Muscle physiologists study the accumulation of lactic acid [CH3 CH(OH) COOH] during exercise. Fo

step 1 Question 127 is simply a buffer solution calculation with a mixture of lactic acid and sodium la

Muscle physiologists study the accumulation of lactic acid...

Muscle physiologists study the accumulation of lactic acid $\left[\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COOH}\right]$ during exercise. Food chemists study its occurrence in sour milk, beer, wine, and fruit. Industrial microbiologists study its formation by various bacterial species from carbohydrates. A biochemist prepares a lactic acid-lactate buffer by mixing 225 $\mathrm{mL}$ of 0.85$M$ lactic acid $\left(K_{\mathrm{a}}=1.38 \times 10^{-4}\right)$ with 435 $\mathrm{mL}$ of 0.68 $\mathrm{M}$ sodium lactate. What is the buffer pH?

Key Concepts

Acid-Base Equilibrium

This concept refers to the dynamic balance in solution between acids, which donate protons (H?), and bases, which accept protons. In aqueous solutions, many weak acids and bases do not fully dissociate, resulting in an equilibrium state that is characterized by a constant called the acid dissociation constant (Ka). Understanding this equilibrium is essential when analyzing how solutions respond to changes in pH or when mixed with other species.

Buffer Solutions

Buffer solutions are systems that resist significant changes in pH when small amounts of acid or base are added. They typically consist of a weak acid and its conjugate base or a weak base and its conjugate acid. The ability of a buffer to maintain a nearly constant pH stems from the equilibrium established between the weak acid and its conjugate base, making them crucial in both biological systems and industrial applications.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical expression that relates the pH of a buffer solution to the pKa of the acid and the ratio of the concentrations of its conjugate base and the acid. It is given by pH = pKa + log([conjugate base]/[acid]). This equation is a key tool in calculating the pH of buffer solutions and designing buffers with desired pH levels.

Molarity and Mixing Solutions

Molarity is a measure of concentration that refers to the number of moles of a solute present in one liter of solution. When solutions with different solute concentrations are mixed, calculating the total number of moles of the solute in the combined volume is crucial. This concept is applied in buffer preparation where accurate determining of the acid and its conjugate base’s moles ensures the proper functioning of the buffer system.

Acid Dissociation Constant (Ka) and pKa

The acid dissociation constant, Ka, quantifies the strength of a weak acid in solution, expressing the extent to which the acid donates protons to water. The pKa, being the negative logarithm of Ka, is used frequently because it provides a more convenient scale to compare acid strengths. The relationship between pKa and the pH of a buffer is pivotal in determining and maintaining the correct balance between the acid and its conjugate base.

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