_(3)]` in mixture `= ((5xxV))/((V +10))`
`pH = pK_(a) + log .(["salt"])/(["acid"])`
`7.4 = - log 4.0 xx 10^(-7) + "log"((5xxV)//(V+10))/((2xx10)//(V+10))`
`V = 40mL`