The pH of 0.5 M mono basic acid, HCl is 4.50. Calculate the acidity constant (Ka) and pKa , concentration of H+ and HCl at equilibrium.

To solve this problem, we need to use several equations related to pH, pKa, and the equilibrium of acids in solution. Here are the steps:

1. Calculate the concentration of H+ ions: The pH is given as 4.50. The pH is defined as pH = -log[H+], where [H+] is the concentration of H+ ions. So, we can rearrange this equation to find [H+]: [H+] = 10^(-pH) = 10^(-4.50) = 3.16 x 10^-5 M.

2. Calculate the concentration of HCl at equilibrium: The initial concentration of HCl is given as 0.5 M. When HCl dissociates, it forms H+ and Cl- ions. Since the concentration of H+ ions at equilibrium is 3.16 x 10^-5 M, the concentration of HCl at equilibrium is the initial concentration minus the concentration of H+ ions: [HCl] = 0.5 M - 3.16 x 10^-5 M = 0.49997 M.

3. Calculate the acidity constant (Ka): The equilibrium for the dissociation of HCl can be written as: HCl ↔ H+ + Cl-. The Ka expression for this equilibrium is Ka = [H+][Cl-]/[HCl]. Since HCl is a strong acid, we can assume that [H+] = [Cl-]. So, Ka = (3.16 x 10^-5)^2 / 0.49997 = 1.00 x 10^-9.

4. Calculate the pKa: The pKa is defined as pKa = -log(Ka) = -log(1.00 x 10^-9) = 9.00.

So, the acidity constant (Ka) is 1.00 x 10^-9, the pKa is 9.00, the concentration of H+ ions at equilibrium is 3.16 x 10^-5 M, and the concentration of HCl at equilibrium is 0.49997 M.