If the pH of a 0.46 M aqueous solution of a weak base is 9.2, estimate the Kb of the base:
pH + pOH = pKw = 14. Solve for pOH.
Then pOH = -log(OH^-). Solve for (OH^-).
Call the weak base BOH.
.......BOH ==> B^+ + OH^-
I......0.46....0......0
C......-x......x......x
E....0.46-x....x......x
You know x from above. Substitute x and 0.46-x into the Kb expression and solve for Kb. Piece of cake.
To estimate the Kb of a weak base based on its pH and concentration, you can use the following steps:
Step 1: Calculate the concentration of hydroxide ions (OH-) in the solution using the equation pH = 14 - pOH, where pOH is the negative logarithm of the OH- concentration.
Given that the pH of the solution is 9.2, we can solve for pOH:
pOH = 14 - 9.2
pOH = 4.8
Step 2: Convert the pOH value to OH- concentration using the equation [OH-] = 10^(-pOH).
[OH-] = 10^(-4.8)
[OH-] ≈ 1.58 × 10^(-5) M
Step 3: Use the known concentration of the weak base and the concentration of hydroxide ions to calculate Kb using the formula Kb = [OH-]^2 / [B], where [B] is the concentration of the weak base.
Kb = (1.58 × 10^(-5))^2 / 0.46
Kb ≈ 5.44 × 10^(-11)
Therefore, the estimated Kb of the weak base is approximately 5.44 × 10^(-11).
To estimate the value of Kb for a weak base based on its pH and concentration, we need to use the relationship between pOH and Kb. Here are the steps to follow:
Step 1: Convert the pH to pOH.
pOH = 14 - pH
pOH = 14 - 9.2
pOH = 4.8
Step 2: Convert pOH to [OH-].
[OH-] = 10^(-pOH)
[OH-] = 10^(-4.8)
[OH-] = 1.58 x 10^(-5) M
Step 3: Use the molarity of the weak base to calculate the concentration of the weak acid produced by the reaction of the base with water. In this case, we can assume that the concentration of the weak acid is the same as the concentration of the weak base because it is a 1:1 ratio.
[OH-] = [A-]
Step 4: Set up an ICE table (Initial, Change, Equilibrium) for the reaction:
Base + H2O ⇌ A- + H3O+
Initial: [Base] = 0.46 M, [A-] = 0 M, [H3O+] = 0 M
Change: -x, +x, +x
Equilibrium: 0.46 - x, x, x
Step 5: Use the equilibrium concentrations to set up an expression for Kb.
Kb = ([A-][H3O+])/[Base]
Since [A-] and [Base] are equal, we can substitute [OH-] for both:
Kb = ([OH-][H3O+])/[OH-]
Kb = [H3O+]
Kb = x
Step 6: Plug in the value of [OH-] calculated in step 2 to find Kb.
Kb = [H3O+] = 1.58 x 10^(-5) M
Therefore, the estimated value of Kb for the weak base is 1.58 x 10^(-5) M.