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Calculate the \(\mathrm{pH}\) at the equivalence point for these titrations: (a) \(0.10 M \mathrm{HCl}\) versus \(0.10 \mathrm{M} \mathrm{NH}_{3}\), (b) \(0.10 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) versus \(0.10 \mathrm{M} \mathrm{NaOH}\).

Short Answer

Expert verified
(a) \\mathrm{pH} < 7 (acidic); (b) \\mathrm{pH} > 7 (basic).

Step by step solution

01

Identify Reaction Type for Part (a)

The reaction involves a strong acid (HCl) and a weak base (NH鈧). In such a reaction, at the equivalence point, the resulting solution contains the conjugate acid of the weak base, which is NH鈧勨伜.
02

Determine Ion Hydrolysis for Part (a)

At the equivalence point, the solution will contain NH鈧勨伜. NH鈧勨伜 will undergo hydrolysis to produce H鈦 ions according to the equation: NH鈧勨伜 + H鈧侽 鈬 NH鈧 + H鈧僌鈦.
03

Calculate Kb for Ammonia (NH鈧)

Find the Kb for NH鈧, which is around 1.8 脳 10鈦烩伒. Use the relation: Kb = Kw/Ka, where Kw = 1.0 脳 10鈦宦光伌. Re-arrange and solve for Ka of NH鈧勨伜.
04

Calculate pH Using Ion Concentration for Part (a)

The concentration of NH鈧勨伜 at equivalence is 0.10 M. Use the formula for pH from the hydrolysis, pH = 7 - 0.5(pKa + log(c)), where c is the concentration of the NH鈧勨伜. Calculate the pH to find it is acidic, less than 7.
05

Identify Reaction Type for Part (b)

Here, a weak acid (CH鈧僀OOH) is being titrated with a strong base (NaOH). At the equivalence point, the solution will contain the conjugate base of the weak acid, CH鈧僀OO鈦.
06

Determine Ion Hydrolysis for Part (b)

At the equivalence point, the solution contains CH鈧僀OO鈦. CH鈧僀OO鈦 will undergo hydrolysis: CH鈧僀OO鈦 + H鈧侽 鈬 CH鈧僀OOH + OH鈦. This produces OH鈦 which makes the solution basic.
07

Calculate Ka for Acetic Acid (CH鈧僀OOH)

Find the Ka for CH鈧僀OOH, which is about 1.8 脳 10鈦烩伒. Use the formula Ka = Kw/Kb to find Kb for the CH鈧僀OO鈦 ion.
08

Calculate pH Using Ion Concentration for Part (b)

The concentration of CH鈧僀OO鈦 at equivalence is 0.10 M. Calculate the pH from hydrolysis, pH = 7 + 0.5(pKb + log(c)), where c is the concentration of the CH鈧僀OO鈦. Calculate the pH to confirm it is basic, greater than 7.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Titration
Titration is a process used to determine the concentration of a substance in a solution by adding a titrant of known concentration until the reaction reaches completion. This completion is often indicated by a color change or a stable pH level. Titration is a fundamental technique in chemistry used to understand the behavior of acids and bases. It is crucial for calculating the pH at different stages of a reaction.
During a titration of an acid with a base, the acid reacts with the base. The amount of titrant added allows us to calculate the concentration of the solution. There are different types of titrations based on the nature of the reactants: acid-base titrations, redox titrations, complexometric titrations, and more.
In acid-base titrations, the pH of the solution changes depending on the nature of the acid and base involved. This can be a strong acid with a weak base, a weak acid with a strong base, or any combination. Understanding titration is critical for calculating the pH at any point within a chemical reaction.
Equivalence Point
The equivalence point in titration is the stage at which the quantity of titrant added equals the amount of substance initially present in the solution. At this point, the acid and base have completely reacted with each other.
The pH at the equivalence point provides insight into the nature of the products formed. For strong acids and strong bases, the pH at the equivalence point is typically 7, which is neutral. However, with strong acid-weak base reactions or weak acid-strong base reactions, the pH will vary due to the formation of either acidic or basic products, respectively.
It is important to understand the equivalence point because it represents the completion of the titration. Knowing the pH at this point helps to calculate the final concentrations of the resultant products and understand the chemical properties of the solution.
Ion Hydrolysis
Ion hydrolysis refers to the reaction of an ion with water to produce acidic or basic conditions. During titrations, after the equivalence point, the ions formed can react with water to change the pH of the solution.
For instance, when ammonium ions ( NH鈧勨伜 ) are present, they undergo hydrolysis to produce hydronium ions ( H鈧僌鈦 ), making the solution acidic. This is due to the equilibrium reaction: NH鈧勨伜 + H鈧侽 鈬 NH鈧 + H鈧僌鈦.
Similarly, acetate ions ( CH鈧僀OO鈦 ) can undergo hydrolysis to form hydroxide ions ( OH鈦 ), creating a basic solution: CH鈧僀OO鈦 + H鈧侽 鈬 CH鈧僀OOH + OH鈦.
Understanding ion hydrolysis is essential to accurately determine the pH of the solution at the equivalence point and conclusions about the basicity or acidity of the resulting solution.
Strong Acid and Weak Base
When titrating a strong acid with a weak base, the outcome at the equivalence point tends toward acidity. A strong acid completely ionizes in solution, while a weak base only partially ionizes.
For example, in a titration of HCl (a strong acid) with NH鈧 (a weak base), the complete ionization of HCl results in the formation of NH鈧勨伜 (the conjugate acid of NH鈧 ). This conjugate acid can undergo ion hydrolysis, producing an excess of H鈦 ions which contribute to an acidic pH.
This type of titration is important because it illustrates how the strength of the acid and base affects the pH at the equivalence point. With strong acids and weak bases, the resulting solution is typically acidic.
Weak Acid and Strong Base
In contrast to strong acids and weak bases, when a weak acid reacts with a strong base during titration, the solution tends toward basicity at the equivalence point.
With weak acids like CH鈧僀OOH (acetic acid) and strong bases such as NaOH , the weak acid only partially ionizes. When it reacts with the strong base, the conjugate base CH鈧僀OO鈦 is formed. This ion can undergo hydrolysis to produce hydroxide ions ( OH鈦 ), making the solution basic: CH鈧僀OO鈦 + H鈧侽 鈬 CH鈧僀OOH + OH鈦.
Titration of a weak acid with a strong base is a classic scenario in many chemical contexts, helping students understand how different combinations of acids and bases influence a solution's pH at the equivalence point. Here, the basic nature of the resultant solution emerges due to the excess of hydroxide ions.

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