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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.
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Recall: Strong versus Weak Bases
Strong bases dissociate completely in solution to produce OH.
Weak bases only partially react in solution.
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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
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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.
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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
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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
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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
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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
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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
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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)
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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)
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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)
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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)
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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)
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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)
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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
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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
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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]
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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
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Recall: Relationships Between pH, pOH, and pKw
pH + pOH = pKw
pKw = log [1.01014] = 14 (at 25C)
pH + pOH = 14 (at 25C)
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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
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Next up, Conjugate Acid/Base Pairs and Relationships Between
Ka, Kb, and Kw.
(Pt 7)