Find the concentration of the polyprotic weak acid given the following:
- 1 equiv needs 6 ml NaOH, 2 equiv needs 18 ml NaOH, 3 equiv needs 28 ml NaOH
- pKa1 = 2, pKa2 = 3.9, pKa3, 10
- Molarity of NaOH = 0.175
- Total volume of NaOH = 28 ml
- Volume of weak acid = 30 ml
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To find the concentration of the polyprotic weak acid, we can use the concept of titrations and the given information about the volumes of NaOH needed for each equivalence point.
Step 1: Calculate the number of moles of NaOH used for each equivalence point.
- For 1 equiv: 6 ml NaOH is used.
Number of moles of NaOH = volume (in L) x molarity = 6 ml / 1000 ml/L x 0.175 M = 0.00105 moles
- For 2 equiv: 18 ml NaOH is used.
Number of moles of NaOH = 18 ml / 1000 ml/L x 0.175 M = 0.00315 moles
- For 3 equiv: 28 ml NaOH is used.
Number of moles of NaOH = 28 ml / 1000 ml/L x 0.175 M = 0.0049 moles
Step 2: Find the concentration of the weak acid at each equivalence point using the stoichiometry of the reaction.
- For 1 equiv: The weak acid reacts with NaOH in a 1:1 ratio.
Concentration of weak acid = number of moles of weak acid / volume of weak acid in liters = 0.00105 moles / 0.030 L = 0.035 M
- For 2 equiv: The weak acid reacts with NaOH in a 2:1 ratio.
Concentration of weak acid = number of moles of weak acid / volume of weak acid in liters = 0.00315 moles / 0.030 L = 0.105 M
- For 3 equiv: The weak acid reacts with NaOH in a 3:1 ratio.
Concentration of weak acid = number of moles of weak acid / volume of weak acid in liters = 0.0049 moles / 0.030 L = 0.163333 M
Note: Since this is a polyprotic weak acid with three dissociation constants (pKa1, pKa2, and pKa3), each step of reaction corresponds to a different equilibrium and concentration of the weak acid.
Therefore, the concentration of the polyprotic weak acid is:
- 0.035 M for the first equiv
- 0.105 M for the second equiv
- 0.163333 M for the third equiv.