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 strength of the acids or bases involved. The lower the pH, the more acidic the solution, and the higher the pOH, the more basic the solution.

a. In this case, we are comparing a 0.1 M solution of a strong acid and a 0.1 M solution of a weak acid. Strong acids completely dissociate in water, resulting in a high concentration of H+ ions, which leads to a low pH. Weak acids partially dissociate in water, resulting in a lower concentration of H+ ions and a higher pH compared to a strong acid. Therefore, the 0.1 M solution of a strong acid will have a lower pH than the 0.1 M solution of a weak acid.

b. Here, we are comparing two acids with different acid dissociation constants (Ka). The Ka value represents the extent of acid dissociation. A large Ka value indicates a stronger acid. Comparing the Ka values provided (2×10^-3 and 8×10^-6), it is clear that the acid with the smaller Ka value is weaker. Since a weaker acid has a higher pH, the 0.1 M solution of acid with Ka = 8×10^-6 will have a lower pH than the one with Ka = 2×10^-3.

c. In this case, we are comparing two bases with different base dissociation constants (Kb). The pKb value is the negative logarithm of the Kb value. If we compare the pKb values provided (4.5 and 6.5), the base with the smaller pKb value is stronger, meaning it has a higher Kb value. Since a stronger base has a higher concentration of OH- ions, the 0.1 M solution of the base with pKb = 4.5 will have a higher OH- concentration and a lower pH.

In summary, the solutions in order of decreasing pH (more acidic) are:
a. 0.1 M solution of a strong acid > 0.1 M solution of a weak acid
b. 0.1 M solution of acid with Ka = 8×10^-6 > 0.1 M solution of acid with Ka = 2×10^-3
c. 0.1 M solution of a base with pKb = 4.5 > 0.1 M solution of a base with pKb = 6.5

ii. To calculate Kb for cocaine, we can use the relationship between Kb and Ka for a conjugate acid-base pair. In this case, the conjugate acid of cocaine is formed by protonation of the nitrogen atom in the molecule.

The balanced equation for the reaction between cocaine and water can be written as follows:
C17H21NO4 + H2O ⇌ C17H22NO4+ + OH-

From the given information, we know that the pH of the solution is 8.53, which indicates the concentration of OH- ions. pH and pOH are related by the equation pH + pOH = 14. Therefore, we can calculate the pOH as 14 - 8.53 = 5.47.

Since the reaction is in equilibrium, the concentrations of cocaine, its conjugate acid, and OH- are all equal. Let's assume the concentration of OH- is x M.

Using the balanced equation, we can set up an expression for the equilibrium constant, Kb:
Kb = [C17H22NO4+][OH-] / [C17H21NO4]

Since the concentration of the base (cocaine) is given as 0.10 M, we have:
[Kb] = x^2 / 0.10

Using the calculated pOH value, we can convert it back to x concentration:
10^(-pOH) = [OH-] = x

Now, substituting the values, we can solve for Kb:
Kb = (10^(-pOH))^2 / 0.10

Calculating this expression will give the value of Kb for cocaine.

i.

a. A strong acid is completely ionized in solution, so a 0.1 M solution of a strong acid would have a higher concentration of H+ ions and therefore a lower pH compared to a 0.1 M solution of a weak acid.

b. The acidity of an acid is determined by its acid dissociation constant (Ka). A larger value of Ka corresponds to a stronger acid. Therefore, a 0.1 M solution of an acid with Ka=2×10-3 has a higher Ka and therefore a lower pH compared to a 0.1 M solution of an acid with Ka=8×10-6.

c. The basicity of a base is determined by its base dissociation constant (Kb). A larger value of Kb corresponds to a stronger base. However, in this case, we are looking for the solution with the lowest pH, which means we are looking for the more acidic solution. A base with a higher Kb corresponds to a less acidic solution. Therefore, a 0.1 M solution of a base with pKb=4.5 has a higher Kb and therefore a higher pH compared to a 0.1 M solution of a base with pKb=6.5.

ii.

To calculate Kb for cocaine, we can use the relationship between H+ and OH- concentration in water.

Water dissociates into H+ and OH- ions, so in a neutral solution, the concentration of H+ ions is equal to the concentration of OH- ions, which is 1 x 10^-7 M (at 25°C).

Since cocaine is a weak base, it reacts with water according to the following equation:

C17H21NO4 + H2O ⇌ C17H21NO4H+ + OH-

From this equation, we can see that the concentration of OH- ions is equal to the concentration of the dissociated cocaine (C17H21NO4H+). Since the initial concentration of cocaine is 0.10 M and it partially dissociates, the concentration of OH- ions can be considered approximately equal to the concentration of the dissociated cocaine.

Given that the pH of the solution is 8.53, we can use the pH equation: pH = -log[H+]

We know that pH + pOH = 14, so we can rearrange the equation to find pOH: pOH = 14 - pH = 14 - 8.53 = 5.47.

Since pOH = -log[OH-], we can calculate the concentration of OH- ions:

OH- = 10^(-pOH) = 10^(-5.47) M = 3.09 x 10^(-6) M.

Since the concentration of OH- is equal to the concentration of the dissociated cocaine, the concentration of the dissociated cocaine is also 3.09 x 10^(-6) M.

Now, we can write the equation for cocaine reacting with water and the equilibrium expression for Kb:

C17H21NO4 + H2O ⇌ C17H21NO4H+ + OH-

Kb = ([C17H21NO4H+][OH-]) / [C17H21NO4]

Substituting the given values:

Kb = (3.09 x 10^(-6) M) / (0.10 M) = 3.09 x 10^(-5)