Question

Carbonate buffers are important in regulating the pH of blood at \(7.40 .\) If the carbonic acid concentration in a sample of blood is 0.0012 M, determine the bicarbonate ion concentration required to buffer the pH of blood at pH \(=7.40\) $$ \mathrm{H}_{2} \mathrm{CO}_{3}(a q) \rightleftharpoons \mathrm{HCO}_{3}^{-}(a q)+\mathrm{H}^{+}(a q) \quad K_{\mathrm{a}}=4.3 \times 10^{-7} $$

Short answer

The bicarbonate ion concentration (HCO₃⁻) required to buffer the pH of blood at pH = 7.40 is approximately 0.0021 M, calculated using the Henderson-Hasselbalch equation and given the carbonic acid concentration and Ka value.

Step-by-step solution

Calculate pKa

To calculate the pKa, use the following equation: pKa = -log(Ka). We're given the Ka value for carbonic acid, which is 4.3 x 10⁻⁷. Therefore: pKa = -log(4.3 x 10⁻⁷) Now, calculate the pKa value: pKa ≈ 6.37

Use the Henderson-Hasselbalch equation

Now that we have the pKa value, we can use the Henderson-Hasselbalch equation to solve for the bicarbonate ion concentration: pH = pKa + log([A⁻]/[HA]) We are given the pH (7.40) and the concentration of carbonic acid ([HA]) which is 0.0012 M. Plug in these values into the equation: 7.40 = 6.37 + log([HCO₃⁻]/0.0012)

Solve for bicarbonate ion concentration [HCO₃⁻]

Now, solve for the [HCO₃⁻] concentration: 7.40 - 6.37 = log([HCO₃⁻]/0.0012) 1.03 = log([HCO₃⁻]/0.0012) To undo the logarithm, raise 10 in power of both sides: 10^1.03 = [HCO₃⁻]/0.0012 Now, simply solve for [HCO₃⁻]: [HCO₃⁻] = 0.0012 x 10^1.03 [HCO₃⁻] ≈ 0.0021 M The bicarbonate ion concentration required to buffer the pH of blood at pH = 7.40 is approximately 0.0021 M.

Key concepts

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation provides a way to determine the pH of a buffer solution. It is helpful in cases where you are trying to maintain the pH of a solution at a certain level. Typically, it is used to calculate the ratio of conjugate base to acid needed to achieve this desired pH.

This equation is derived from the expression for the dissociation constant of the acid, and can be written as follows:

• \( \text{pH} = \text{pKa} + \log \left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \)

Here, \([\text{A}^-]\) is the concentration of the conjugate base, \([\text{HA}]\) is the concentration of the acid, and \(\text{pKa}\) is the negative logarithm of the acid dissociation constant \(K_a\).

In the context of the carbonic acid-bicarbonate buffer system, this equation helps us find the necessary bicarbonate ion concentration required to maintain blood pH at 7.40 under given conditions.

bicarbonate ion concentration

Bicarbonate ions (\(\text{HCO}_3^-\)) play a crucial role in maintaining the pH of blood through the carbonate buffer system. They act as a buffer to neutralize acids added to the blood, thus preventing drastic changes in its pH.

From the Henderson-Hasselbalch equation, once the pKa is known (in this case, 6.37 derived from \( \text{K}_a = 4.3 \times 10^{-7} \)), you can calculate the concentration of these bicarbonate ions necessary to maintain the pH of the blood.

In the provided exercise, the calculation went as follows:

• Given: \( [\text{HA}] = 0.0012 \text{ M} \), \( \text{pH} = 7.40 \)
• Seek \([\text{HCO}_3^-]\) such that \( 7.40 = 6.37 + \log \left(\frac{[\text{HCO}_3^-]}{0.0012}\right) \)
• Solve the above equation for \([\text{HCO}_3^-]\)
• The needed bicarbonate concentration turned out to be approximately \(0.0021 \text{ M}\)

By adjusting the bicarbonate ion concentrations, our blood is able to resist significant fluctuations in pH, emphasizing the importance of these ions in biological systems.

pH regulation

pH regulation is a critical function in biological systems, especially in humans, where the proper functioning of enzymes and metabolic processes is highly dependent on a stable pH environment.

In the blood, the pH is tightly regulated around 7.40 through various mechanisms, one of the most important being the bicarbonate buffer system. This system works by adjusting the levels of carbonic acid (H₂CO₃) and bicarbonate ions (HCO₃⁻), balancing the shift in hydrogen ion (H⁺) concentration, which in turn stabilizes the pH.

• Increased H⁺ concentration results in a lower pH (more acidic). The bicarbonate ions can neutralize these excess H⁺ ions.
• Conversely, a decrease in H⁺ concentration (higher pH) means carbonic acid will dissociate, releasing H⁺ ions to bring the pH back to a neutral level.

In situations where pH regulation fails, serious health conditions can arise, such as acidosis or alkalosis, which can have severe biological implications. Thus, the bicarbonate buffering mechanism is essential for healthcare professionals to understand when dealing with such issues. Through the use of buffer systems, organisms are able to maintain a relatively constant internal environment which is crucial for survival.