The total Carbon dioxide content (HCO3- + CO2) in a blood sample is determined by acidifiying the sample and measuring the volume of CO2 evolved with a van slyke manometric apparatuses. The total concent was determined to be 28.5 mmol/L. The blood pH at 37o was determined to be 7.48. What are the concentrations of HCO3- and CO2 in the blood? pKa= 6.10
I looked up the eqzn for CO2 in blood
and it was
CO2 + H2O=> H2CO3
H2CO3=> H+ + HCO3-
why is there this conversion factor online for the H-H eqzn for this rxn??
pH = 6.1 + log [HCO3-/(0.03)(PCO2)]
I don't think that I have to use this b/c It wasn't in the problem Q but
anyways I'll post what I did and say what I can't figure out..
and another thing HCO3- is a base??
while CO2 is a acid??
tot concent= (28.5mmol/L)/1000= 0.0285mol/L
pH = pKa+ log(cHCO3-/cCO2-)
but since I like the other eqzn better...
[H30+]= 10^-pH= 10^-7.48= 3.31e-8
Ka= 10^-pKa= 10^-6.10= 7.94e-7
[H30+]= Ka(cCO2/cHCO3-)
3.31e-8= 7.94e-7(cCO2/cHCO3-)
0.04168= (cCO2/cHCO3-)
After this I don't know what to do with the total concentration of 0.0285mol/L
um..help?
I think that I get this now but just to make sure...
since the total concent is 28.5mmol/L
[HCO3-]+[CO2]=28.5mmol/L
[HCO3-]=
I plugged it into the eqzn for the H3O+
[H30+]= Ka(cCO2/(28.5mmol/L-[CO2]))
0.04168= (cCO2/(28.5mmol/L-[CO2]))
0.04168(28.5mmol-cCO2)=cCO2
1.187-0.0416cCO2=cCO2
1.187= 1.0416cCO2
cCO2= 1.139
Plugged into the eqzn for the total
[HCO3-]= 28.5mmol- 1.139= 27.36mmol
Using that found concent of the HCO3- & CO2 I plugged it into the eqzn to check the answer.
[H30+]= Ka(cCO2/cHCO3-)
= (7.94e-7)(1.139/27.36)
= 3.30e-8
pH= -log(3.30e-8)= 7.48
which was the pH given..but I had read online that usually the concentration of CO2 is larger than HCO3- but that wasn't the case here. Unless that information is wrong...
and CO2 IS the acid right?
while the HCO3- is the base?
b/c if that wasn't the case then the ratio would be flipped around.
I would like if someone looked at my work and see if it's correct...
thanks =)
Thanks Christina,this is 2019 here and I'm amazed at your work cuz it is difficult for me now .my only problem is that I think you have reversed the concentrations for CO2 and HCO3- respectively.I don't know if you could still look into it
Your work is mostly correct, but there are a few errors and misconceptions that I will address.
First, the equation you provided for the conversion of CO2 and H2O to H2CO3 is correct, and the subsequent dissociation of H2CO3 to H+ and HCO3- is also correct.
Regarding the conversion factor equation you found online, pH = pKa + log [HCO3-/(0.03)(PCO2)], it is derived from the Henderson-Hasselbalch equation for a weak acid-base system. In this equation, the pKa value represents the acidity constant of carbonic acid (H2CO3), and the 0.03 represents the solubility coefficient of CO2 in blood. However, you are correct that for this specific problem, you do not need to use this equation.
Next, let's clarify the concepts of acid and base in this context. In this reaction, CO2 can be considered as an acid, as it reacts with water to form carbonic acid (H2CO3). HCO3- can be considered as a conjugate base, as it is formed from the dissociation of carbonic acid. So, CO2 is the acid and HCO3- is the base in this reaction.
Moving on to your calculations, the total concentration of CO2 + HCO3- is indeed 28.5 mmol/L, as you correctly calculated. To find the concentrations of HCO3- and CO2, you can use the equation pH = pKa + log (cHCO3-/cCO2), where cHCO3- and cCO2 represent the concentrations of HCO3- and CO2, respectively.
You correctly substituted the pH value into the equation and rearranged it to isolate cCO2. However, there is an error in your calculation. The correct equation should be 0.04168(28.5 mmol - cCO2) = cCO2, which simplifies to 1.187 - 0.04168cCO2 = cCO2. Solving this equation gives cCO2 = 1.18 mmol/L.
To find cHCO3-, you can substitute the value of cCO2 into the equation [HCO3-] + [CO2] = 28.5 mmol/L. Rearrange this equation to isolate [HCO3-], which gives [HCO3-] = 28.5 mmol - cCO2 = 28.5 mmol - 1.18 mmol = 27.32 mmol/L.
Finally, to verify your solution, you can substitute the calculated concentrations into the equation pH = pKa + log (cHCO3-/cCO2), and you should obtain the given pH value of 7.48.