A 40.0 mL sample of a mixture of HCl and H₃PO₄ was titrated with 0.100 M NaOH. The first equivalence point was reached after 88.0 mL of base, and the second equivalence point was reached after 126.4 mL of base. (b) What are the initial concentrations of HCl and H₃PO₄ in the mixture?

Verified step by step guidance

1. First, let's understand the problem. We have a mixture of HCl and H3PO4, both of which can react with NaOH. HCl is a strong monoprotic acid (it donates one proton per molecule), while H3PO4 is a triprotic acid (it donates three protons per molecule). The first equivalence point corresponds to the neutralization of HCl and the first proton of H3PO4, and the second equivalence point corresponds to the neutralization of the second proton of H3PO4. The third proton of H3PO4 is not considered because it is weakly acidic and does not fully ionize.
2. Next, we calculate the moles of NaOH used to reach the first equivalence point. This is done by multiplying the volume of NaOH (in liters) by its molarity. The moles of NaOH used to reach the first equivalence point are equal to the total moles of protons donated by HCl and the first proton of H3PO4.
3. Then, we calculate the moles of NaOH used between the first and second equivalence points. This is equal to the moles of protons donated by the second proton of H3PO4.
4. Knowing the moles of protons donated by HCl and H3PO4, we can calculate the initial concentrations of these acids in the mixture. The concentration is calculated by dividing the moles of the acid by the initial volume of the acid mixture (in liters).
5. Finally, we can conclude that the initial concentration of HCl is equal to the moles of HCl divided by the initial volume of the mixture, and the initial concentration of H3PO4 is equal to the moles of H3PO4 divided by the initial volume of the mixture.

Key Concepts

Titration

Titration is a quantitative analytical technique used to determine the concentration of a solute in a solution. It involves the gradual addition of a titrant (a solution of known concentration) to a sample until a reaction reaches its equivalence point, where the amount of titrant equals the amount of substance in the sample. In this case, NaOH is the titrant used to determine the concentrations of HCl and H3PO4 in the mixture.

Equivalence Point

The equivalence point in a titration is the stage at which the amount of titrant added is stoichiometrically equivalent to the amount of substance present in the sample. For polyprotic acids like H3PO4, there can be multiple equivalence points corresponding to the neutralization of each acidic proton. The volumes at which these points are reached provide critical information for calculating the concentrations of the acids in the mixture.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equations. It allows chemists to determine the relationships between the quantities of substances involved in a reaction. In this titration problem, stoichiometry is essential for relating the volumes of NaOH used to the concentrations of HCl and H3PO4, enabling the calculation of their initial concentrations in the mixture.