Malic acid is a weak diprotic organic acid with K1 = 4.0x 10-4 and K2 = 9.0 x 10-6.

(a) Letting the symbol H2A represent malic acid, write the chemical equations that
represent K1 and K2 . Write the chemical equation that represents K] xK2 .
(b) Qualitatively describe the relative concentrations of H2A, HA-, A 2-, and H30+ in a
solution that is about one molar in malic acid.
(c) Calculate the pH of a 0.0100 M malic acid solution and the equilibrium
concentration of [H2A].
(d) What is the A 2- concentration?

I would like to know what you don't understand about this. It would help answer the questions.

H2A ==> H^+ + HA^-
HA^- ==> H^+ + A^2-

Surely you know how to write Ka1 and Ka2 expressions. If not explain and I can help you through them.

b. (H2A) > (H^+) = (HA^-) > (A^2-)

c. .........H2A ==> H^+ + HA^-
I..........0.01.....0......0
C...........-x......x......x
E........0.01-x....x......x

Substitute the E line into Ka1 expression and solve for x = H^+, then convert to pH. (H2A) = 0.01-x

d. (A^2-) = ka2. Why? Write Ka2 expression.
ka2 = (H^+)(A^2-)/(HA^-)
From Ka1 (see c above), (H^+) = (HA^-) so (H^+) and (HA^-) cancel each other in Ka2 expression, so (A^2-) = Ka2.

(a) The chemical equations that represent K1 and K2 are as follows:

K1: H2A ⇌ H+ + HA-
K2: HA- ⇌ H+ + A2-

The chemical equation that represents K1 x K2 is obtained by multiplying the individual equations:

K] x K2: H2A ⇌ 2H+ + A2-

(b) In a solution that is about one molar in malic acid, the relative concentrations of the species can be described as follows:
- H2A: Initially, the concentration of H2A is highest.
- HA-: As H2A dissociates, the concentration of HA- increases.
- A2-: As HA- further dissociates, the concentration of A2- increases.
- H3O+: Due to the dissociation of H2A and HA-, the concentration of H3O+ (hydronium ions) increases.

(c) To calculate the pH of a 0.0100 M malic acid solution, we need to identify the dominant species in the solution. At this concentration, we can assume that most of the malic acid has dissociated.

Using the formula for K1, we can write the equilibrium expression:

K1 = [H+][HA-] / [H2A]

Since the concentration of H2A is initially 0.0100 M, and assuming x is the concentration of H+ and HA-, we can write:

4.0 x 10^-4 = x^2 / (0.0100 - x)

To simplify the equation, we can assume that x is small compared to 0.0100 M, so we can ignore it in the denominator:

4.0 x 10^-4 = x^2 / 0.0100

Solving for x, we find x ≈ 0.0063 M.

Since the concentration of H+ is equal to the concentration of HA-, and the pH is defined as the negative logarithm of the H+ concentration, the pH of the solution is approximately -log(0.0063) ≈ 2.2.

To calculate the equilibrium concentration of [H2A], we can subtract the concentration of H+ from the original concentration of H2A:

[H2A] = 0.0100 - 0.0063 = 0.0037 M.

(d) To find the concentration of A2-, we can use the expression for K2:

K2 = [H+][A2-] / [HA-]

Assuming x is the concentration of H+ and A2-, and that the concentration of HA- is approximately equal to the concentration of H+, we can write:

9.0 x 10^-6 = x^2 / 0.0063

Solving for x, we find x ≈ 4.4 x 10^-4 M.

Therefore, the concentration of A2- is approximately 4.4 x 10^-4 M.

(a) The symbol H2A represents malic acid. The dissociation of malic acid can be represented by the following chemical equations:

For K1: H2A ⇌ H+ + HA-

For K2: HA- ⇌ H+ + A2-

To find the chemical equation that represents K1 x K2, we multiply the two equations together:

H2A ⇌ H+ + HA-
HA- ⇌ H+ + A2-

Multiplying these two equations gives:

H2A ⇌ H+ + HA- + H+ + A2-
H2A ⇌ 2H+ + HA- + A2-

(b) In a solution that is about one molar in malic acid, the relative concentrations of the species can be inferred based on the equilibrium constants and the concentration of malic acid. Since malic acid is a diprotic acid, we can assume that the majority of it will first dissociate in accordance with K1.

At equilibrium, the concentration of H2A will be significantly higher than the concentration of HA- and A2-. The concentration of H3O+ (hydronium ions) will depend on the dissociation of both K1 and K2, and will be less than the concentration of H2A. The exact concentration ratios can be calculated using the equations and mathematical methods.

(c) To calculate the pH of a 0.0100 M malic acid solution and the equilibrium concentration of [H2A], we can use the equilibrium constant expressions and the acid dissociation constants:

K1 = [H+][HA-] / [H2A]
K2 = [H+][A2-] / [HA-]

Given the values of K1 and K2, and the initial concentration of malic acid [H2A] = 0.0100 M, we can set up an equilibrium table and solve for the concentrations of [H+], [HA-], [A2-], and [H2A]. From the concentration of [H+], we can calculate the pH using the equation: pH = -log[H+].

(d) To find the concentration of A2-, we need to use the values obtained from the calculations in part (c). A2- concentration can be determined by subtracting the concentration of HA- from the total concentration of malic acid ([H2A] = 0.0100 M).

[A2-] = [H2A] - [HA-]

By plugging in the calculated values, we can find the concentration of A2-.