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 the Henderson-Hasselbalch equation and some additional information provided in the question. Let's break down each part:
a) Total CO2 in the specimen:
To calculate the total CO2 in the specimen, we need to determine the amount of CO2 present in the plasma sample and the amount of CO2 produced upon acidification.
The CO2 produced upon acidification is given as 5.91 ml. Since 1 mole of CO2 at STP is 22.26 L, we need to convert the volume to moles:
5.91 ml x (1 L / 1000 ml) x (1 mol / 22.26 L) = 0.000265 mol
This gives us the amount of CO2 produced. However, we also need to account for the CO2 already present in the arterial blood sample. The concentration of CO2 can be calculated using the Henderson-Hasselbalch equation:
[HCO3-] = K * (pCO2 / pKa)
Where:
[HCO3-] is the concentration of bicarbonate (HCO3-)
K is the solubility coefficient (0.031 mmol/LmmHg at 37°C)
pCO2 is the partial pressure of CO2 (which we will calculate later)
pKa is the dissociation constant (6.1 at 37°C)
We can rearrange the equation to solve for pCO2:
pCO2 = [HCO3-] * pKa / K
Given that the pH of the arterial blood sample is 7.15, we can determine the bicarbonate concentration ([HCO3-]) using the following relationship:
pH = pKa + log ([HCO3-] / [H2CO3])
Since the pH and pKa are known, we can rearrange the equation to solve for [HCO3-]:
[HCO3-] = [H2CO3] * 10^(pH - pKa)
The concentration of H2CO3 can be approximated as equal to [CO2], as the majority of CO2 in the blood is present as H2CO3. Therefore, [H2CO3] = [CO2].
Now, we can substitute these values into the equation to calculate pCO2, which will help us determine the amount of CO2 already present in the sample:
pCO2 = [CO2] * pKa / K
Substituting the values, we get:
pCO2 = [H2CO3] * pKa / K
We know that 1 mole of CO2 is 22.26 L at STP, and from the given information, we have:
[H2CO3] = 0.000265 mol (from above)
pKa = 6.1
K = 0.031 mmol/LmmHg
Converting the units:
0.000265 mol * (1000 mmol / 1 mol) = 0.265 mmol
Substituting these values into the equation:
pCO2 = 0.265 mmol * 6.1 / 0.031 = 51.94 mmHg
Therefore, the total CO2 in the specimen is the sum of the CO2 produced upon acidification and the CO2 already present:
Total CO2 = CO2 produced + CO2 already present
Total CO2 = 0.000265 mol + 0.265 mmol
Total CO2 = 0.00053 mol
b) Individual concentration of dissolved CO2 (H2CO3) and HCO3-:
The concentration of H2CO3 can be approximated as equal to [CO2]. Using the given information, we know that 1 mole of CO2 is 22.26 L at STP, and we calculated the CO2 produced upon acidification as 0.000265 mol. Therefore:
[H2CO3] = [CO2] = 0.000265 mol
To find the concentration of HCO3-, we can use the same Henderson-Hasselbalch equation:
[HCO3-] = [H2CO3] * 10^(pH - pKa)
Substituting the values:
[HCO3-] = 0.000265 mol * 10^(7.15 - 6.1)
Using a calculator:
[HCO3-] = 10.5 mmol/L
Therefore, the individual concentrations are:
[H2CO3] = 0.000265 mol
[HCO3-] = 10.5 mmol/L
c) Partial pressure of the dissolved CO2 in mmHg:
We have already calculated the pCO2 as 51.94 mmHg, which represents the partial pressure of CO2.
To solve this problem, we'll need to use the Henderson-Hasselbalch equation and the solubility coefficient of CO2. Let's break it down step-by-step:
Step 1: Calculate the total CO2 in the specimen
The total CO2 can be calculated using the following equation:
total CO2 (mmol/L) = dissolved CO2 (mmol/L) + HCO3- (mmol/L)
Step 2: Calculate the individual concentration of dissolved CO2 (H2CO3) and HCO3-.
To calculate the concentration of H2CO3 (dissolved CO2), we'll use the Henderson-Hasselbalch equation:
[H2CO3] (mmol/L) = dissolved CO2 (mmol/L) × solubility coefficient (mmol/LmmHg) × partial pressure of dissolved CO2 (mmHg)
To calculate the concentration of HCO3-, we'll use the equation:
[HCO3-] (mmol/L) = total CO2 (mmol/L) - [H2CO3] (mmol/L)
Step 3: Calculate the partial pressure of the dissolved CO2 in mm Hg.
The partial pressure of dissolved CO2 can be calculated using the equation:
Partial pressure of dissolved CO2 (mmHg) = [H2CO3] (mmol/L) / solubility coefficient (mmol/LmmHg)
Now, let's apply these steps to solve the problem:
Given:
pH of arterial blood sample = 7.15
acidification of plasma produces 5.91 ml of CO2
10 ml of plasma is used
1 mole of CO2 at stp is 22.26 L
Pka of H2CO3 = 6.1 at 37°C
Solubility coefficient = 0.031 mmol/LmmHg at 37°C
a) Total CO2 in the specimen:
To determine the total CO2 in the specimen, we need to calculate the moles of CO2 produced.
Moles of CO2 produced = volume of CO2 produced / molar volume at STP
Moles of CO2 produced = 5.91 ml / 22.26 L/mol = 0.265 mol
Total CO2 in the specimen = moles of CO2 produced / volume of plasma used
Total CO2 in the specimen = 0.265 mol / 10 ml = 0.0265 mol/L
b) Individual concentration of dissolved CO2 (H2CO3) and HCO3-:
Using the Henderson-Hasselbalch equation, we can find H2CO3 concentration:
[H2CO3] = (dissolved CO2) × (solubility coefficient) × (partial pressure of dissolved CO2)
[H2CO3] = (0.0265 mol/L) × (0.031 mmol/LmmHg) × (partial pressure of dissolved CO2)
Next, we can determine HCO3- concentration:
[HCO3-] = (total CO2) - [H2CO3]
[HCO3-] = (0.0265 mol/L) - (calculated H2CO3 concentration)
c) Partial pressure of the dissolved CO2 in mmHg:
To find the partial pressure of dissolved CO2, we'll rearrange the Henderson-Hasselbalch equation:
Partial pressure of dissolved CO2 = [H2CO3] / (solubility coefficient)
Partial pressure of dissolved CO2 = calculated H2CO3 concentration / (0.031 mmol/LmmHg)
Remember to substitute the calculated H2CO3 concentration into the equations in step b) to find the individual concentration of H2CO3 and HCO3-.