The pH of an arterial blood sample is 7.15. Upon acidification of 10 ml of the plasma 5.91ml of CO2 is produced at standard temperature and presure.
Calculate:
a) total CO2 in the specimen
b) the individual concentration of disolved CO2(H2CO3) and HCO3-
c) The partial pressure of the dissolved CO2 in mm Hg.
*1 mole of CO2 at stp is 22.26L
Pka=6.1 at 37C
Solubility coefecient =0.031 mmol/LmmHg at 37 C
To calculate the values requested, we need to use some equations and constants related to the dissolved CO2 equilibrium in blood plasma.
First, let's define some variables:
Ct = Total CO2 concentration (in mmol/L)
[CO3] = HCO3- concentration (in mmol/L)
[H2CO3] = Dissolved CO2 (in mmol/L)
P = Partial pressure of dissolved CO2 (in mm Hg)
Now, let's solve the questions step by step:
a) Total CO2 in the specimen (Ct):
To calculate the total CO2 concentration, we need to consider that CO2 in blood exists in three forms: dissolved CO2 (H2CO3), bicarbonate ions (HCO3-), and carbonic acid (H2CO3). The equation relating these forms is:
Ct = [CO3] + [H2CO3]
b) Individual concentration of dissolved CO2 (H2CO3) and bicarbonate ions (HCO3-):
Using the Henderson-Hasselbalch equation, we can calculate the individual concentrations:
[H2CO3] = Ct / (1 + 10^(pH - pKa))
[CO3] = Ct - [H2CO3]
To determine the values, we need the pKa value at 37°C. The pKa value given is 6.1.
c) Partial pressure of dissolved CO2 (P):
To calculate the partial pressure of dissolved CO2, we can use Henry's Law:
P = [H2CO3] x (Solubility coefficient)
Now, let's substitute the given values into the equations:
Given:
pH = 7.15
Acidified plasma volume = 10 ml
CO2 produced = 5.91 ml
1 mole of CO2 at STP = 22.26 L (V = 0.00591 L)
pKa = 6.1
Solubility coefficient = 0.031 mmol/LmmHg
a) Total CO2 in the specimen (Ct):
Ct = [CO3] + [H2CO3]
b) Individual concentration of dissolved CO2 (H2CO3) and bicarbonate ions (HCO3-):
[H2CO3] = Ct / (1 + 10^(pH - pKa))
[CO3] = Ct - [H2CO3]
c) Partial pressure of dissolved CO2 (P):
P = [H2CO3] x (Solubility coefficient)
Now, let's plug in the numbers and calculate the values:
a) Total CO2 in the specimen (Ct):
Ct = [CO3] + [H2CO3]
Ct = [CO3] + Ct / (1 + 10^(pH - pKa))
Ct * (1 + 10^(pH - pKa)) = [CO3] + Ct
Ct * 10^(pH - pKa) = [CO3]
Ct = [CO3] * (10^(pKa - pH) + 1)
b) Individual concentration of dissolved CO2 (H2CO3) and bicarbonate ions (HCO3-):
[H2CO3] = Ct / (1 + 10^(pH - pKa))
[CO3] = Ct - [H2CO3]
c) Partial pressure of dissolved CO2 (P):
P = [H2CO3] x (Solubility coefficient)
Now let's perform the calculations substituting the given values:
pH = 7.15
pKa = 6.1
a) Total CO2 in the specimen (Ct):
Ct = [CO3] * (10^(pKa - pH) + 1)
Ct = [CO3] * (10^(6.1 - 7.15) + 1)
Ct = [CO3] * (10^(-1.05) + 1)
b) Individual concentration of dissolved CO2 (H2CO3) and bicarbonate ions (HCO3-):
[H2CO3] = Ct / (1 + 10^(pH - pKa))
[CO3] = Ct - [H2CO3]
c) Partial pressure of dissolved CO2 (P):
P = [H2CO3] x (Solubility coefficient)
To solve for the actual values, we need to know the actual concentration of total CO2 (bicarbonate + dissolved CO2) in the specimen. Could you provide that?