Question

Consider the titration of a 25.0 \(\mathrm{mL}\) sample of 0.115 \(\mathrm{M} \mathrm{RbOH}\) with 0.100 \(\mathrm{M} \mathrm{HCl} .\) 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 \(\mathrm{mL}\) of added acid d. the pH at the equivalence point e. the pH after adding 5.0 \(\mathrm{mL}\) of acid beyond the equivalence point

Short answer

a) initial pH of RbOH is strong base: pH > 7, b) volume of HCl required for equivalence point is the volume where moles of RbOH equals moles of HCl, c) pH at 5.0 mL of added HCl is less than initial but still basic, d) pH at equivalence point is neutral, e) pH after 5.0 mL beyond equivalence point is acidic.

Step-by-step solution

- Calculate the initial pH of RbOH

Since RbOH is a strong base that dissociates completely, we can find the initial pOH by taking the negative logarithm of the concentration of OH- ions provided by RbOH and then find the pH by subtracting the pOH from 14. The initial concentration of OH- ions is equal to the concentration of RbOH, 0.115 M. Using the formula pOH = -log[OH-] and pH = 14 - pOH, calculate the initial pH.

- Determine the volume of HCl required to reach equivalence point

At the equivalence point, moles of acid equal moles of base. Use the formula n1V1 = n2V2, where n1 is the concentration of RbOH, V1 is the volume of RbOH, n2 is the concentration of HCl, and V2 is the volume of HCl. Solve for V2 to find the volume of HCl required.

- Calculate the pH after adding 5.0 mL of HCl before reaching the equivalence point

Before the equivalence point, the mixture contains unreacted RbOH. Calculate the remaining moles of RbOH after adding 5.0 mL of 0.100 M HCl. Then calculate the concentration of OH- ions in the new total volume and find the pOH and subsequently the pH.

- Determine the pH at the equivalence point

At the equivalence point, all the RbOH has been neutralized by the HCl to form water. The pH at this point is determined by the autoionization of water and is 7, assuming room temperature and no contribution from other ions.

- Calculate the pH after adding 5.0 mL of acid beyond the equivalence point

Beyond the equivalence point, calculate the number of moles of excess HCl added past the equivalence point. Determine the concentration of the excess H+ ions in the new total volume and then calculate the pH directly from the concentration of H+ ions.

- Final calculations and answers

Use the formulas and calculations from previous steps to determine the pH values at different stages of the titration as described in steps 1 to 5.

Key concepts

Titration Equivalence Point

The titration equivalence point is a pivotal moment in any acid-base reaction. It's the juncture where the amount of acid equals the amount of base, signifying that the reactants have been completely neutralized. In a strong acid-strong base titration, like the one we're considering with RbOH (a strong base) and HCl (a strong acid), the equivalence point is characterized by a pH of 7, which occurs only at 25°C (room temperature).

When calculating the volume of HCl needed to reach this point, remember, it's all about the moles. Equal moles of acid and base react to form water and a salt, leaving no excess of hydrogen (H+) or hydroxide (OH-) ions in the solution. This stoichiometric balance is found using the molarity and volume of the solutions involved, aligned with the formula 111V1 = 222V2, where 111 and 222 are the molar concentrations and V1 and V2 are the respective volumes of the titrant and analyte.

pH Calculation

To grasp pH calculations in a titration process, it's essential to start with the basics. pH is a measure of acidity or alkalinity in a solution, with a scale ranging from 0 (strongly acidic) to 14 (strongly basic). In a strong acid-strong base titration, initially, you can determine the pH by directly calculating the concentration of OH- ions for a base or H+ ions for an acid.

The initial pH is deduced using the formula pH = 14 − pOH, where pOH is the negative logarithm of the hydroxide ion concentration. During the titration, as acid is added to the base, the pH gradually decreases until it reaches 7 at the equivalence point. If the titration continues beyond this point, the solution becomes acidic, and the pH can be calculated by finding the concentration of excess H+ ions.

Strong Acid-Strong Base Titration

A strong acid-strong base titration is an enthralling dance between equally powerful partners. In such titrations, both the acid and base completely dissociate in water, releasing all their H+ and OH- ions, respectively. This process is a showcase of stoichiometry—where the chemical equation guides us to predict the outcome of mixing these reactants.

At various points of the titration, the pH can show significant changes. Before the equivalence point, the predominating base results in a basic pH. Right at the equivalence point, the neutralization produces a neutral pH of 7 in a perfect scenario, typically assumed to be at room temperature. After the equivalence point, when excess acid is introduced, the solution swings to an acidic pH. Understanding these transitions is crucial for accurate titration and pH calculations.