Problem 102 - Chemistry The Molecular Science

Question

When asked to prepare a carbonate buffer with \(\mathrm{pH}=10\) a lab technician wrote this equation to determine the ratio of weak acid to conjugate base needed: $$ 10=10.32+\log \frac{\left[\mathrm{HCO}_{3}^{-}\right]}{\left[\mathrm{H}_{2} \mathrm{CO}_{3}\right]} $$ What is wrong with this setup? If the technician prepared a solution containing equimolar concentrations of \(\mathrm{HCO}_{3}^{-}\) and \(\mathrm{CO}_{3}^{2-},\) calculate the \(\mathrm{pH}\) of the resulting buffer.

Step-by-Step Solution

Answer

The pH is 10.32 using the correct buffer, bicarbonate/carbonate.

Step 1: Identify the Correct Buffer System

The technician's equation incorrectly uses the pH and pKa values for the wrong buffer pair. The correct pair for a pH of 10 is the bicarbonate (\[ \mathrm{HCO}_3^- \]) and carbonate ion (\[ \mathrm{CO}_3^{2-} \]) system, not bicarbonate and carbonic acid, which works for around pH 6.3. The relevant equation for the bicarbonate-carbonate buffer is\[ \text{pH} = 10.32 + \log \frac{[\mathrm{CO}_3^{2-}]}{[\mathrm{HCO}_3^-]} \].

Step 2: Apply the Henderson-Hasselbalch Equation

To find the pH of the solution prepared by the technician with equimolar concentrations of bicarbonate and carbonate:If \([\mathrm{HCO}_3^-] = [\mathrm{CO}_3^{2-}]\), then using the equation \[\text{pH} = \text{pKa} + \log \frac{[\mathrm{CO}_3^{2-}]}{[\mathrm{HCO}_3^-]}\], the log term becomes log(1) = 0. Thus,\[ \text{pH} = 10.32 + 0 = 10.32 \].

Key Concepts

pH calculation

Calculating the pH of a solution is a fundamental skill in chemistry. The pH is a measure of how acidic or basic a solution is. It is determined as the negative logarithm of the hydronium ion concentration, represented as:\[\text{pH} = -\log [\text{H}^+]\]Here, \([\text{H}^+]\) signifies the concentration of hydrogen ions in moles per liter. The scale ranges from 0, which is very acidic, to 14, which is very basic, with 7 being neutral.
For buffer solutions, pH calculations involve understanding the equilibrium between weak acids and their conjugate bases. These buffers resist drastic pH changes upon dilution or addition of small amounts of acids or bases.
It is crucial to choose the right buffer system based on the desired pH range. Incorrectly choosing components, as highlighted by the technician's error, can lead to a miscalculated pH. The ideal buffer system provides an equilibrium that stabilizes the pH at the needed level.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch Equation is a critical tool for understanding and computing the pH of buffer solutions. It modifies the basic pH formula by accounting for the concentrations of the acid and base components of the buffer.
The equation is given by:\[\text{pH} = \text{pKa} + \log \frac{[\text{A}^-]}{[\text{HA}]}\]where \( \text{A}^- \) is the concentration of the conjugate base, and \( \text{HA} \) is the concentration of the acid. The \( \text{pKa} \) is the negative logarithm of the acid dissociation constant \( K_a \).

• It relates the pH, \( \text{pKa} \), and the concentration ratio of conjugate base to acid.
• It allows us to calculate pH if \( \text{pKa} \) and component concentrations are known.
• The equation simplifies to \( \text{pH} = \text{pKa} \) when concentrations are equal as the log(1) becomes zero.

Understanding this relationship helps choose the correct acids and bases to achieve the desired pH in a buffer solution.

bicarbonate-carbonate buffer system

The bicarbonate-carbonate buffer system is a crucial component in maintaining the pH of solutions around a more alkaline level, typically around pH 10. This system involves the interconversion of bicarbonate ions \( \text{HCO}_3^- \) and carbonate ions \( \text{CO}_3^{2-} \).
Key points of this buffer system include:

• It offers a buffering range suitable for alkaline conditions, making it useful in various biochemical and industrial applications.
• The equilibrium reaction between bicarbonate and carbonate ions stabilizes the pH against changes from added acids or bases.
• The Henderson-Hasselbalch Equation is used to derive the pH of mixtures containing both components, as the technician in the exercise attempted with equimolar amounts of bicarbonate and carbonate ions.

When setting up this buffer, ensure the correct use of the equation with the corresponding \( \text{pKa} \) value for accurate pH prediction. The technician's original setup didn't account for this specific reaction pair, highlighting the need for precise pair selection based on the desired pH.