Question

Calculate the \(\mathrm{pH}\) at the equivalence point in titrating 0.100 M solutions of each of the following with 0.080 \(\mathrm{M}\) NaOH: (a) hydrobromic acid (HBr), (b) chlorous acid (HClO_{2} ) , (c) benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\)

Short answer

The pH at the equivalence points for each titration are: (a) Hydrobromic acid (HBr): pH = 7, (b) Chlorous acid (HClO₂): pH ≈ 6.96, and (c) Benzoic acid (C₆H₅COOH): pH ≈ 8.63.

Step-by-step solution

Write the balanced equation for the reaction.

The reaction between HBr (a strong acid) and NaOH (a strong base) can be written as: HBr + NaOH -> NaBr + H₂O

Calculate the moles of reactants at the equivalence point

At the equivalence point, both reactants are completely consumed: moles_HBr = moles_NaOH Let V (in liters) be the volume of NaOH required to reach the equivalence point: 0.100 M * V = 0.080 M * V The volume, V, is not needed as it cancels out as they are equal.

Calculate the pH

Since both the acid and the base are strong, the resulting solution will be neutral (pH = 7) at the equivalence point. #b) Chlorous acid (HClO₂)#:

Write the balanced equation for the reaction.

The reaction between HClO₂ (a weak acid) and NaOH (a strong base) can be written as: HClO₂ + NaOH -> NaClO₂ + H₂O

Calculate the moles of reactants at the equivalence point.

At the equivalence point, both reactants are completely consumed: moles_HClO₂ = moles_NaOH Let V₂ (in liters) be the volume of NaOH required to reach the equivalence point: 0.100 M * V₂ = 0.080 M * V₂ The volume, V₂, is not needed as it cancels out as they are equal.

Calculate the concentration of ClO₂- (A-) at the equivalence point.

Since at equivalence point, [HClO₂] = [NaOH], so the concentration of ClO₂- will also be equal to the initial concentration of HClO₂: [A-] = 0.100 M

Use Kb for ClO₂- to find the hydroxide ion concentration ([OH⁻]).

The Kb for ClO₂- can be found using the Ka relationship: Kb = Kw / Ka Where Kw = 1.0 × 10-14 and Ka = 1.2 x 10^{-2}. Kb = (1.0 × 10-14) / (1.2 × 10^{-2}) Solving for Kb, we get: Kb = 8.33 × 10^{-13} Now we make an ICE table for ClO₂-, knowing that the initial concentration of OH⁻ is 0: Initial: [ClO₂-] = 0.100 M | [OH⁻] = 0 Change: [ClO₂-] = -x | [OH⁻] = x Equilibrium: [ClO₂-] = 0.100-x | [OH⁻] = x Now, as Kb is very small, we can assume that x will be very small and 0.100 - x will be approximately equal to 0.100: Kb = (x)(x) / 0.100 Solving for x, we get: x = [OH⁻] = 9.13 × 10^{-8} M

Calculate the pH.

Since we have calculated the [OH⁻], we can now find the pOH using the following equation: pOH = -log([OH⁻]) pOH = -log(9.13 × 10^{-8}) pOH ≈ 7.04 Finally, using the relationship between pH and pOH: pH = 14 - pOH pH ≈ 6.96 #c) Benzoic acid (C₆H₅COOH)#: Repeat steps 1-5 from case (b), but instead of HClO₂, use C₆H₅COOH with Ka = 6.3 × 10^{-5}. After performing the calculations, we get: pH ≈ 8.63 Thus, the pH at the equivalence points for each titration are: (a) HBr: pH = 7, (b) HClO₂: pH ≈ 6.96, and (c) C₆H₅COOH: pH ≈ 8.63.

Key concepts

Equivalence Point

The equivalence point in a titration is reached when the amount of acid is stoichiometrically equal to the amount of base added. This point is crucial as it signifies that the acid and base have completely reacted with each other. It is different from the end point, which is simply the point at which the indicator changes color.
During titrations, the equivalence point is determined by monitoring the change in pH. When titrating a strong acid with a strong base, or vice versa, the equivalence point will generally be at pH 7, indicating a neutral solution. However, this is not always the case for weak acids in combination with strong bases, which requires more complex calculations to determine the exact pH at equivalence.

• In strong acid-strong base reactions, the pH at the equivalence point is usually neutral (pH=7).
• For weak acid-strong base reactions, the equivalence point will result in a basic pH due to the production of the conjugate base.

Understanding the equivalence point allows chemists to calculate and predict the concentrations of unknown solutions efficiently.

Strong Acid and Base Reaction

A reaction between a strong acid and a strong base results in the formation of water and a salt. This is called a neutralization reaction. Strong acids and bases fully dissociate into ions in aqueous solutions, leading to a complete reaction when mixed. For example, the reaction between hydrobromic acid (HBr) and sodium hydroxide (NaOH) is given by:
\[ \text{HBr} + \text{NaOH} \rightarrow \text{NaBr} + \text{H}_2\text{O} \]
Here, hydrobromic acid and sodium hydroxide fully dissociate, HBr provides protons (H⁺) and NaOH provides hydroxide ions (OH⁻). These combine to form water. The remaining ions, Na⁺ and Br⁻ form the salt NaBr.
Because these reactions result in complete neutralization, the solution at the equivalence point typically has a pH of 7, assuming no other factors affect the solution. These reactions are predictable and often used in laboratory settings for titration experiments due to their straightforward nature.

Weak Acid and Strong Base Reaction

In contrast to strong acids, weak acids do not fully dissociate in water. When a weak acid is titrated with a strong base, the pH at the equivalence point is not neutral. This is because the reaction results in the formation of the conjugate base of the weak acid, which can affect the solution's pH. Chlorous acid (HClO₂) reacting with sodium hydroxide is one such example:
\[ \text{HClO}_2 + \text{NaOH} \rightarrow \text{NaClO}_2 + \text{H}_2\text{O} \]
After neutralization, the resultant solution contains NaClO₂, which can further react with water to influence the pH:
\[ \text{ClO}_2^- + \text{H}_2\text{O} \leftrightarrow \text{HClO}_2 + \text{OH}^- \]
This reaction generates hydroxide ions and makes the solution basic, leading to a higher pH than 7. Calculations involving the weak acid's dissociation constant (Ka) are essential to accurately determine the pH at the equivalence point in these types of titrations.

pH Calculation

Calculating pH in titration reactions involves understanding the concentration of hydrogen ions in the solution. For strong acid-strong base reactions, the pH at equivalence is straightforward as it equates to 7. However, with weak acids, additional steps are necessary due to the dissociation constant (Ka) and subsequent reaction with the base to form the conjugate base.
For example, using the given Ka for chlorous acid (1.2 x 10^{-2}), the Kb can be calculated using the relationship:\[ K_{b} = \frac{K_{w}}{K_{a}} \]
where \(K_w\) is the ion product of water, \(1.0 \times 10^{-14}\). The pH is determined from the hydroxide ion concentration \([OH^-]\) obtained from the Kb. Finally, the pH is calculated using the equation:
\[ pH = 14 - pOH = 14 - (-\log [OH^-]) \]
This involves using logarithmic functions and precise calculations to ensure accurate results, highlighting the complexity in handling weak acids in titrations.

Acid-Base Reactions

Acid-base reactions are vital in chemistry due to their various applications, such as titrations. These reactions involve the transfer of protons between reactants, forming water and salts as products. The two main types involved in titrations are:

• Strong acid and base reactions: Involve complete dissociation. Result in neutral solutions if equal strengths and concentrations.
• Weak acid and strong base reactions: Form conjugate bases that affect the resultant pH, making solutions basic at equivalence.

In a lab setting, titrations provide a methodical approach to determine unknown concentrations. This is achieved by adding a substance of known concentration to react with the unknown, using indicators to signal equivalence. By understanding these reactions, chemists can design experiments that yield precise and informative results, fundamental in both educational and industrial chemistry applications.