What mass of sodium benzoate should you add to 150.0 mL of a 0.15 M benzoic acid solution to obtain a buffer with a pH of 4.25? (Assume no volume change.)

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Step 1: Write down the Henderson-Hasselbalch equation, which is used to calculate the pH of a buffer solution: pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the base (sodium benzoate) and [HA] is the concentration of the acid (benzoic acid).

Step 2: The pKa of benzoic acid is 4.20. Substitute the given pH and pKa into the Henderson-Hasselbalch equation to solve for the ratio [A-]/[HA].

Step 3: Since the volume of the solution doesn't change, the ratio [A-]/[HA] is equal to the ratio of the moles of A- (sodium benzoate) to the moles of HA (benzoic acid). You know the moles of benzoic acid from its molarity and volume, so you can solve for the moles of sodium benzoate.

Step 4: Convert the moles of sodium benzoate to grams using its molar mass. This will give you the mass of sodium benzoate you need to add to the solution.

Step 5: Remember to check your answer to make sure it makes sense. The mass of sodium benzoate should be a positive number, and it should be reasonable given the volume and molarity of the solution.

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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, benzoic acid (weak acid) and sodium benzoate (conjugate base) form a buffer that can maintain a stable pH when mixed.

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 negative logarithm of the acid dissociation constant. This equation is essential for calculating the required concentrations of benzoic acid and sodium benzoate to achieve the desired pH.

Molarity and Mass Calculations

Molarity (M) is a measure of concentration defined as moles of solute per liter of solution. To find the mass of sodium benzoate needed, one must first determine the number of moles required using the desired concentration and volume of the buffer solution. This can then be converted to mass using the molar mass of sodium benzoate, allowing for precise preparation of the buffer.