A food chemist studying the formation of lactic acid in sour milk prepares a buffer that is 0.58 M in lactic acid (HC3H5O3) and 0.36 M in sodium lactate (NaC3H5O3). Use the Henderson–Hasselbalch equation to calculate the pH of the buffer solution.

Verified step by step guidance

Identify the components of the buffer solution: lactic acid (HC3H5O3) as the weak acid and sodium lactate (NaC3H5O3) as the conjugate base.

Write the Henderson–Hasselbalch equation: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \), where \([\text{A}^-]\) is the concentration of the conjugate base and \([\text{HA}]\) is the concentration of the weak acid.

Look up or calculate the \(\text{pK}_a\) of lactic acid. The \(\text{pK}_a\) is the negative logarithm of the acid dissociation constant \(K_a\).

Substitute the given concentrations into the Henderson–Hasselbalch equation: \([\text{A}^-] = 0.36\, \text{M}\) and \([\text{HA}] = 0.58\, \text{M}\).

Calculate the pH by solving the Henderson–Hasselbalch equation with the substituted values.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a buffer solution. It relates the pH of the solution to the pKa of the weak acid and the ratio of the concentrations of the conjugate base to the weak acid. The equation is expressed as pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid.

Buffer Solutions

Buffer solutions are mixtures that resist 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. In this case, lactic acid and sodium lactate form a buffer system that helps maintain a stable pH in the solution, which is crucial for many biochemical processes.

pKa and Acid-Base Equilibrium

The pKa is a measure of the strength of an acid in solution, defined as the negative logarithm of the acid dissociation constant (Ka). It indicates the pH at which half of the acid is dissociated into its conjugate base. Understanding pKa is essential for using the Henderson-Hasselbalch equation, as it helps determine the pH of the buffer solution based on the concentrations of the acid and its conjugate base.

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Calculate the pH of 0.375 L of a 0.18 M acetic acid–0.29 M sodium acetate buffer before and after the addition of (a) 0.0060 mol of KOH. Assume that the volume remains constant.

Textbook Question

Calculate the pH of 0.375 L of a 0.18 M acetic acid–0.29 M sodium acetate buffer before and after the addition of (b) 0.0060 mol of HBr. Assume that the volume remains constant.

Textbook Question

Use the Henderson–Hasselbalch equation to calculate the pH of a buffer solution that is 0.25 M in formic acid (HCO2H) and 0.50 M in sodium formate (HCO2Na).

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The ratio of HCO3- to H2CO3 in blood is called the 'bicarb number' and is used as a measure of blood pH in hospital emergency rooms. A newly diagnosed diabetic patient is admitted to the emergency room with ketoacidosis and a bicarb number of 10. Calculate the blood pH. Ka for carbonic acid at room temperature (37 degrees Celsius) os 7.9 x 10^-7).

Textbook Question

In what volume ratio should you mix 1.0 M solutions of NH4Cl and NH3 to produce a buffer solution having pH = 9.80?