In the study of polyprotic acids, such as phosphoric acid, it is essential to understand the concept of equivalence points during titration. Polyprotic acids can donate more than one proton (H⁺), leading to multiple equivalence points in a titration with a strong base. For phosphoric acid, there are three equivalence points, which means three distinct volumes of strong base are required to fully neutralize the acid.

The relationship between the molarity and volume of the acid and base can be expressed with the equation:

M_a \cdot V_a = M_b \cdot V_b

where M_a and V_a are the molarity and volume of the acid, and M_b and V_b are the molarity and volume of the base. For example, if the molarity of the strong base is 0.100 M, the first equivalence volume needed to neutralize phosphoric acid is 50 mL. Consequently, the total volumes required for each equivalence point are 50 mL for the first, 100 mL for the second, and 150 mL for the third.

Before any strong base is added, the solution contains only the weak acid. To analyze the equilibrium state, an ICE (Initial, Change, Equilibrium) chart is utilized. For the first dissociation of phosphoric acid, the equilibrium expression involves the first dissociation constant, K_a1, which is defined as:

K_a1 = \frac{[H_2PO_4^-][H_3O^+]}{[H_3PO_4]}

In this case, the initial concentration of phosphoric acid is 0.100 M, and since no products are present initially, the change in concentration will reflect the loss of reactants as products form. The 5% approximation method can help determine if the change in concentration (denoted as x) can be ignored. However, for phosphoric acid, the calculated value of K_a1 is 7.5 x 10^-3, which indicates that the approximation cannot be applied, necessitating the use of the quadratic formula to solve for x.

Upon applying the quadratic formula, the concentration of hydrogen ions, [H^+] , is found to be approximately 0.0239 M. The pH of the solution can then be calculated using the formula:

pH = -\log[H^+]

This results in a pH of approximately 1.62, indicating a strongly acidic solution before any base is added. As titration begins and strong base is introduced, the pH will increase, reflecting the neutralization process. Understanding these concepts is crucial for mastering the behavior of polyprotic acids in titration scenarios.

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