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 `7.8 xx 10^(-7)`?

Explanation

To solve the problem of determining the volume of 5M NaHCO₃ solution needed to maintain a pH of 7.4 in a 10 mL blood sample that is 2M in H₂CO₃, we can follow these steps:

### Step 1: Understand the relationship between pH, pKa, and concentrations
We can use the Henderson-Hasselbalch equation, which is given by:
\[ \text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \]
where:
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