i. Which of the following solutions has the lowest pH (more acidic). Explain you answers.
a. a 0.1 M solution of a strong acid or a 0.1 M solution of a weak acid.
b. a 0.1 M solution of an acid with Ka=2×10-3 or one with Ka=8×10-6
c. a 0.1 M solutions of a base with pKb=4.5 or one with pKb=6.5
ii.. Cocaine is a weak organic base with a chemical formula C17H21NO4. A 0.10M aqueous solution of cocaine was found to have a pH of 8.53. Calculate Kb for cocaine.
i. To determine which solution has the lowest pH, we need to compare the strengths of the acids and bases involved.
a. In the case of a 0.1 M solution of a strong acid, we can consider it to be completely ionized in water, resulting in a high concentration of H+ ions. On the other hand, a 0.1 M solution of a weak acid will only partially ionize, resulting in a lower concentration of H+ ions. Therefore, the 0.1 M solution of a strong acid will have a lower pH and be more acidic compared to the weak acid solution.
b. The Ka values for acids indicate their acid strength. A higher Ka means a stronger acid. Comparing the two options:
- The acid with Ka=2×10^(-3) has a higher Ka value compared to the acid with Ka=8×10^(-6). This means the acid with Ka=2×10^(-3) is stronger and will ionize more, resulting in a higher concentration of H+ ions. Thus, the 0.1 M solution of acid with Ka=2×10^(-3) will have a lower pH and be more acidic.
c. The pKb values for bases indicate their basicity. A lower pKb value means a stronger base. Comparing the two options:
- The base with pKb=4.5 has a lower pKb value compared to the base with pKb=6.5. This means the base with pKb=4.5 is stronger and will ionize more, resulting in a higher concentration of OH- ions. The higher the OH- concentration, the lower the H+ concentration, leading to a higher pH and less acidity. Thus, the 0.1 M solution of base with pKb=4.5 will have a higher pH and be less acidic.
Therefore, based on the explanations above, the answer is:
a. A 0.1 M solution of a strong acid (option a) has the lowest pH, making it more acidic.
ii. To determine Kb for cocaine, we can use the relationship between Kw (the ionization constant of water) and Ka (the acid dissociation constant) or Kb (the base dissociation constant).
Kw = Ka × Kb
Given Kw = 1.0 × 10^(-14) at 25°C (standard conditions), we can rearrange the equation to solve for Kb:
Kb = Kw / Ka
However, the given information only provides the pH of the solution. We can use the pH to calculate the concentration of H+ ions, which is related to the concentration of OH- ions. Then, using the fact that the concentration of H+ ions equals the concentration of OH- ions in a neutral solution, we can find the concentration of OH- ions.
Lastly, knowing the concentration of OH- ions and the initial concentration of cocaine, we can calculate Kb using the equation for base dissociation constant:
Kb = [OH-]^2 / [cocaine]
Overall, the process involves:
1. Calculating the concentration of OH- ions using the pH of the solution.
2. Determining the concentration of cocaine.
3. Calculating Kb using the concentration of OH- ions and cocaine.
Unfortunately, without the specific concentration of OH- ions or cocaine in the solution, we cannot provide a direct answer to the question.