How many grams of solid ammonium chloride should be added to 1.50 L of a 0.224 M ammonia solution to prepare a buffer with a pH of 8.720 ?

Set up an ICE chart and use the Henderson-Hasselbalch equation.

To determine the number of grams of solid ammonium chloride needed to prepare a buffer with a specific pH, you need to follow several steps:

Step 1: Identify the relevant chemical reaction
In this case, the relevant reaction is the hydrolysis of ammonium chloride (NH4Cl) in water:

NH4Cl + H2O ⇌ NH4OH + HCl

Ammonium chloride reacts with water to form ammonium hydroxide (NH4OH) and hydrochloric acid (HCl).

Step 2: Write the equilibrium expression for the reaction
The equilibrium expression for the hydrolysis reaction is:

Kw = [NH4OH][HCl] / [NH4Cl]

where Kw is the equilibrium constant for water, which is equal to 1.0 x 10^-14 at 25°C.

Step 3: Relate pH to the concentrations of NH4OH and HCl
Since the pH of the buffer solution is given (pH = 8.720), you can use the formula:

pH = -log[H+]

to find the concentration of hydrogen ions [H+] in the solution.

[H+] = 10^(-pH)

Step 4: Find the concentrations of NH4OH and HCl
Since the reaction is in a 1:1 ratio, the concentrations of NH4OH and HCl are equal to each other.

[NH4OH] = [HCl] = [H+]

Step 5: Calculate the concentration of NH4Cl
Using the equilibrium expression and the concentrations of NH4OH and HCl, you can calculate the concentration of NH4Cl:

[NH4Cl] = [NH4OH][HCl] / Kw

Step 6: Convert the concentration of NH4Cl to grams
To convert the concentration to grams, you need to use the molar mass of NH4Cl, which is 53.49 g/mol. The formula to calculate the number of grams is:

Mass (g) = Concentration (mol/L) x Volume (L) x Molar mass (g/mol)

Given that the volume of the ammonia solution is 1.50 L, you can substitute the values into the formula to calculate the mass of NH4Cl.

Keep in mind that these calculations assume complete dissociation of NH4Cl in water, which may not be entirely accurate. However, it provides a reasonable approximation for most practical purposes.