A buffer is prepared by adding \(10.0 \mathrm{~g}\) of ammonium chloride \(\left(\mathrm{NH}_{4} \mathrm{Cl}\right)\) to \(250 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{NH}_{3}\) solution. (a) What is the \(\mathrm{pH}\) of this buffer? (b) Write the complete ionic equation for the reaction that occurs when a few drops of nitric acid are added to the buffer. (c) Write the complete ionic equation for the reaction that occurs when a few drops of potassium hydroxide solution are added to the buffer.

To find the pH of the buffer, first calculate the concentrations of the weak acid \(\mathrm{NH}_{4}^{+}\) and the conjugate base \(\mathrm{NH}_{3}\). The concentration of the ammonia \((\mathrm{NH}_{3})\) is given as \(1.00 \mathrm{M}\). To calculate the concentration of \(\mathrm{NH}_{4}^{+}\), you can use the formula: \(\frac{mass}{molar\ mass \times volume}\) Using the molar mass of NH4Cl as 53.49 g/mol and the volume of NH3 as 0.250 L (equiv. to 250 mL), we have: \(\frac{10.0\mathrm{g}}{53.49\mathrm{g/mol} \times 0.250\mathrm{L}} = 0.747\mathrm{M}\)

The next step is to find the K_a of \(\mathrm{NH}_{4}^{+}\) using the K_b of its conjugate base, ammonia (\(\mathrm{NH}_{3}\)). You can find the K_a value through the formula: \(K_a = \frac{K_w}{K_b}\), where \(K_w\) is the ion-product constant for water (\(1.0 \times 10^{-14}\)) and the K_b of ammonia is \(1.8 \times 10^{-5}\). Calculate K_a: \(K_a = \frac{1.0 \times 10^{-14}}{1.8 \times 10^{-5}} = 5.56 \times 10^{-10}\)

Now you can use the Henderson-Hasselbalch equation to calculate the pH of the buffer solution: \(pH = pK_a + log(\frac{[A^-]}{[HA]})\) \(pH = -log(5.56 \times 10^{-10}) + log(\frac{1.00}{0.747})\) \(pH = 9.25 + 0.146 = 9.40\) The pH of the buffer solution is 9.40. b) Complete ionic equation with nitric acid

When nitric acid (\(\mathrm{HNO}_{3}\)) is added to the buffer, the weak acid, ammonium ion (\(\mathrm{NH}_{4}^{+}\)), reacts with the added strong acid, as follows: \(\mathrm{NH}_{4}^{+}(aq) + \mathrm{HNO}_{3}(aq) \rightarrow \mathrm{NH}_{3}(aq) + \mathrm{H}_{2}\mathrm{O}(l) + \mathrm{NO}_{3}^{-}(aq)\) c) Complete ionic equation with potassium hydroxide

When potassium hydroxide (\(\mathrm{KOH}\)) is added to the buffer, the conjugate base, ammonia (\(\mathrm{NH}_{3}\)), reacts with the added strong base, as follows: \(\mathrm{NH}_{3}(aq) + \mathrm{KOH}(aq) \rightarrow \mathrm{NH}_{4}^{+}(aq) + \mathrm{OH}^{-}(aq) + \mathrm{K}^{+}(aq)\) To summarize: a) The pH of the buffer solution is 9.40. b) The complete ionic equation for the reaction with nitric acid is: \(\mathrm{NH}_{4}^{+}(aq) + \mathrm{HNO}_{3}(aq) \rightarrow \mathrm{NH}_{3}(aq) + \mathrm{H}_{2}\mathrm{O}(l) + \mathrm{NO}_{3}^{-}(aq)\) c) The complete ionic equation for the reaction with potassium hydroxide is: \(\mathrm{NH}_{3}(aq) + \mathrm{KOH}(aq) \rightarrow \mathrm{NH}_{4}^{+}(aq) + \mathrm{OH}^{-}(aq) + \mathrm{K}^{+}(aq)\)