Use the systematic treatment of equilibrium to determine the pH and concentrations of species in 1.00 L of solution containing 0.065 mol citric acid (H3A), 0.025 mol 8-hydroxyquinoline (HB), and 0.040 mol KOH. Consider just acid-base chemistry. Ignore ion pairing and activity coefficients. Citric acid (H3A) is a triprotic acid with pKH3A = 3.128, pKH2A– = 4.761, and pKHA2– = 6.396. 8-Hydroxyquinoline (HB) is derived from the diprotic acid H2B with pKH2B = 4.94 and pKHB = 9.82.

To determine the pH and concentrations of species in the given solution, we will follow the systematic treatment of equilibrium approach. Let's start with the dissociation of citric acid (H3A) and 8-hydroxyquinoline (HB):

1. Citric acid (H3A) dissociation:
H3A ⇌ H+ + H2A–
H2A– ⇌ H+ + HA2–
HA2– ⇌ H+ + A3–

The given pKH values for citric acid are:
pKH3A = 3.128
pKH2A– = 4.761
pKHA2– = 6.396

We can use these values to calculate the equilibrium constants for each step:
Ka1 = 10^(-pKH3A) = 10^(-3.128)
Ka2 = 10^(-pKH2A–) = 10^(-4.761)
Ka3 = 10^(-pKHA2–) = 10^(-6.396)

2. 8-Hydroxyquinoline (HB) dissociation:
HB ⇌ H+ + B2–
H2B ⇌ H+ + HB–

The given pKH values for 8-hydroxyquinoline are:
pKH2B = 4.94
pKHB = 9.82

We can use these values to calculate the equilibrium constants for each step:
Ka1' = 10^(-pKH2B) = 10^(-4.94)
Ka2' = 10^(-pKHB) = 10^(-9.82)

Now, let's calculate the concentrations of species in the solution step-by-step:

Step 1: Calculate the concentration of H+.
The concentration of H+ can be obtained by considering the dissociation of all acidic species (H3A, H2A-, HB, HB-):
[H+] = [H3A] + [HA2–] + [HB] + [HB–]
[H+] = 0 + 0 + 0 + 0 = 0 (since these species are not yet dissociated)

Step 2: Calculate the concentration of A3–.
Since there is no A3– present initially, [A3–] = 0.

Step 3: Calculate the concentration of HA2–.
Since there is no HA2– present initially, [HA2–] = 0.

Step 4: Calculate the concentration of HA.
Since HA is derived from HB, [HB] = 0 at this stage. Thus, [HA] = 0.

Step 5: Calculate the concentration of H2A.
H2A is derived from H3A, so [H2A] = [H3A] = 0.065 mol/L (given).

Step 6: Calculate the concentration of HB–.
HB– is derived from H2B, so [HB–] = [H2B] = 0.025 mol/L (given).

Step 7: Calculate the concentration of HB.
[HB] = [HB–] + [HA] (Since HB is derived from both HB– and HA)
[HB] = 0.025 + 0 = 0.025 mol/L.

Step 8: Calculate the concentration of B2–.
B2– is derived from HB, so [B2–] = [HB] = 0.025 mol/L.

Step 9: Calculate the concentration of H3A.
H3A is already given as 0.065 mol/L.

Finally, the pH can be determined using the equation:
pH = -log[H+]

Since [H+] is 0, pH cannot be determined and is undefined in this case.

The concentrations of species in the solution are as follows:
[H+] = 0 (undefined)
[A3–] = 0
[HA2–] = 0
[HA] = 0
[H2A] = 0.065 mol/L
[HB–] = 0.025 mol/L
[HB] = 0.025 mol/L
[B2–] = 0.025 mol/L
[H3A] = 0.065 mol/L

To determine the pH and concentrations of species in the given solution, we can use the systematic treatment of equilibrium. Let's break it down step by step:

1. Write down the balanced chemical equations for the reactions involving the acids and bases present in the solution:

Citric acid, H3A:
H3A ⇌ H+ + H2A-
H2A- ⇌ H+ + HA2-
HA2- ⇌ H+ + A3-

8-hydroxyquinoline, HB:
H2B ⇌ H+ + HB-
HB- ⇌ H+ + B2-

KOH:
KOH → K+ + OH-

2. Determine the initial moles and concentrations of each species:
Given that we have 0.065 mol of citric acid (H3A), 0.025 mol of 8-hydroxyquinoline (HB), and 0.040 mol of KOH in 1.00 L of solution, we can use these values to determine the initial moles and concentrations of each species.

For citric acid (H3A):
[H3A] = 0.065 mol/1.00 L
[H2A-] = 0 mol/1.00 L
[HA2-] = 0 mol/1.00 L
[A3-] = 0 mol/1.00 L

For 8-hydroxyquinoline (HB):
[H2B] = 0 mol/1.00 L
[HB-] = 0.025 mol/1.00 L
[B2-] = 0 mol/1.00 L

For KOH:
[K+] = 0.040 mol/1.00 L
[OH-] = 0.040 mol/1.00 L

3. Use the acid dissociation constants (pKa values) to calculate the equilibrium concentrations of each species:
For citric acid (H3A), we have 3 dissociation constants (pKH3A = 3.128, pKH2A– = 4.761, and pKHA2– = 6.396). We can use these values to calculate the equilibrium concentrations of each species at each step of dissociation.

[H+] = [H3A] * 10^(-pKH3A)
[H2A-] = [H+] * [H3A] / 10^(-pKH2A–)
[HA2-] = [H+] * [H2A-] / 10^(-pKHA2–)
[A3-] = [H+] * [HA2-]

For 8-hydroxyquinoline (HB), we have 2 dissociation constants (pKH2B = 4.94 and pKHB = 9.82). We can use these values to calculate the equilibrium concentrations of each species at each step of dissociation.

[H+] = [HB-] * 10^(-pKH2B)
[B2-] = [H+] * [HB-] / 10^(-pKHB)

4. Calculate the concentration of hydroxide ion (OH-):
Since KOH dissociates to give hydroxide ions (OH-), we can directly use the concentration of [OH-], which is 0.040 mol/1.00 L.

5. Calculate the concentration of hydrogen ions (H+):
To find the concentration of hydrogen ions (H+), we need to consider the contributions from all the acids in the solution. This can be done by summing up the [H+] concentrations obtained from the previous calculations:

[H+] = [H+] (from H3A) + [H+] (from HB) + [H+] (from KOH)

6. Calculate the pH of the solution:
pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration, so we can calculate the pH using the equation:

pH = -log10[H+]

Now that we have the concentration of [H+], we can plug it into the equation to find the pH.

This systematic treatment of equilibrium allows us to determine the pH and concentrations of species in the given solution.