Problem 67 - Chemistry: Structure and Properties

Question

Consider the titration of a 25.0-mL sample of 0.115 M RbOH with 0.100 M HCl. Determine each quantity. a. the initial pH b. the volume of added acid required to reach the equivalence point c. the pH at 5.0 mL of added acid d. the pH at the equivalence point e. the pH after adding 5.0 mL of acid beyond the equivalence point

Step-by-Step Solution

Answer

a. Initial pH is high since RbOH is a strong base (pH > 12). b. Equal moles HCl to moles RbOH gives equivalence volume. c. pH at 5 mL added acid depends on remaining RbOH. d. At the equivalence point, pH is 7. e. After equivalence, excess HCl lowers pH (< 7).

Step 1: Calculate the initial pH of RbOH solution

To calculate the initial pH, use the concentration of RbOH to find the hydroxide ion (OH-) concentration. RbOH is a strong base and dissociates completely in water: RbOH → Rb⁺ + OH⁻. Thus, the initial concentration of OH⁻ is also 0.115 M. Use the equation: pOH = -log[OH⁻] and pH = 14 - pOH to find the initial pH.

Step 2: Determine the volume of HCl required to reach the equivalence point

At the equivalence point, moles of RbOH initially in solution will equal the moles of HCl added. Use the mole ratio from the balanced chemical equation, which is 1:1 for a strong base and a strong acid, along with the initial concentration and volume of RbOH and the concentration of HCl to determine the volume needed.

Step 3: Calculate the pH after adding 5.0 mL of HCl before the equivalence point

Determine the moles of RbOH and HCl, calculate the remaining moles of RbOH after reaction with the added HCl, and find the concentration of the RbOH in the total volume of the solution. Then, use this concentration to calculate the OH⁻ concentration and the pOH and pH of the solution.

Step 4: Calculate the pH at the equivalence point

At the equivalence point, all the RbOH has been neutralized by HCl, yielding water and the salt RbCl. The solution is neutral because both Rb⁺ and Cl⁻ are from strong base and acid, respectively, so the pH is 7.

Step 5: Calculate the pH after adding 5.0 mL of HCl beyond the equivalence point

After the equivalence point, excess HCl will determine the pH. Calculate the moles of excess HCl, find its concentration in the total volume of the solution, and use the negative logarithm of the H⁺ concentration (or HCl concentration) to determine the pH.

Key Concepts

Acid-Base Titration

Acid-base titration is a quantitative analytical method used to determine the concentration of an acid or a base in a solution. It involves adding a titrant (a solution of known concentration) to a solution of the substance being analyzed, known as the analyte, until the chemical reaction between the two is complete. This point of completion is known as the equivalence point.

In our example, the titration involves the reaction between RbOH, a strong base, and HCl, a strong acid. The process monitors the change in pH as the HCl is added to the RbOH solution. When the titrant is added, it reacts with the analyte to form water and a salt, and the change in the pH is recorded to determine when the equivalence point is reached.

Calculating the initial pH of a strong base, finding the volume of acid required to reach the equivalence point, and determining the pH at various stages of the titration, are key aspects of this process. These calculations rely on stoichiometric relationships between the acid and base, the concept of pH, and an understanding of the properties of strong acids and bases, which dissociate completely in water.

pH at Equivalence Point

The pH at the equivalence point of a titration between a strong acid and a strong base is a fundamental concept in acid-base chemistry. This pH signifies a neutral solution because at the equivalence point, equal amounts of the acid and base have reacted to form water and a neutral salt.

In the example provided, we reach the equivalence point when the amount of HCl added is stoichiometrically equivalent to the amount of RbOH present in the solution. Since both RbOH and HCl are strong (meaning they completely dissociate in water), the resulting salt, RbCl, has no acidic or basic properties and the solution is pure water, leading to a neutral pH of 7.

Under the assumption that the reaction between the strong base and the strong acid is going to completion, no additional calculations are needed to determine the pH at the equivalence point. However, for weak acids or bases, the pH at the equivalence point can be acidic, basic, or neutral depending on the relative strengths of the acids and bases involved.

Initial pH of Strong Base

Determining the initial pH of a strong base like RbOH involves understanding how it reacts in water. Strong bases dissociate completely in aqueous solutions to form hydroxide ions (OH⁻). The concentration of these hydroxide ions directly influences the pH of the solution.

To calculate the initial pH, one must take the negative logarithm of the hydroxide ion concentration to find the pOH, and then subtract this value from 14 (since pH + pOH = 14 in aqueous solutions at 25°C). In the exercise given, the initial concentration of RbOH is equal to the initial concentration of OH⁻ because RbOH is a strong base that dissociates completely. Hence, the initial pOH is calculated from the concentration of RbOH, and consequently, the initial pH is found to be basic due to the presence of hydroxide ions.