Calculate the change in pH when 9.00 mL of 0.100 M NaOH(aq) is added to 100.0 mL of a buffer solution that is 0.100 M in NH3(aq) and 0.100 M in NH4Cl(aq).

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To calculate the change in pH when a base is added to a buffer solution, you need to determine the change in concentration of the conjugate acid and the conjugate base. The Henderson-Hasselbalch equation can then be used to calculate the change in pH.

First, write out the balanced chemical equation of the reaction between NaOH(aq) and NH4Cl(aq):

NH4Cl(aq) + NaOH(aq) → NaCl(aq) + NH3(aq) + H2O(l)

From this equation, you can see that NH4Cl is the conjugate acid of NH3 and NaOH is the strong base that reacts with NH4Cl to form NH3.

Now, calculate the amount of NH4Cl and NH3 present in the initial buffer solution:

NH4Cl concentration = 0.100 M
NH4Cl volume = 100.0 mL = 0.100 L
Amount of NH4Cl initially = Concentration x Volume
= 0.100 M x 0.100 L
= 0.010 mol

NH3 concentration = 0.100 M
NH3 volume = 100.0 mL = 0.100 L
Amount of NH3 initially = Concentration x Volume
= 0.100 M x 0.100 L
= 0.010 mol

Since the initial amounts of NH4Cl and NH3 are equal, the buffer solution has equal concentrations of the conjugate acid and base in a 1:1 ratio. This means that the pH of the buffer solution is determined by the pKa value of NH4Cl/NH3 system.

The pKa value of NH4Cl/NH3 is given as 9.25. You can use this value and the Henderson-Hasselbalch equation to calculate the initial pH of the buffer solution:

pH = pKa + log([conjugate base]/[conjugate acid])

Since [conjugate base] = [conjugate acid] (0.010 M) in the initial buffer solution,

pH = pKa + log(1)
= pKa

Therefore, the initial pH of the buffer solution is 9.25.

Next, calculate the change in concentration of NH4Cl and NH3 when 9.00 mL of 0.100 M NaOH is added. Note that NaOH is a strong base, so it will completely react with NH4Cl to form NH3:

NaOH concentration = 0.100 M
NaOH volume = 9.00 mL = 0.00900 L
Amount of NaOH added = Concentration x Volume
= 0.100 M x 0.00900 L
= 0.000900 mol

Since NaOH reacts with NH4Cl in a 1:1 ratio, the amount of NH4Cl decreases by 0.000900 mol, and the amount of NH3 increases by the same amount.

Now, calculate the new concentrations of NH4Cl and NH3 in the buffer solution:

NH4Cl concentration = (0.010 mol - 0.000900 mol) / (0.100 L) = 0.00910 M
NH3 concentration = (0.010 mol + 0.000900 mol) / (0.100 L) = 0.0109 M

Now, you can calculate the new pH of the buffer solution using the Henderson-Hasselbalch equation:

pH = pKa + log([conjugate base]/[conjugate acid])
= 9.25 + log(0.0109 M / 0.00910 M)

Using a calculator, calculate the logarithm and add it to the pKa value of 9.25 to find the new pH.

Thus, the change in pH when 9.00 mL of 0.100 M NaOH is added to 100.0 mL of the buffer solution is the new pH value minus the initial pH value.