Find the initial concentration of the weak
acid or base in an aqueous solution of pyridine
(C5H5N) with a pH of 8.65. Kb = 1.80×10−9
.
Answer in units of mol/L
To find the initial concentration of the weak acid or base in an aqueous solution, we can use the pH and the equilibrium constant (Kb in this case).
First, we need to determine if pyridine (C5H5N) is acting as an acid or base. Since we have the Kb value given, we know that pyridine is acting as a base. Kb represents the base dissociation constant.
The formula for Kb is:
Kb = [OH-][HB+]/[B]
Where:
OH- represents the hydroxide concentration,
HB+ represents the conjugate acid concentration, and
B represents the base concentration.
In this case, we need to find the concentration of pyridine (B). Since it is a weak base, it partially dissociates in water to form hydroxide ions (OH-) and its conjugate acid (HB+).
To calculate the concentration of OH- from the given pH of 8.65, we can use the following formula:
pOH = 14 - pH
Given that pH = 8.65, we can calculate pOH:
pOH = 14 - 8.65 = 5.35
To convert pOH to OH- concentration, we use the formula:
[OH-] = 10^(-pOH)
Therefore, [OH-] = 10^(-5.35) = 2.74 × 10^(-6) mol/L
Next, we can assume that the concentration of the conjugate acid, HB+, is negligible compared to the initial concentration of the base (pyridine). This assumption allows us to simplify the Kb equation as follows:
Kb ≈ [OH-][HB+]/[B]
Kb ≈ [OH-]/[B]
Since HB+ is negligible, we can further simplify the equation to:
Kb ≈ [OH-]/[B] = 2.74 × 10^(-6) mol/L / [B]
Finally, we can solve for [B] (the initial concentration of pyridine) by rearranging the equation:
[B] = [OH-] / Kb
[B] = 2.74 × 10^(-6) mol/L / (1.80×10^(-9))
[B] ≈ 1.52 mol/L
Therefore, the initial concentration of pyridine (C5H5N) in the aqueous solution is approximately 1.52 mol/L.