Final answer:
The Ka of hypobromous acid can be approximated by using the given pH of the solution and the initial concentration of HBrO. By applying the equilibrium expression and assuming x is small, we can find the value of the acid dissociation constant.
Step-by-step explanation:
To calculate the acid dissociation constant (Ka) of hypobromous acid (HBrO) from its pH, we need to understand the dissociation process of the acid in the solution and apply the equilibrium expression. The dissociation of hypobromous acid can be represented as HBrO → H+ + BrO-. The pH of the solution is 4.51, which means the concentration of hydrogen ions [H+] is 10-4.51 M.
Using the initial concentration of HBrO (0.42 M) and assuming x is the concentration of H+ and BrO-, the expression for Ka is Ka = [H+][BrO-]/[HBrO - x]. Because the pH suggests that x is small compared to the initial concentration, it can be approximated that [HBrO - x] ≈ 0.42 M. Therefore, Ka is simply [H+]2/[HBrO]. Plugging in the values we get Ka ≈ (10-4.51)2/0.42 M. After calculating, we obtain the Ka of Hipodromos acid.