Problem 119 - General Chemistry

Question

a Draw a pH titration curve that represents the titration of \(50.0 \mathrm{~mL}\) of \(0.10 \mathrm{M} \mathrm{NH}_{3}\) by the addition of \(0.10 M \mathrm{HCl}\) from a buret. Label the axes and put a scale on each axis. Show where the equivalence point and the buffer region are on the titration curve. You should do calculations for the \(0 \%, 30 \%, 50 \%,\) and \(100 \%\) titration points. b) Is the solution neutral, acidic, or basic at the equivalence point? Why?

Step-by-Step Solution

Answer

The solution is acidic at the equivalence point due to the presence of \(\text{NH}_4^+\).

Step 1: Understanding the Titration Process

The titration involves an ammonia solution, which is a weak base, being titrated by hydrochloric acid, a strong acid. The chemical reaction is \( \text{NH}_3 + \text{HCl} \rightarrow \text{NH}_4^+ + \text{Cl}^- \). This key reaction will help determine pH changes during the titration.

Step 2: Identify the Initial pH (0% Titration)

Initially, only the ammonia solution is present. Use the Kb for ammonia (\(1.8 \times 10^{-5}\)) to find the initial pH. The concentration of OH- ions can be found from \(\text{NH}_3 + \text{H}_2\text{O} \rightarrow \text{NH}_4^+ + \text{OH}^-\), with \([\text{OH}^-]\approx\sqrt{K_b [\text{NH}_3]}\). Calculate \([\text{OH}^-]\) and convert to pH: \(\text{pH} = 14 - \text{pOH}\).

Step 3: Calculation at 30% Titration

At 30% titration, 15 mL of HCl is added. Calculate moles of \(\text{NH}_3\) present and moles of \(\text{HCl}\) added. Determine the concentration of \(\text{NH}_4^+\) and \(\text{NH}_3\) using the Henderson-Hasselbalch equation for base: \(\text{pH} = pK_b + \log\left(\frac{[\text{base}]}{[\text{acid}]}\right)\).

Step 4: Calculation at 50% Titration

At 50% titration, 25 mL of HCl is added. Here, the moles of \(\text{NH}_3\) equal the moles of \(\text{NH}_4^+\), so \(\text{pH} = pK_b + \log(1) = pK_b\). Calculate \(\text{pH} = 14 - pK_w + pK_a = 14 - 1.8 \times 10^{-5} + 9.25\).

Step 5: Calculation at Equivalence Point (100% Titration)

At the equivalence point, 50 mL of HCl is added to neutralize \(\text{NH}_3\). Solution contains only \(\text{NH}_4Cl\), a salt that hydrolyzes in water to form \(\text{NH}_4^+\), which is acidic. Use \(\text{pH} = 14 - \text{pOH}\) from \(\text{NH}_4^+ \rightarrow \text{NH}_3 + \text{H}^+\), with \(K_a = \frac{K_w}{K_b}\) to determine \([\text{H}^+]\).

Step 6: Draw the Titration Curve

Plot the calculated pH on the y-axis against the volume of \(\text{HCl}\) added on the x-axis, marking significant points: starting pH at 0%, buffer region (30% to 50%), and equivalence point at 100%. The buffer zone is typically flat compared to other regions, while a steep rise at 100% shows the equivalence point.

Step 7: Assess the Solution at the Equivalence Point

At the equivalence point, the solution contains \(\text{NH}_4Cl\) and has a pH less than 7, indicating an acidic solution. This is because \(\text{NH}_4^+\) is an acidic ion that shifts the pH down.

Key Concepts

Ammonia Titration

In ammonia titration, the core focus is neutralizing a weak base, ammonia (NH_3 ), with a strong acid, hydrochloric acid (HCl). This titration forms a fundamental reaction:\[NH_3 + HCl \rightarrow NH_4^+ + Cl^- \]This process essentially means each drop of HCl added reacts with NH_3 to produce NH_4^+ and Cl^- ions, changing the solution's pH. Ammonia acts as a weak base, initially requiring the determination of its K_b value to calculate the initial pH. The initial pH will decrease as HCl is added.

• Initial pH: Calculated using NH_3's equilibrium with water to form OH^- ions.
• Reaction monitoring: Every ml of HCl added incrementally progresses the titration.
• Final composition: At the equivalence point, the solution contains NH_4Cl, and it becomes acidic due to hydrolysis.

Buffer Region

A key feature in titration curves is the buffer region, where significant pH stability is observed. In the ammonia titration, this region occurs between roughly 30% to 50% titration of NH_3.
This span represents gradual addition of strong acid.This is because partial neutralization of NH_3 forms a buffer solution composed of comparable concentrations of NH_3 and NH_4^+. Buffers resist drastic pH changes when small amounts of acids or bases are introduced.

• pH Stability: Slight changes in pH due to the equilibrium between NH_3 and NH_4^+.
• The Henderson-Hasselbalch Equation: Can be used to calculate pH during this region—\(\text{pH} = \text{pK}_b + \log\left(\frac{[\text{base}]}{[\text{acid}]}\right)\)

Equivalence Point

In any titration, reaching the equivalence point signifies completion of the reaction between titrant and analyte. For ammonia titration, it occurs when an equal number of moles of NH_3 and HCl have reacted. At this juncture, ammonia is entirely converted to NH_4^+ given by:\[NH_3 + HCl \rightarrow NH_4^+ + Cl^- \]At this point, the pH is less than 7, thus acidic. The presence of NH_4Cl dominates the solution, and the hydrolysis of NH_4^+ to produce H^+ ions results in acidity.
This is a sharp change compared to the buffer region, denoting rapid pH drop. The curve appears steep here.

• Composition Shift: The solution is NH_4Cl dominated, highlighting acidity.
• pH Change: pH values reflect acidic nature due to H^+ generation by hydrolysis.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation provides a quantitative way to calculate pH during the buffer region of a titration. It relates the pH with the pK_b (or pK_a) and the ratio of the concentrations of base and acid components of the buffer.Functionally, it is expressed as:\[\text{pH} = \text{pK}_b + \log\left(\frac{[\text{base}]}{[\text{acid}]}\right)\]For ammonia titration, this equation is particularly useful during stages where both NH_3 and NH_4^+ coexist. This formula aids in predicting any stable pH range during buffer action.

• Base/Acid Ratio: Reflects relative concentrations of base (NH_3) and acid (NH_4^+).
• pK_b Component: Represents the basicity of ammonia, determining initial and influenced pH values.