Problem 25 - Chemistry and Chemical Reactivity

Question

You require 36.78 mL of 0.0105 M HCl to reach the equivalence point in the titration of 25.0 mL of aqueous ammonia. (a) What was the concentration of \(\mathrm{NH}_{3}\) in the original ammonia solution? (b) What are the concentrations of \(\mathrm{H}_{3} \mathrm{O}^{+}, \mathrm{OH}^{-},\) and \(\mathrm{NH}_{4}^{+}\) at the equivalence point? (c) What is the pH of the solution at the equivalence point?

Step-by-Step Solution

Answer

a) 0.0155 M NH3. b) Need to find concentration using realized steps in Steps 5-6. c) Calculate pH using Step 7.

Step 1: Determine Moles of HCl Used

Calculate the number of moles of HCl used in the titration using the formula: \( ext{moles of HCl} = ext{Molarity} \times \text{Volume in Liters} \).\[ \text{moles HCl} = 0.0105 \frac{\text{mol}}{\text{L}} \times 0.03678 \text{ L} = 3.8629 \times 10^{-4} \text{ moles} \]

Step 2: Equivalence Point Stoichiometry

At the equivalence point, the moles of HCl will be equal to the moles of \( \mathrm{NH}_{3} \) reacting since they react in a 1:1 ratio. Therefore, moles of \( \mathrm{NH}_{3} = 3.8629 \times 10^{-4} \text{ moles} \).

Step 3: Find Initial Concentration of Ammonia

Calculate the initial concentration of \( \mathrm{NH}_{3} \) using its volume and moles: \( C = \frac{\text{moles}}{\text{volume}} \).\[ C_{\mathrm{NH}_3} = \frac{3.8629 \times 10^{-4} \text{ moles}}{0.025 \text{ L}} = 0.0155 \text{ M} \]

Step 4: Determine Ammonium Ion Concentration

Since all \( \mathrm{NH}_{3} \) is converted to \( \mathrm{NH}_{4}^{+} \) at the equivalence point, the concentration of \( \mathrm{NH}_{4}^{+} \) is \( 0.0155 \text{ M} \).

Step 5: Calculate Hydronium Ion Concentration

The concentration of \( \mathrm{H}_{3} \mathrm{O}^{+} \) can be determined using the ion product of water: \( K_w = \left[ \mathrm{H}_{3} \mathrm{O}^{+} \right] \left[ \mathrm{OH}^{-} \right] \). At this point, calculate \( \left[ \mathrm{H}_{3} \mathrm{O}^{+} \right] = \frac{1.0 \times 10^{-14}}{\sqrt{K_b \cdot C \text{ of } \mathrm{NH}_{4}^{+}}} \).

Step 6: Determine Hydroxide Ion Concentration

Because \( K_w = \left[ \mathrm{H}_{3} \mathrm{O}^{+} \right] \left[ \mathrm{OH}^{-} \right] \), calculate \( \left[ \mathrm{OH}^{-} \right] = \frac{K_w}{\left[ \mathrm{H}_{3} \mathrm{O}^{+} \right]} \) once \( \left[ \mathrm{H}_{3} \mathrm{O}^{+} \right] \) is found.

Step 7: Calculate pH from Hydronium Ion Concentration

After calculating \( [\mathrm{H}_{3} \mathrm{O}^{+}] \), find pH: \( \text{pH} = -\log ( [\mathrm{H}_{3} \mathrm{O}^{+}] ) \).

Key Concepts

Equivalence Point

During an acid-base titration, the equivalence point is a key milestone. It's when the acid and base have completely reacted with each other. In this exercise, the equivalence point is reached when 36.78 mL of 0.0105 M HCl reacts with 25.0 mL of aqueous ammonia. At this point, the number of moles of HCl equals the number of moles of ammonia (NH₃) because both substances react in a 1:1 ratio. Understanding this concept is crucial to solving the problem as it allows you to determine how much of each reactant is present at the equivalence point. Knowing when this point is reached gives insight into the reaction's completion.

Molarity Calculations

Calculating molarity is essential in determining the concentration of a solution. Molarity, or concentration, is defined as the number of moles of solute per liter of solution. The formula used is:

• Molarity (C) = moles of solute / volume of solution in liters

In the solution provided, we first calculate the moles of HCl used by converting its volume from mL to liters and using its molarity. After establishing that the moles of HCl are equal to the moles of NH₃ at the equivalence point, we use the given volume of NH₃ solution to find its initial concentration. This way, we determine that the original ammonia solution's concentration (before titration) is 0.0155 M.

pH Determination

The pH of a solution is a quantitative measure of its acidity or basicity. It is calculated using the formula:

• \[\text{pH} = -\log ([\mathrm{H}_{3}\mathrm{O}^{+}])\]

In this exercise, once the equivalence point is achieved, calculations can be made to determine the hydronium ion concentration, \( [\mathrm{H}_{3} \mathrm{O}^{+}] \), by using the ion product of water. After determining the hydronium concentration, you substitute this into the pH formula to find the pH. Since the reaction involves a weak base (NH₃) and a strong acid (HCl), the pH at the equivalence point will be less than 7, indicating an acidic solution.

Stoichiometry

Stoichiometry is a fundamental concept in chemistry. It allows us to predict the outcomes of chemical reactions quantitatively. In this titration problem, stoichiometry helps in determining the initial concentration of the ammonia solution by using the 1:1 mole ratio between NH₃ and HCl. Stoichiometry also confirms that at the equivalence point, all NH₃ has reacted with HCl to form NH₄⁺ ions. By understanding the stoichiometric relationships, we solve for unknowns in the reaction, such as the starting concentrations and the pH at the equivalence point. Comprehending these relationships is vital for successful calculations in any chemical titration problem.