Problem 47 - Chemistry: The Central Science in SI Units, Global Edition

Question

Calculate the \(\mathrm{pH}\) at the equivalence point for titrating \(0.200 \mathrm{M}\) solutions of each of the following bases with 0.200 \(M\) HBr: \((\mathbf{a})\) sodium hydroxide \((\mathrm{NaOH}),(\mathbf{b})\) hydroxylamine \(\left(\mathrm{NH}_{2} \mathrm{OH}\right),(\mathbf{c})\) aniline \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\right)\).

Step-by-Step Solution

Answer

In summary, the pH at the equivalence point for each titration is: a) NaOH: pH = 7.00 b) NH2OH: pH ≈ 10.77 c) C6H5NH2: pH ≈ 10.66

Step 1: Identify the species formed at the equivalence point

At the equivalence point, the moles of base will be equal to the moles of acid. Since the given bases are strong bases that react completely with HBr, we can predict the species formed as follows: a) NaOH + HBr -> NaBr + H2O b) NH2OH + HBr -> NH3 + H2O c) C6H5NH2 + HBr -> C6H5NH3+ + Br-

Step 2: Determine concentrations of the species formed at the equivalence point

The concentration of the species formed depends only on the concentration of the base and acid used in the titration because of their equal molar concentrations at the equivalence point. For a), the concentration of NaBr is 0.200 M. For b), the concentration of NH3 is 0.200 M. For c), the concentration of C6H5NH3+ is 0.200 M.

Step 3: Calculate the pH

For the pH calculation, we need to consider the different equilibria. a) Since the formation of NaBr involves a strong base and a strong acid, there is no hydrolysis, and the pH at the equivalence point is 7.00. b) For NH3, we must consider the ammonia equilibrium: NH3 + H2O <-> NH4+ + OH- We apply the Kb for NH3: Kb = [NH4+][OH-] / [NH3] = 1.8 x 10^-5 Since the system is at the equivalence point and [NH3] = [NH4+], we can express Kb in terms of x (the concentration of OH- ions): Kb = x^2 / (0.200 - x) Solving the quadratic equation for x, we get: x ≈ 5.9 x 10^-4 M Then, the pOH can be calculated: pOH = - log10(5.9 x 10^-4) ≈ 3.23 Finally, the pH is obtained by subtracting pOH from 14: pH = 14 - pOH ≈ 10.77 c) For C6H5NH3+, the acid dissociation constant (Ka) of its conjugate acid (C6H5NH2) is 2.5 x 10^-10. Submitting a mass balance, we obtain the following equation for the acid-base equilibrium of aniline and its conjugate acid: 2.5 x 10^-10 = x*(0.200 + x) / (0.200 - x) Solving the quadratic equation for x yields: x ≈ 2.2 x 10^-11 M The H3O+ ion concentration (x) can be directly used to calculate the pH: pH = - log10(2.2 x 10^-11) ≈ 10.66 In summary, the pH at the equivalence point for each titration is: a) NaOH: pH = 7.00 b) NH2OH: pH ≈ 10.77 c) C6H5NH2: pH ≈ 10.66

Key Concepts

Equivalence Point

The equivalence point in a titration occurs when the amount of titrant added is chemically equivalent to the amount of substance present in the sample. Essentially, it's the point at which the number of moles of acid equals the number of moles of base in the solution, leading to neutralization. In an ideal titration, this means all the acid and base have reacted completely.
This is a critical point because it allows us to calculate various properties, such as pH.

• For strong acids and strong bases, the equivalence point typically results in a neutral pH of 7.
• For weak bases titrated with strong acids, the solution is slightly acidic at the equivalence point.
• Knowing the pH at the equivalence point allows chemists to characterize the acid or base being titrated.

The equivalence point can be determined using indicators or pH meters, and its accuracy is vital for correct analysis.

Titration

Titration is an analytical method used to determine the concentration of an unknown solution by reacting it with a solution of known concentration. The known solution is usually referred to as the titrant. By measuring the volume of titrant needed to reach the equivalence point, one can calculate the concentration of the unknown solution.
There are different types of titrations based on the reactions:

• Acid-Base Titration: This involves the neutralization between an acid and a base and is used often in determining the strength of an unknown acid or base.
• Redox Titration: Involves a reduction-oxidation reaction between the titrant and the analyte.
• Complexometric Titration: Used to determine metal ions concentration through complexation reactions.

Diverse indicators can be employed for different types of titrations to identify the end point, which must be carefully distinguished from the equivalence point for accurate results.

Acid-Base Equilibrium

The concept of acid-base equilibrium is vital in understanding how solutions can balance feelings of acidity or basicity based on their components. In water, this equilibrium is expressed through the dissociation of water molecules, shown by:
\[H_2O(l) ⇌ H^+(aq) + OH^-(aq)\]The equilibrium constant for this reaction is known as the ion-product constant of water, \(K_w\), with a value of \(1.0 \times 10^{-14}\) at 25°C. Acid-base equilibrium calculations can predict the concentration of \([H^+]\) and \([OH^-]\), and hence the pH, in a solution.
In the context of weak bases:

• These do not fully ionize in solution, leading to an equilibrium state where both the base and its ions are present.
• The equilibrium constant, \(K_b\), measures the strength of a weak base, similar to how \(K_a\) measures acid strength.

This equilibrium plays an important role in the titration of weak bases as it directly affects the pH at which the equivalence point is achieved.

Strong Base

Strong bases are compounds that completely dissociate in water to release hydroxide ions, \(OH^-\). This complete dissociation means they readily react with acids in titrations to reach the equivalence point.
A classic example is sodium hydroxide, \(NaOH\). When it reacts with an acid like hydrochloric acid (HCl), the resulting product is water and a salt, specifically sodium chloride. The reaction can be written as:
\[NaOH(aq) + HCl(aq) ightarrow NaCl(aq) + H_2O(l)\]Here are some characteristics of strong bases:

• They have a high \([OH^-]\) concentration in solution.
• They have a significant impact on the pH due to this high concentration of hydroxide ions.
• The pH of strong base solutions tends to be much higher than 7.

Understanding strong bases is crucial when dealing with titrations, as their behavior at the equivalence point differs noticeably from weak bases.

Weak Base

Weak bases are substances that partially ionize in water, which means they do not entirely dissociate into their component ions. This partial ionization is what makes titration involving weak bases more complex.
An example of a weak base is ammonia, \(NH_3\), which reacts with water in an equilibrium process rather than a complete dissociation:
\[NH_3(aq) + H_2O(l) ⇌ NH_4^+(aq) + OH^-(aq)\]Key points about weak bases include:

• They have a low \(K_b\) value, indicating their weak tendency to release \(OH^-\) ions.
• The pH of a solution containing a weak base is typically less than that of a strong base but greater than pure water.
• Equilibrium calculations involving weak bases are necessary to predict the pH of the solution during titration at the equivalence point.

Understanding weak bases helps us predict and control the outcomes of titrations, especially when weak bases are titrated with strong acids, as seen with aniline or hydroxylamine.