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.
Well, blood sure can be a tough cookie to crack! But don't worry, I'm here to help you with a dose of humor. Let's tackle these questions one by one.
a) To find the total CO2 in the specimen, we need to determine the amount of CO2 produced from the 10 ml of plasma. Since 5.91 ml of CO2 was produced, it means that 5.91/10 ml of plasma contains CO2. So the total CO2 in the specimen would be 5.91/10 multiplied by the amount of plasma you have. And remember, always be careful when handling CO2 – it's a gas that likes to escape and fizz!
b) Now, let's get acquainted with our CO2 companions – dissolved CO2 (H2CO3) and bicarbonate (HCO3-). To find their individual concentrations, we need to know the ratio between them. It's like a waltz between two partners! Fortunately, at standard temperature and pressure, for every 1 molecule of H2CO3, you'll have 20 molecules of HCO3-. So divide the amount of H2CO3 (CO2) you calculated in part a) by 21 (20 + 1) to find the concentration of H2CO3, and multiply it by 20 for HCO3-.
c) Lastly, to find the partial pressure of dissolved CO2 in mm Hg, we can use Henry's Law. At normal body temperature, the solubility of CO2 is about 0.03 mmol/mm Hg. So, multiply the concentration of dissolved CO2 (H2CO3) you calculated in part b) by 0.03 mmol/mm Hg to find the partial pressure of dissolved CO2 in mm Hg. Just don't let it get your head spinning too much!
Remember, pH levels and blood chemistry should always be taken seriously. These calculations provide approximate values, so please consult a qualified healthcare professional for accurate results. Stay healthy and keep those questions coming!
To solve this problem, we need to use the Henderson-Hasselbalch equation and the Henry's Law equation. Here are the step-by-step calculations:
a) Total CO2 in the specimen:
We can calculate the total CO2 by using the equation: Total CO2 (mmol/L) = [HCO3-] + [H2CO3]
Given:
pH = 7.15
Standard temperature and pressure (STP) means 0°C and 1 atm pressure.
Using the Henderson-Hasselbalch equation:
pH = pKa + log10([HCO3-] / [H2CO3])
From the Henderson-Hasselbalch equation, we know that pKa = 6.1 (at 37°C). However, it is not specified if the given pH is at 37°C or not. Assuming it is at 37°C, we can proceed with the calculation.
7.15 = 6.1 + log10([HCO3-]/[H2CO3])
Rearranging the equation:
log10([HCO3-]/[H2CO3]) = 7.15 - 6.1
log10([HCO3-]/[H2CO3]) = 1.05
Taking the antilog of both sides:
[HCO3-] / [H2CO3] = 10^1.05
[HCO3-] / [H2CO3] = 10.5
Now we know that the ratio of [HCO3-] to [H2CO3] is 10.5. Given that 5.91 mL of CO2 is produced from 10 mL of plasma, we can calculate the concentration:
[HCO3-] + [H2CO3] = 10.5 * 5.91 mmol/L
[HCO3-] + [H2CO3] = 61.995 mmol/L
Therefore, the total CO2 in the specimen is approximately 61.995 mmol/L.
b) Individual concentration of dissolved CO2 (H2CO3) and HCO3-:
Using the ratio we found earlier, we can calculate the individual concentrations:
[H2CO3] = [HCO3-] * 1 / (1 + [HCO3-] / [H2CO3])
[H2CO3] = 61.995 * 1 / (1 + 10.5)
[H2CO3] = 5.539 mmol/L
[HCO3-] = [H2CO3] * 10.5
[HCO3-] = 5.539 * 10.5
[HCO3-] = 58.17 mmol/L
Therefore, the concentration of dissolved CO2 (H2CO3) is 5.539 mmol/L, and the concentration of bicarbonate (HCO3-) is 58.17 mmol/L.
c) Partial pressure of dissolved CO2 in mm Hg:
To calculate the partial pressure of dissolved CO2, we can use Henry's Law equation:
Partial pressure of dissolved CO2 = solubility coefficient * concentration of dissolved CO2
The solubility coefficient of CO2 in blood at 37°C is approximately 0.03 mmol/mmHg/L.
Partial pressure of dissolved CO2 = 0.03 * 5.539 mmHg
Partial pressure of dissolved CO2 = 0.1657 mmHg
Therefore, the partial pressure of dissolved CO2 in this arterial blood sample is approximately 0.1657 mmHg.
To calculate the different values in this question, we need to apply some principles from chemistry and use a few formulas. I'll go through each calculation step by step:
a) To find the total CO2 in the specimen, we need to calculate the amount of CO2 present in the plasma before the acidification. We know that 5.91 ml of CO2 is produced from 10 ml of plasma after acidification. Therefore, we can assume that the original plasma also contained 5.91 ml of CO2.
b) The individual concentrations of dissolved CO2 (H2CO3) and bicarbonate ions (HCO3-) can be determined using the Henderson-Hasselbalch equation. The equation is: pH = pKa + log ([HCO3-]/[H2CO3]).
In this case, the pH is 7.15. The pKa value for the carbonic acid (H2CO3) and bicarbonate (HCO3-) equilibrium is approximately 6.1. Plugging in these values, we get:
7.15 = 6.1 + log ([HCO3-]/[H2CO3]).
Rearranging the equation, we have:
log ([HCO3-]/[H2CO3]) = 7.15 - 6.1 = 1.05.
Now, we need to convert this logarithmic equation into an exponential one:
[HCO3-]/[H2CO3] = 10^1.05.
Using a calculator, we find that 10^1.05 is approximately 11.22. Therefore, the ratio of [HCO3-]/[H2CO3] is 11.22.
Let's represent the concentration of H2CO3 as x. Then, the concentration of HCO3- is 11.22x.
The sum of the concentrations of H2CO3 and HCO3- is the "total CO2" concentration that we calculated in part a, which is 5.91 ml.
So, we have the equation: x + 11.22x = 5.91.
Simplifying, we get: 12.22x = 5.91.
Solving for x, we find: x = 5.91 / 12.22.
Therefore, the concentration of H2CO3 (dissolved CO2) is approximately 0.48 M, and the concentration of HCO3- (bicarbonate) is approximately 11.22 times that, which is 5.38 M.
c) To calculate the partial pressure of the dissolved CO2 in mm Hg, we need to use Henry's Law, which states that the concentration of a gas dissolved in a liquid is directly proportional to its partial pressure.
The equation for Henry's Law is: P = k * C,
where P is the partial pressure of the gas, k is the Henry's Law constant, and C is the concentration of the gas.
In this case, we need to calculate the partial pressure of dissolved CO2 (H2CO3). Let's represent the partial pressure of CO2 as P and the concentration of H2CO3 as C. We can rearrange the formula as: P = k * C.
The Henry's Law constant for CO2 at standard temperature and pressure is approximately 0.03 mm Hg/M. We calculated the concentration of H2CO3 in part b, which is approximately 0.48 M.
Now, we can plug in the values into the equation: P = 0.03 mm Hg/M * 0.48 M.
Simplifying, we find: P ≈ 0.0144 mm Hg.
Therefore, the partial pressure of the dissolved CO2 is approximately 0.0144 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