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Acid-Base Equilibria (Pt. 6)
Weak Base Equilibria and Kb- Calculating pH and pOH for a
Weak Base SolutionBy Shawn P. Shields, Ph.D.
This work is licensed by Dr. Shawn P. Shields-Maxwell under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Recall: Strong versus Weak Bases
Strong bases dissociate completely in solution to produce OH.
Weak bases only partially react in solution.
Recall: BrΓΈnsted-Lowry Bases
BrΓΈnsted-Lowry bases accept protons H+.
NH3 accepts H+ from water (H2O) (NH3 acts as a base)
Ammonium (NH4+) is the
conjugate acid for NH3
Calculating the pH of a Weak Base Solution
An equilibrium exists between the weak base and its products.
We can use the relationship between the value of the equilibrium constant K and the initial concentration of weak base in solution as we did for weak acids.
The Equilibrium Constant Kb for Weak Bases
An equilibrium exists between the weak base (B) and its products.
conjugate acid of the weak base
weak base
The Equilibrium Constant Kb for Weak Bases
An equilibrium exists between the weak base (B) and its products.
The equilibrium constant K is βrenamedβ for bases to Kb
π π=[ππβ ] [ππ ]
[πβ ]π Recall heterogeneous equilibriaβ¦ the activity for pure liquids and solids is β1β
Example: The Equilibrium Constant Kb for NO2
Kb is called the βbase dissociation constant.βThe value of Kb for NO2
is 2.2 10-11
π π=[ππβ ] [ππππ ]
[πππβ ]
=π .πΓππβππ
ICE Tables, Kb, and Calculating pH for a Weak Base Solution
Use Kb and an ICE table to determine the [OH] at equilibrium. Next, calculate pOH and use this value to calculate pH.Calculate the pOH using the equilibrium [OH]
π π=[ππβ ] [ππππ ]
[πππβ ]
=π .πΓππβππ
A 0.25 M NO2 solution is prepared.
The Kb for NO2 is 2.2 10-11.
Calculate the pH of this solution.
Example Problem: Calculate the pH of a Weak Base Solution
A 0.25 M NO2 solution is prepared. The Kb for
NO2 is 2.2 10-11. Calculate the pH of this
solution.
The first step⦠Write the chemical equation for the weak base equilibrium.
Example Problem: Calculate the pH of a Weak Base Solution
πππβ (ππͺ )+πππ (π₯ )βππβ (ππͺ )+ππππ(ππͺ)
A 0.25 M NO2 solution is prepared. The Kb for
NO2 is 2.2 10-11. Calculate the pH of this
solution.
ICE
Example Problem: Calculate the pH of a Weak Base Solution
πππβ (ππͺ )+πππ (π₯ )βππβ (ππͺ )+ππππ(ππͺ)
A 0.25 M NO2 solution is prepared. The Kb for
NO2 is 2.2 10-11. Calculate the pH of this
solution.
Example Problem: Calculate the pH of a Weak Base Solution
ICE
0.25 0 0πππ
β (ππͺ )+πππ (π₯ )βππβ (ππͺ )+ππππ(ππͺ)
A 0.25 M NO2 solution is prepared. The Kb for
NO2 is 2.2 10-11. Calculate the pH of this
solution.
Example Problem: Calculate the pH of a Weak Base Solution
ICE
+ x
0 00.25 x +
x
πππβ (ππͺ )+πππ (π₯ )βππβ (ππͺ )+ππππ(ππͺ)
A 0.25 M NO2 solution is prepared. The Kb for
NO2 is 2.2 10-11. Calculate the pH of this
solution.
Example Problem: Calculate the pH of a Weak Base Solution
ICE
+ x
0 00.25 x +
x0.25 x xx
πππβ (ππͺ )+πππ (π₯ )βππβ (ππͺ )+ππππ(ππͺ)
A 0.25 M NO2 solution is prepared. The Kb for
NO2 is 2.2 10-11. Calculate the pH of this
solution.
Example Problem: Calculate the pH of a Weak Base Solution
E 0.25 x xx
π π=[ππβ ] [ππππ ]
[πππβ ]
= π± βπ±π .ππβπ±= π±π
π .ππβπ±
πππβ (ππͺ )+πππ (π₯ )βππβ (ππͺ )+ππππ(ππͺ)
A 0.25 M NO2 solution is prepared. The Kb for
NO2 is 2.2 10-11. Calculate the pH of this
solution.
Example Problem: Calculate the pH of a Weak Base Solution
E 0.25 x xx
π .πΓππβππ= π±π
π .ππβπ±
πππβ (ππͺ )+πππ (π₯ )βππβ (ππͺ )+ππππ(ππͺ)
Solve for x
Solving for x (assuming x is negligible)
π .πΓππβππ= π±π
π .ππβπ±
Because Kb is small, x is very small. Assume x is zero to simplify the calculation.
π .πΓππβππ= π±π
π .ππβπ=π±π
π .ππ
π .πΓππβππ= π±π
π .ππ (π .πΓππβππ)π .ππ=π±π
Solving for x (assuming x is negligible)
(π .πΓππβππ)π .ππ=π±π
π .πΓππβππ=π±π
(π .πΓππβππ)ππ=(π±π )
ππ
π .ππΓππβπ=π±x is the [OH]
Calculate the pOH of the Weak Base Solution
A 0.25 M NO2 solution is prepared. The Kb for NO2
is 2.2 10-11. Calculate the pH of this solution.
pOH = log [OH] = log [2.3510-6 ] = 5.63We still need the pH!
0.25 2.3510-
6
~ 0.25 M
2.3510-6 M
πππβ (ππͺ )+πππ (π₯ )βππβ (ππͺ )+ππππ(ππͺ)
2.3510-6 M
Recall: Relationships Between pH, pOH, and pKw
pH + pOH = pKw
pKw = log [1.01014] = 14 (at 25C)
pH + pOH = 14 (at 25C)
For the weak base solution pOH = 5.63
Use the relationship:
Calculate the pH of a Weak Base Solution using the pOH
π©π+π©ππ=ππ
A basic solution! (pH greater than 7)
π©π=ππβπ©ππ=ππβπ .ππ=π .ππ
Next up, Conjugate Acid/Base Pairs and Relationships Between
Ka, Kb, and Kw.
(Pt 7)