We are being asked to determine the ratio of HCO_{3}^{-} to H_{2}CO_{3} in

a. the blood of pH 7.4

b. an exhausted marathon runner whose blood pH is 7.2

H_{2}CO_{3} is a weak acid (*and based on the Bronsted-Lowry definition, an acid is a proton (H^{+}) donor. Once *H

H_{2}CO_{3} + H_{2}O ⇋ HCO_{3}^{-} + H_{3}O^{+}

Whenever we have a conjugate base and weak acid, we have a buffer.

We will use the Henderson-Hasselbalch equation

$\overline{){\mathbf{pH}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathbf{pK}}}_{{\mathbf{a}}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{log}}\mathbf{\left(}\frac{\mathbf{conjugate}\mathbf{}\mathbf{base}}{\mathbf{weak}\mathbf{}\mathbf{acid}}\mathbf{\right)}}$

Derive the ratio of HCO_{3}^{-} to H_{2}CO_{3}

$\left(\frac{\mathrm{conjugate}\mathrm{base}}{\mathrm{weak}\mathrm{acid}}\right)\mathbf{}\mathbf{=}\mathbf{}{\mathbf{10}}^{\mathbf{pH}\mathbf{}\mathbf{-}\mathbf{}{\mathbf{pK}}_{\mathbf{a}}}$

where HCO_{3}^{-} is the conjugate base and H_{2}CO_{3} is the weak acid

A. What is the ratio of HCO_{3}^{-} to H_{2}CO_{3} in the blood of pH 7.4?

B. What is the ratio of HCO_{3}^{-}- to H_{2}CO_{3} in an exhausted marathon runner whose blood pH is 7.2?

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