Calculate the pH and the concentrations of all species present(H2CO3, HCO3-, CO32-, H3O+ , and OH-) in 0.010 MH2CO3 1Ka1 = 4.3 * 10-7; Ka2 = 5.6 * 10-112.

Verified step by step guidance

1. 1. First, we need to calculate the concentration of HCO3- and H3O+ ions produced by the first ionization of H2CO3. This can be done by setting up an ICE (Initial, Change, Equilibrium) table and using the expression for Ka1 (Ka1 = [HCO3-][H3O+]/[H2CO3]).
2. 2. After finding the concentrations of HCO3- and H3O+, we can calculate the pH of the solution using the formula pH = -log[H3O+].
3. 3. Next, we need to calculate the concentration of CO32- and additional H3O+ ions produced by the second ionization of HCO3-. This can be done by setting up another ICE table and using the expression for Ka2 (Ka2 = [CO32-][H3O+]/[HCO3-]).
4. 4. The concentration of H3O+ ions will increase due to the second ionization. Therefore, we need to add the H3O+ ions produced in the first and second ionization to get the total concentration of H3O+ ions in the solution.
5. 5. Finally, we can calculate the concentration of OH- ions using the Kw expression (Kw = [H3O+][OH-]). Since we know the concentration of H3O+ ions and the value of Kw (1.0 x 10^-14 at 25°C), we can solve for [OH-].

Key Concepts

Acid-Base Equilibria

Acid-base equilibria involve the dissociation of acids and bases in solution, which can be described using equilibrium constants (Ka for acids and Kb for bases). In this case, H2CO3 (carbonic acid) dissociates in two steps, leading to the formation of bicarbonate (HCO3-) and carbonate (CO32-) ions. Understanding these equilibria is essential for calculating the concentrations of all species in the solution.

pH Calculation

pH is a measure of the hydrogen ion concentration in a solution, defined as pH = -log[H3O+]. To calculate pH, one must first determine the concentration of H3O+ ions produced from the dissociation of the acid. This involves using the equilibrium expressions derived from the acid dissociation constants (Ka) to find the concentrations of H3O+ and other species at equilibrium.

Equilibrium Constants (Ka)

The acid dissociation constant (Ka) quantifies the strength of an acid in solution, indicating the extent to which it donates protons (H+) to water. For polyprotic acids like H2CO3, there are multiple Ka values corresponding to each dissociation step. These constants are crucial for calculating the concentrations of all species in the solution, as they dictate the equilibrium positions of the reactions involved.