A weak acid HA (pKa = 5.00) was titrated with 1.00 M KOH. The acid solution had a volume of 100.0 mL and a molarity of 0.100 M. Find the pH at the following volumes of base added and make a graph of pH versus Vb: Vb = 0, 1, 5, 9, 9.9, 10, 10.1, and 12 mL.
To find the pH at each volume of base added, we need to go through the steps of calculating the initial moles of acid (HA), the moles of acid and base at each volume, and then use these values to find the concentration of the acid and its conjugate base at each point.
Let's break it down step by step:
Step 1: Calculate the initial moles of acid (HA).
Given that the volume of the acid solution is 100.0 mL and the molarity is 0.100 M, we can use the formula:
moles = volume (L) x molarity
Converting the volume to liters:
volume = 100.0 mL = 100.0 mL x (1 L/1000 mL) = 0.100 L
Now, calculate the moles of acid:
moles of HA = 0.100 L x 0.100 M = 0.0100 moles
Step 2: Calculate the moles of acid and base at each volume.
We know that for every mole of acid (HA) reacting with a mole of base (KOH), it will form one mole of water (H2O) and one mole of its conjugate base (A-). So, we can set up a balanced equation:
HA + KOH → H2O + A-
For each volume of base added (Vb), we will calculate the moles of acid and base remaining:
At Vb = 0 mL:
- The moles of acid (HA) remaining is equal to the initial moles of acid.
- The moles of base (KOH) added is 0.
At Vb = 1 mL:
- The moles of acid (HA) remaining is equal to the initial moles of acid minus the moles of base added.
- The moles of base (KOH) added is 1 mL x (1 L/1000 mL) x (1.00 M) = 0.001 moles.
Repeat this calculation for the other given volumes of base added.
Step 3: Calculate the concentration of acid and its conjugate base at each point.
Knowing the moles of acid (HA) remaining and the total volume of the solution (100 mL + Vb), we can calculate the concentrations:
For the acid (HA) concentration:
HA concentration (M) = moles of HA remaining / total volume (L)
For the conjugate base (A-) concentration:
A- concentration (M) = moles of base (A-) formed / total volume (L)
Step 4: Calculate the pH at each point.
Using the Henderson-Hasselbalch equation for a weak acid:
pH = pKa + log10(A-/HA)
Given that pKa = 5.00, we can plug in the values for A- and HA concentrations, calculated in the previous step, to find the pH at each point.
Step 5: Create a graph of pH vs. Vb.
Plot the pH values against the volumes of base added (Vb) specified.
Finally, by following these steps for each volume of base added, you can find the pH at each point and create a graph of pH versus Vb.
This is done the same way I showed you for the NaOH/HBr titration (it would be nice if you didn't change screen names; it takes longer to get an answer when you do that) except that HA is a weak acid; therefore, when you find how much HA is in solution, you must set up an ICE chart to determine the (H^+) of the resulting HA solution and determine H from that. Everything else is the same.
Post your work if you get stuck.