A volume of \(25.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{HCl}\) is titrated against a \(0.100 \mathrm{M} \mathrm{NH}_{3}\) solution added to it from a buret. Calculate the \(\mathrm{pH}\) values of the solution (a) after \(10.0 \mathrm{~mL}\) of \(\mathrm{NH}_{3}\) solution have been added, \((\mathrm{b})\) after \(25.0 \mathrm{~mL}\) of \(\mathrm{NH}_{3}\) solution have been added, (c) after \(35.0 \mathrm{~mL}\) of \(\mathrm{NH}_{3}\) solution have been added.

Short Answer

Expert verified
a) pH=1.2 , b) pH=9.25 , c) pH= 9.7. These values might slightly vary based on the exact pKa value used.

Step by step solution

01

Calculating the moles of HCl and NH3

First, calculate the number of moles of HCl in the 25.0 mL solution using the molarity formula M = n/V. Thus, n(HCl) = M x V = 0.100 mol/L x 0.025 L = 0.0025 mol. Similarly, the number of moles of NH3 added at each point can be calculated as n(NH3) = M x V.
02

Calculating the moles of NH3 for each given volume and determining the resulting species

Next, calculate the amount of NH3 in mol that was added in each case (10.0 mL, 25.0 mL, and 35.0 mL). In each case, deduct the mol of HCl present initially from moles of NH3 added. If the moles of NH3 are greater than HCl, then they will neutralize HCl and NH4Cl will form. If the moles of NH3 are less than HCl, then it will be a case of a weak base titrated with a strong acid.
03

Calculating the pH using the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation (pH = pKa + log([A-]/[HA])) can be applied, keeping in mind that A- and HA will be different for each part of the scenario. [A-] is the concentration for the excess substance after reaction while [HA] is the concentration for the substance which was initially higher and has been partially neutralized. pKa in case of NH3 is the pKa of the conjugate acid (NH4+) which is 9.25.

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