How many grams of dipotassium succinate trihydrate (K2C4H4O4·3H2O, MW = 248.32 g/mol) must be added to 790.0 mL of a 0.0522 M succinic acid solution to produce a pH of 5.872? Succinic acid has pKa values of 4.207 (pKa1) and 5.636 (pKa2).
is the pH of the current solution before the addition of the buffer 1/2(pka1+pka2)? otherwise, what is the first step to be taken in this problem?
No, the pH of the current solution before the addition of the buffer is not necessarily 1/2(pKa1 + pKa2). The first step in this problem is to understand that a buffer system can be created by adding a weak acid and its conjugate base (or a weak base and its conjugate acid) to resist changes in pH. In this case, you need to determine the ratio of succinic acid (weak acid) to dipotassium succinate (conjugate base) needed to achieve a pH of 5.872.
To determine the required ratio, you can use the Henderson-Hasselbalch equation:
pH = pKa + log ([conjugate base] / [weak acid])
In this equation, [conjugate base] refers to the concentration of the conjugate base (dipotassium succinate), and [weak acid] refers to the concentration of the weak acid (succinic acid).
Since the pH, pKa, and concentration of the weak acid are given, you can rearrange the equation to solve for the concentration of the conjugate base:
[conjugate base] = 10^(pH - pKa) * [weak acid]
Once you have the concentration of the conjugate base, you can convert it to grams using its molar mass to find out how many grams of dipotassium succinate trihydrate (K2C4H4O4·3H2O) need to be added to achieve the desired pH.