If the Kb of a weak base is 2.6 × 10-6, what is the pH of a 0.24 M solution of this base?
Call the weak base ANH2
........ANH2 + HOH ==> ANH3^+ + OH^-
I.......0.24.............0........0
C.........-x.............x........x
E......0.24-x............x.........x
Kb = (ANH3^+()(OH^-)/(ANH2)
Substitute from the ICE chart and solve for x = (OH^-) and convert to pH.
To find the pH of a weak base solution, we need to use the Kb value (base dissociation constant) of the base. The Kb value is a measure of the strength of a base. The larger the Kb value, the stronger the base.
In this case, the Kb value of the weak base is given as 2.6 × 10^(-6).
To calculate the pH of the solution, follow these steps:
Step 1: Write the chemical equation for the dissociation of the weak base in water. Let's represent the weak base as B and its conjugate acid as BH+.
B + H2O ⇌ BH+ + OH-
Step 2: Set up the equilibrium expression for the dissociation of the weak base. Since the concentration of the weak base is given as 0.24 M and the concentration of OH- can be assumed to be x, the equilibrium expression becomes:
Kb = [BH+][OH-] / [B]
Kb = x * x / (0.24 - x) (since [BH+] ≈ [OH-])
Step 3: Since the Kb value is small (2.6 × 10^(-6)), we can assume that the value of x is negligible compared to 0.24. This allows us to simplify the equation as:
Kb = x^2 / 0.24
Step 4: Solve the equation for x. Rearrange the equation:
x^2 = Kb * 0.24
x = √(Kb * 0.24)
Step 5: Substitute the given Kb value to calculate x:
x = √(2.6 × 10^(-6) * 0.24)
Step 6: Calculate the OH- concentration and convert it to pOH:
OH- concentration = x
pOH = -log(OH- concentration)
Step 7: Calculate the pH using the equation:
pH = 14 - pOH
By following these steps, you can find the pH of the 0.24 M solution of the weak base.