Question

Calculation of Blood pH from \(\mathrm{CO}_{2}\) and Baicarbonate Levels Calculate the \(\mathrm{pH}\) of a blood plasma sample with a total \(\mathrm{CO}_{2}\) concentration of \(26.9 \mathrm{~mm}\) and bicarbonate concentration of \(25.6 \mathrm{~mm}\). Recall from page 63 that the relevant \(\mathrm{p} K_{\mathrm{a}}\) of carbonic acid is \(6.1\).

Short answer

The pH of the blood plasma is approximately 6.08.

Step-by-step solution

Understand the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is used to calculate the pH of blood plasma. It is given by the formula: \[\mathrm{pH} = \mathrm{p}K_a + \log_{10}{\left(\frac{[\mathrm{HCO}_3^-]}{[\mathrm{CO}_2]}\right)}\] where \(\mathrm{p}K_a = 6.1\), \([\mathrm{HCO}_3^-]\) is the bicarbonate concentration, and \([\mathrm{CO}_2]\) is the carbon dioxide concentration.

Assign the Given Values

From the problem statement, assign the given values to the appropriate variables: - \([\mathrm{HCO}_3^-] = 25.6\ \mathrm{mM}\)- \([\mathrm{CO}_2] = 26.9\ \mathrm{mM}\)- \(\mathrm{p}K_a = 6.1\).

Calculate the Ratio

Substitute the given concentrations into the ratio part of the Henderson-Hasselbalch equation: \[\frac{[\mathrm{HCO}_3^-]}{[\mathrm{CO}_2]} = \frac{25.6}{26.9} \approx 0.9517.\]

Calculate the Logarithm

Find the logarithm of the ratio calculated in Step 3: \[\log_{10}{(0.9517)} \approx -0.021.\]

Calculate the pH

Now, substitute the \(\log_{10}{(0.9517)}\) and \(\mathrm{p}K_a = 6.1\) into the Henderson-Hasselbalch equation: \[\mathrm{pH} = 6.1 - 0.021 = 6.079.\] Thus, the pH of the blood plasma is approximately 6.08.

Key concepts

blood plasma pH

The pH of blood plasma is a measure of how acidic or basic the blood is. Normal human blood plasma has a pH range of 7.35 to 7.45. A pH lower than 7.35 indicates acidity, while a pH higher than 7.45 indicates alkalinity. The pH level is crucial for proper metabolic function and overall health.
A small change in blood pH can lead to significant changes in biological processes. The body has different mechanisms to maintain a stable pH, including the respiratory system, which regulates carbon dioxide levels, and the kidneys, which regulate bicarbonate and hydrogen ions.
Understanding blood plasma pH is essential in medical scenarios, such as evaluating a patient’s acid-base balance, diagnosing conditions like acidosis or alkalosis, and determining the effectiveness of treatments.

bicarbonate concentration

Bicarbonate (HCO₃⁻) is a vital component in the blood that acts as a buffer, helping maintain the blood's pH within a normal range. It is primarily regulated by the kidneys, which can reabsorb or excrete bicarbonate as needed to balance pH levels.
The concentration of bicarbonate in the blood is usually about 22-28 mEq/L in healthy individuals. This concentration is important for buffering acids produced in metabolism and is often measured in various medical tests to assess an individual's health status.
In the context of the Henderson-Hasselbalch equation, bicarbonate concentration is the numerator in the formula used to calculate blood pH. This concentration, along with carbon dioxide levels, directly influences pH calculations and can indicate metabolic imbalances if abnormal.

carbon dioxide concentration

Carbon dioxide (CO₂) in the blood is another critical factor affecting blood pH. It is a waste product of metabolism that is regulated primarily by the lungs. In the physiology of the body, CO₂ acts as an acid because it can combine with water to form carbonic acid (H₂CO₃).
The normal range for carbon dioxide concentration in blood plasma is typically 35-45 mmHg. If carbon dioxide levels become too high, it could cause respiratory acidosis, a condition where the blood becomes too acidic. Conversely, if CO₂ levels are too low, it can lead to alkalosis, where the blood becomes too basic.
In terms of the Henderson-Hasselbalch equation, carbon dioxide concentration is the denominator, and along with bicarbonate, it is used to calculate the pH of the blood plasma. Accurate measurement of CO₂ is essential to maintaining acid-base balance in the body.