A 100.0-mL aliquot of 0.100 M diprotic acid H2A (pK1 = 4.00, pK2 = 8.00) was titrated with 1.00 m NaOH. Find the pH at the following volumes of base added and make a graph of pH versus Vb: Vb = 0, 1, 5, 9, 10, 11, 15, 19, 20, and 22 mL
To determine the pH at each volume of base added, we need to calculate the moles of acid and base at each point and then use the Henderson-Hasselbalch equation to find the pH.
Step 1: Calculate the moles of acid and base.
At the beginning (Vb = 0 mL), there is no base added, so the moles of acid are equal to its initial concentration multiplied by the volume:
Moles of acid = initial concentration of acid × volume of acid
= 0.100 M × 100.0 mL
= 10.0 mmol
Since diprotic acid H2A releases 2 moles of H+ ions for every mole of H2A, the initial moles of H+ ions are twice the moles of acid:
Initial moles of H+ ions = 2 × 10.0 mmol
= 20.0 mmol
At Vb = 0 mL, there are no moles of base added.
Step 2: Calculate the moles of H+ ions and OH- ions reacted.
The total moles of H+ ions reacted (H+ reacted) are given by:
H+ reacted = initial moles of H+ ions - moles of H+ ions remaining
At Vb = 0 mL, there is no base added, so all the initial moles of H+ ions remain:
H+ reacted = initial moles of H+ ions
= 20.0 mmol
The moles of OH- ions can be calculated using the relation:
Moles of OH- ions = moles of H+ reacted
So at Vb = 0 mL, there are 20.0 mmol of OH- ions.
Step 3: Calculate the pH using the Henderson-Hasselbalch equation.
The Henderson-Hasselbalch equation is given by:
pH = pKa + log10([A-]/[HA])
where pKa is the negative logarithm of the acid dissociation constant of H2A, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the acid.
At Vb = 0 mL, [A-] = moles of OH- ions / total volume and [HA] = moles of H+ ions / total volume:
[A-] = 20.0 mmol / 100.0 mL
= 0.200 M
[HA] = 20.0 mmol / 100.0 mL
= 0.200 M
Now, substitute the values into the Henderson-Hasselbalch equation:
pH = 4.00 + log10(0.200/0.200)
= 4.00 + log10(1)
= 4.00 + 0
= 4.00
Therefore, at Vb = 0 mL, the pH is 4.00.
Repeat the steps for the other volumes of base added (Vb = 1, 5, 9, 10, 11, 15, 19, 20, and 22 mL) to find the respective pH values.
To make the graph of pH versus Vb, plot the volumes of base added on the x-axis and the corresponding pH values on the y-axis. Connect the data points to form the graph.
To find the pH at various volumes of base added, we need to understand the concept of acid-base titrations. In this case, we have a diprotic acid, which means it can donate two protons (H+ ions) per molecule.
First, let's identify the different regions of the titration curve:
1. Before the first equivalence point (Vb = 0-10 mL): In this region, only the first proton is being neutralized. The pH is determined by the concentration of the acid and the dissociation of the first proton.
2. Between the first and second equivalence points (Vb = 10-20 mL): In this region, the first proton has been neutralized, and the second proton is being neutralized. The pH is determined by the concentration of the acid and the dissociation of both protons.
3. After the second equivalence point (Vb > 20 mL): In this region, all the acid has been neutralized, and excess base is present. The pH is determined by the concentration of the excess base.
To calculate the pH at each volume of base added, we need to consider the following steps:
Step 1: Calculate the amount of acid remaining before each volume of base is added.
- To do this, use the following equation: moles of acid = (initial volume of acid) × (initial concentration of acid).
Step 2: Calculate the moles of base added.
- For each volume of base added, use the following equation: moles of base = (added volume of base) × (concentration of base).
Step 3: Calculate the moles of acid neutralized.
- Since the acid is diprotic, each mole of base neutralizes two moles of acid.
Step 4: Calculate the concentration of acid remaining.
- Subtract the moles of acid neutralized from the moles of acid at the start.
Step 5: Calculate the concentration of conjugate base formed.
- Since each mole of neutralized acid forms one mole of conjugate base, the concentration of conjugate base is equal to the moles of acid neutralized.
Step 6: Calculate the pH.
- The pH can be calculated using the Henderson-Hasselbalch equation: pH = pKa + log10 ([conjugate base]/[acid]).
By following these steps, you can calculate the pH at each volume of base added. Once you have the pH values, you can create a graph of pH versus Vb.
Patrick, Meg, Sandy,....
This is done the same way as the weak acid except you work two problems. One until you have titrated the first acid, then start titrating the second acid. Post your work if you get stuck.