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 (i.e., is more acidic), we need to consider the strength of the acid or base involved.
a. In general, a strong acid is completely ionized in water, resulting in a high concentration of H+ ions, making the solution more acidic. On the other hand, a weak acid only partially ionizes, resulting in a lower concentration of H+ ions. Therefore, a 0.1 M solution of a strong acid would have a lower pH than a 0.1 M solution of a weak acid.
b. The acid dissociation constant (Ka) measures the strength of an acid. A higher Ka value indicates a greater tendency to donate protons, making the solution more acidic. Comparing the given Ka values, an acid with Ka=8×10-6 is weaker (lower Ka) than an acid with Ka=2×10-3. Therefore, a 0.1 M solution of an acid with Ka=8×10-6 would have a lower pH than a 0.1 M solution of an acid with Ka=2×10-3.
c. The pKb value measures the strength of a base. It is the negative logarithm of the base dissociation constant (Kb). A lower pKb value indicates a stronger base, which would result in a higher concentration of OH- ions and a lower pH. Comparing the given pKb values, a base with pKb=4.5 is stronger (lower pKb) than a base with pKb=6.5. Therefore, a 0.1 M solution of a base with pKb=4.5 would have a lower pH than a 0.1 M solution of a base with pKb=6.5.
ii. To calculate Kb for cocaine, we can use the concept of the pH of a basic solution. Given that the pH of the cocaine solution is 8.53, we can determine the concentration of OH- ions in the solution and then use that information to calculate Kb.
1. Calculate the concentration of H+ ions (using the equation pH = -log[H+]):
pH = 8.53
[H+] = 10^(-pH) = 10^(-8.53) mol/L
2. Since cocaine is a base that accepts protons (H+ ions), it reacts with water to form hydroxide ions (OH-) and its conjugate acid. The equation for this reaction is:
Cocaine + H2O ⇌ CocaineH+ + OH-
3. Since we're assuming cocaine is a weak base, we can assume that most of the cocaine molecules react, and the equilibrium concentration of OH- is equal to the concentration of the weak base formed (CocaineH+).
4. Calculate the concentration of OH- ions:
[OH-] = [CocaineH+] = [H+] = 10^(-8.53) mol/L
5. Kb is the base dissociation constant, which can be determined using the equation:
Kb = [OH-]^2 / [Cocaine]
= (10^(-8.53))^2 / 0.10 mol/L
6. Calculate Kb:
Kb = (10^(-8.53))^2 / 0.10 = 10^(-17.06) / 0.10 = 10^(-16.96) mol/L
Therefore, the Kb value for cocaine is approximately 10^(-16.96) mol/L.