Answer :
Final answer:
To calculate the pH of a 0.8 M solution of a weak base A- with a Kb of 1.55 x 10^-6, set up an ICE table and solve for x to find [OH-], then calculate pOH, and finally pH using pH = 14 - pOH.
Explanation:
To find the pH of a solution of a weak base (A-) with a given initial concentration and a known Kb value, you must set up an equilibrium expression. For our base A-, the reaction in water is A- + H2O ⇌ OH- + HA. Using the given Kb and the concentration of A-, we can create an ICE table to determine the concentration of OH- at equilibrium. From the concentration of OH-, we can calculate the pOH and then determine the pH using the formula pH = 14 - pOH.
In this case, the initial concentration of the weak base A- is 0.8 M and Kb = 1.55 x 10^-6. Assuming x is the change in concentration of A- and OH-, the equilibrium reaction is Kb = [OH-][HA]/[A-], therefore 1.55 x 10^-6 = x^2 / (0.8 - x). Since Kb is small and A- is a weak base, we can approximate that 0.8 - x ≈ 0.8. Hence, x^2/0.8 = 1.55 x 10^-6 which gives us x, the concentration of OH-, at equilibrium. After calculating x, the concentration of OH-, we can then calculate the pOH = -log [OH-], and subsequent pH = 14 - pOH.
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