How many microliters of 1.000 M NaOH solution must be added to 25.00 mL of a 0.1000 M solution of lactic acid CH3CH(OH)COOH or HC3H5O3 to produce a buffer with pH = 3.75?

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Identify the components of the buffer system: lactic acid (HC3H5O3) and its conjugate base (C3H5O3^-).

Use the Henderson-Hasselbalch equation: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \) to relate pH, pKa, and the ratio of concentrations of the conjugate base and acid.

Find the \( \text{pK}_a \) of lactic acid, which is approximately 3.86.

Rearrange the Henderson-Hasselbalch equation to solve for the ratio \( \frac{[\text{A}^-]}{[\text{HA}]} \) using the given pH of 3.75.

Calculate the moles of lactic acid initially present and use stoichiometry to determine the moles of NaOH needed to achieve the desired ratio, then convert this to volume in microliters.

Key Concepts

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

Buffer Solutions

A buffer solution is a system that resists changes in pH upon the addition of small amounts of acid or base. It typically consists of a weak acid and its conjugate base or a weak base and its conjugate acid. In this case, lactic acid acts as the weak acid, and the addition of NaOH will create its conjugate base, helping to maintain the desired pH.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentration of its acid and conjugate base. It is expressed as pH = pKa + log([A-]/[HA]), where pKa is the acid dissociation constant. This equation is essential for calculating the required concentrations of lactic acid and its conjugate base after adding NaOH to achieve the target pH of 3.75.

Stoichiometry of Acid-Base Reactions

Stoichiometry involves the calculation of reactants and products in chemical reactions. In the context of this question, it is important to determine how much NaOH is needed to neutralize a portion of lactic acid to form its conjugate base. This requires understanding the molar relationships between the acid and base, which can be calculated using their concentrations and the desired final volume of the buffer solution.

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Acid-Base Reaction

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Suppose you want to do a physiological experiment that calls for a pH 6.50 buffer. You find that the organism with which you are working is not sensitive to the weak acid H2A 1Ka1 = 2 * 10-2; Ka2 = 5.0 * 10-72 or its sodium salts. You have available a 1.0 M solution of this acid and a 1.0 M solution of NaOH. How much of the NaOH solution should be added to 1.0 L of the acid to give a buffer at pH 6.50? (Ignore any volume change.)

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