Consider the titration of 41.5 mL of 0.213 M HCl with 0.123 M KOH. Calculate the pH of the resulting solution after the following volumes of KOH have been added. (Assume that all solutions are at 25°C.)
(a) 0.0 mL
(b) 10.0 mL
(c) 40.0 mL
(d) 80.0 mL
(e) 100.0 mL
To calculate the pH of the resulting solution after each volume of KOH has been added, we need to determine the moles of HCl and KOH reacted and analyze the resulting solution using the principles of acid-base titration.
To solve this problem, we'll use the following steps:
1. Calculate the moles of HCl.
We know the volume (41.5 mL) and concentration (0.213 M) of HCl. First, convert the volume from mL to L by dividing by 1000:
41.5 mL ÷ 1000 = 0.0415 L
Next, use the formula: moles = concentration × volume
Moles of HCl = 0.213 M × 0.0415 L
2. Determine the moles of KOH that will react with HCl.
In a stoichiometric reaction, one mole of HCl reacts with one mole of KOH. Therefore, the moles of KOH will be the same as the moles of HCl.
3. Calculate the moles of KOH in the added volume.
We are given the concentration (0.123 M) and volume for each case. Multiply the concentration by the volume to find the moles of KOH.
4. Calculate the moles of HCl remaining after each addition of KOH.
Subtract the moles of KOH that reacted from the total moles of HCl.
5. Calculate the concentration of HCl remaining.
To find the concentration of HCl, divide the moles of HCl remaining by the total volume of the mixture.
6. Use the concentration of HCl remaining to calculate the pH.
The pH can be calculated using the formula: pH = -log[H+], where [H+] represents the concentration of H+ ions.
Now let's apply these steps to calculate the pH for each case:
(a) 0.0 mL of KOH added
No KOH has been added, so the moles of KOH reacted and remaining are both zero. The concentration of HCl remains the same at 0.213 M. Use the concentration to calculate the pH.
(b) 10.0 mL of KOH added
The moles of KOH added can be calculated by multiplying the concentration (0.123 M) by the volume (10.0 mL converted to L by dividing by 1000). Subtract the moles of KOH added from the moles of HCl to find the moles of HCl remaining. Divide the moles of HCl remaining by the total volume to find the concentration of HCl. Use the concentration to calculate the pH.
(c) 40.0 mL of KOH added
Repeat the same steps as in (b) to find the moles of HCl remaining and the concentration of HCl. Then calculate the pH.
(d) 80.0 mL of KOH added
Repeat the same steps as in (b) and (c) to find the moles of HCl remaining and the concentration of HCl. Then calculate the pH.
(e) 100.0 mL of KOH added
Repeat the same steps as in (b), (c), and (d) to find the moles of HCl remaining and the concentration of HCl. Then calculate the pH.
By following these steps, you can calculate the pH of the resulting solution after each volume of KOH has been added.