Hey there!
The pH of a weak base (in this case, pyridine is a weak base) is calculated by using the weak base equation, and then solving it.
C5H5N; Kb= 1.7 x 10⁻⁹
pH = -log [H⁺]
we can also say that pH = 14 + log [OH⁻]
Plugging into the weak base equation, we know that Kb = [OH⁻][BH⁺] / [B]
This can be solved using an ice chart, which will then simplify to :
Kb = [x][x] / [0.50-x]
We can assume that x is very small in comparison to the 0.5 , so we consider it zero.
Then plug in and solve for x. 1.79 *10-9 = x² / 0.5
x = 2.992 * 10⁻⁵
ince X is equal to the [OH⁻] concentration, we can plug it into the second pH equation, and get the pH!
pH = 14+ log 2.99 * 10⁻⁵
pH = 9.48
Hope that helps!
The pH of a 0.65 M solution of pyridine (C₅H₅N) is 9.52.
The equation for the protonation of the base pyridine is the following:
C₅H₅N + H₂O ⇄ C₅H₅NH⁺ + OH⁻ (1)
The constant of the above reaction is:
[tex] K_{b} = \frac{[C_{5}H_{5}NH^{+}][OH^{-}]}{[C_{5}H_{5}N]} = 1.7 \cdot 10^{-9} [/tex] (2)
To calculate the pH of the solution we need to use the following equation:
[tex] pH + pOH = 14 [/tex]
[tex] pH = 14 - pOH = 14 - (-log[OH^{-}]) = 14 + log[OH^{-}] [/tex] (3)
So, we need to find the concentration of the OH⁻ ions. Since pyridine is a weak base, at the equilibrium we have (eq 1):
C₅H₅N + H₂O ⇄ C₅H₅NH⁺ + OH⁻
0.65 - x x x
After entering the values of [C₅H₅N] = 0.65-x, [C₅H₅NH⁺] = x, and [OH⁻] = x, into equation (2) we can find the concentration of OH⁻:
[tex] 1.7 \cdot 10^{-9} = \frac{[C_{5}H_{5}NH^{+}][OH^{-}]}{[C_{5}H_{5}N]} = \frac{x*x}{0.65 - x} [/tex]
[tex] 1.7 \cdot 10^{-9}(0.65 - x) - x^{2} = 0 [/tex]
Solving the above quadratic equation for x, we have:
[tex] x_{1} = -3.32 \cdot 10^{-5} M [/tex]
[tex] x_{2} = 3.32 \cdot 10^{-5} M [/tex]
We can calculate the pH, after taking the positive value, x₂, (concentrations cannot be negative) and entering into equation (3):
[tex] pH = 14 + log[OH^{-}] = 14 + log(3.32 \cdot 10^{-5}) = 9.52 [/tex]
Therefore, the pH of the solution of pyridine is 9.52.
Find more about pH here:
I hope it helps you!
