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

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Step 1: Identify the buffer system. In this case, the buffer system is NH4Cl/NH3. NH4Cl is the acidic component (NH4+) and NH3 is the basic component.

Step 2: Use the Henderson-Hasselbalch equation, which is pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the base (NH3) and [HA] is the concentration of the acid (NH4+). In this case, we are looking for the ratio [A-]/[HA], so we can rearrange the equation to [A-]/[HA] = 10^(pH - pKa).

Step 3: Find the pKa value. The Ka of NH4+ is 5.6 x 10^-10, so the pKa is -log(5.6 x 10^-10).

Step 4: Substitute the given pH and the calculated pKa into the rearranged Henderson-Hasselbalch equation to find the ratio [A-]/[HA].

Step 5: The ratio [A-]/[HA] is the volume ratio of NH3 to NH4Cl. Therefore, to prepare the buffer solution, you should mix the 1.0 M solutions of NH4Cl and NH3 in this volume ratio.

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Key Concepts

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

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, NH4Cl acts as the weak acid and NH3 as the weak base, allowing the solution to maintain a stable pH.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentration of its acid and base components. It is expressed as pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the base and [HA] is the concentration of the acid. This equation is essential for calculating the required volume ratio of NH4Cl and NH3 to achieve the desired pH.

pKa and pKb Values

The pKa and pKb values are measures of the strength of an acid and a base, respectively. The pKa is the negative logarithm of the acid dissociation constant (Ka), while pKb is the negative logarithm of the base dissociation constant (Kb). For the NH4+/NH3 system, knowing the pKa allows for the calculation of the necessary concentrations to achieve a specific pH, as pKa and pKb are related through the equation pKa + pKb = 14.

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