Question

Following intense exercise, the blood pH was determined to be 7.1. If the HCO3- is 7.5mM and the pKa for HCO3- is 6.1, what is the CO2 concentration in the blood

Answer 1

Answer:

$0.75\ \text{mM}$

Explanation:

Concentration of $HCO_3^-$ = $[HCO_3^-]=7.5\ \text{mM}$

$pK_a$ for $HCO_3^-$ = 6.1

$pH$ of  blood = 7.1

The reaction is as follows

$H_2CO_3+H_2O\rightarrow HCO_3^-+H_3O^+$

From the Henderson equation we get

$pH=pK_a+\log\dfrac{[HCO_3^-]}{[H_2CO_3]}\\\Rightarrow 7.1=6.1+\log \dfrac{7.5}{[H_2CO_3]}\\\Rightarrow 1=\log\dfrac{7.5}{[H_2CO_3]}\\\Rightarrow 10^1=\dfrac{7.5}{[H_2CO_3]}\\\Rightarrow [H_2CO_3]=\dfrac{7.5}{10}\\\Rightarrow [H_2CO_3]=0.75\ \text{mM}$

$CO_2(g)+H_2O(l)\rightarrow H_2CO_3(aq)$

Concentration of $H_2CO_3$, $[H_2CO_3]=[CO_2]$

Concentration of $CO_2$, $[CO_2]=[H_2CO_3]=0.75\ \text{mM}$.