Use a spreadsheet to prepare a family of graphs for the titration of 50.0 mL of 0.020 M H2A with 0.100 M NaOH. Consider the following cases: (a) pK1 = 4.00, pK2 = 8.00; (b) pK1 = 4.00, pK2 = 6.00; (c) pK1 = 4.00, pK2 = 5.00.
You do this the same way you do the H2A problem you posted (pk1 = 4 and pk = 8). Then you graph the results. We can't draw graphs on this board.
To prepare a family of graphs for the titration of 50.0 mL of 0.020 M H2A with 0.100 M NaOH, you can use a spreadsheet to calculate the pH at different points in the titration process. Here's how you can do it:
1. Open a new spreadsheet and label the columns as follows: Volume of NaOH added (mL), moles of NaOH added (mol), moles of H2A remaining (mol), moles of HA- formed (mol), moles of NaA remaining (mol), and pH.
2. Start by calculating the initial moles of H2A. Since the volume is given as 50.0 mL and the concentration is 0.020 M, you can use the formula: moles = volume (L) x concentration (M). In this case, the initial moles of H2A would be 50.0 mL * 0.020 M = 0.001 mol.
3. Fill in the first row of the spreadsheet with the corresponding values. For the initial volume of NaOH added, moles of NaOH added, moles of H2A remaining, moles of HA- formed, and moles of NaA remaining, you can put 0 since no NaOH has been added yet. For the pH, you can use the formula: pH = -log10([H+]), where [H+] is the concentration of H+ ions. Since H2A is a diprotic acid and only one mole of H2A is present initially, the concentration of H+ ions is equal to the initial concentration of H2A remaining.
4. Now, you can start calculating the values as NaOH is added. As NaOH reacts with H2A, it will form HA- and NaA. The moles of NaOH added would be the sum of the volumes of NaOH added in each step. The moles of H2A remaining, moles of HA- formed, and moles of NaA remaining can be calculated using stoichiometry. For example, if x mL of NaOH is added, the number of moles of NaOH added would be x mL * 0.100 M. To calculate moles of H2A remaining, subtract the moles of NaOH added from the initial moles of H2A. To calculate moles of HA- formed and moles of NaA remaining, you can use the balanced equation for the reaction.
5. To calculate the pH, you need to consider the dissociation of H2A into H+ and A- through two reactions, each with its own equilibrium constant. Using the given pK1 and pK2 values, you can calculate the concentrations of H+, A-, and HA- at each step in the titration. The pH can then be calculated using the formula mentioned earlier.
6. Repeat steps 4 and 5 for each volume of NaOH added until the endpoint is reached, which is when all the H2A has been converted into HA-. At this point, you will have a complete set of values for each case (a, b, and c).
7. Plot the pH values against the volume of NaOH added to create the graphs for each case. Label the axes accordingly and include a title for each graph.
By following these steps and using a spreadsheet, you can easily prepare the family of graphs for the titration of H2A with NaOH for the given cases (a, b, and c) with varying pK1 and pK2 values.