Question

Two 20.0-mL samples, one \(0.200 \mathrm{M} \mathrm{KOH}\) and the other \(0.200 \mathrm{M}\) \(\mathrm{CH}_{3} \mathrm{NH}_{2}\), are titrated with \(0.100 \mathrm{M} \mathrm{HI}\). a. What is the volume of added acid at the equivalence point for each titration? b. Is the \(\mathrm{pH}\) at the equivalence point for each titration acidic, basic, or neutral? c. Which titration curve has the lower initial \(\mathrm{pH} ?\) d. Sketch each titration curve.

Short answer

a. 40.0 mL of 0.100 M HI for both titrations. b. KOH with HI: pH is neutral; CH3NH2 with HI: pH is acidic. c. CH3NH2 titration curve has the lower initial pH. d. The curve for KOH starts high with a steep drop at the equivalence point, the curve for CH3NH2 starts lower with a more gradual slope leading up to the equivalence point.

Step-by-step solution

Calculate the moles of KOH and CH3NH2

Calculate the moles of KOH and CH3NH2 by using the molarity and volume. Molarity (M) equals moles (n) divided by volume (V in liters). For both KOH and CH3NH2, the amount of substance is: n(KOH) = n(CH3NH2) = 0.200 M × 0.0200 L = 0.0040 moles.

Determine the volume of 0.100 M HI needed

Use the stoichiometry of the reaction to determine the volume of 0.100 M HI needed to reach the equivalence point for each titration. For KOH and CH3NH2: n(HI) = n(KOH) = n(CH3NH2). Calculate the volume (V) with V(n) = molarity(M). Therefore, V(HI) for both = 0.0040 moles / 0.100 M = 0.040 L or 40.0 mL.

Predict pH at the equivalence point for KOH titration

KOH is a strong base. At the equivalence point, it reacts completely with the strong acid, HI, to produce a neutral salt and water. Therefore, the pH at the equivalence point will be neutral (pH=7).

Predict pH at the equivalence point for CH3NH2 titration

CH3NH2 is a weak base, and HI is a strong acid. Their reaction will form a salt and water. The salt formed from a weak base and strong acid will hydrolyze and produce an acidic solution. Therefore, the pH at the equivalence point will be acidic (pH<7).

Compare initial pH of KOH and CH3NH2 solutions

Compare the initial pH by recognizing that KOH, being a strong base, will have a higher initial pH than CH3NH2, which is a weak base. Thus, the titration curve for KOH will start at a higher initial pH.

Sketch the titration curves

Sketch two titration curves: one for KOH and the other for CH3NH2. The KOH titration curve starts high, increases slowly as the strong acid is added, then drops steeply at the equivalence point and levels off. The CH3NH2 curve starts at a lower pH and has a more gradual slope leading up to the equivalence point, beyond which it decreases rapidly.

Key concepts

Chemical Titration

Chemical titration is a laboratory technique used to determine the concentration of a reactant in a solution. By adding a solution of known concentration, called the titrant, to the solution with the unknown concentration, we can find the point at which the chemical reaction between the two is complete. This point is called the equivalence point. During a titration, the volume or mass of the titrant is measured to find the exact amount needed to fully react with the analyte.

For example, in an exercise where we titrate a base like KOH with an acid like HI, the equivalence point occurs when the number of moles of acid equals the number of moles of base. By knowing the volume and molarity of KOH and applying stoichiometry, we can calculate the amount of HI needed to reach the equivalence point. Understanding titration is fundamental because it allows scientists and students to analyze substances' concentrations in various chemical processes and reactions.

pH Calculation

The pH scale is an essential tool in chemistry used to specify how acidic or basic a water-based solution is. The pH is a logarithmic scale and is calculated by taking the negative logarithm of the hydrogen ion concentration in the solution, expressed as \( pH = -\log[H^+] \).

When dealing with titration problems, pH calculation allows us to predict the nature of the solution at the equivalence point. If we're titrating a strong base with a strong acid, the pH at the equivalence point will be neutral (pH 7). However, if a weak base is titrated with a strong acid, the resulting solution will be acidic, and therefore, the pH will be less than 7. For accurate pH prediction, one must consider the dissociation of water and the strength of the acids and bases involved in the reaction.

Stoichiometry

Stoichiometry is the part of chemistry that deals with the relationships between the amounts of reactants and products in a chemical reaction. It is based on the law of conservation of mass that states that matter is not created or destroyed in a chemical reaction. Thus, the stoichiometry of a balanced chemical equation tells us the proportions of reactants and products that react and form, respectively.

In titration exercises, stoichiometry is crucial to determine the volume of titrant needed at the equivalence point. This can be achieved by using the molarity (moles per liter) and volume to calculate the moles of each reactant and then using the stoichiometry of the balanced chemical equation to find the point where moles of acid equals moles of base. Stoichiometry is the backbone of quantitative chemical analysis and must be fully understood to perform accurate chemical titrations.

Acid-Base Reactions

Acid-base reactions are amongst the most common chemical reactions and are fundamental to understanding titration. An acid is a substance that donates a proton (hydrogen ion), while a base is a substance that accepts a proton. When an acid and a base react, they form water and a salt in a type of reaction known as neutralization.

In the context of titration exercises, recognizing whether an acid or a base is strong or weak is vital because it affects the pH of the equivalence point. For instance, a strong acid will completely dissociate in solution, contributing to a lower pH at the equivalence point when titrated against a weak base. The understanding of acid-base reactions is thus essential for interpreting titration results, predicting the pH at the equivalence point, and sketching the titration curve.