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. (a) What is the concentration of H₃O⁺ at the first equivalence point?

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Identify the acids in the mixture: HCl and H3PO4.

Recognize that the first equivalence point corresponds to the complete neutralization of HCl and the first proton of H3PO4.

Calculate the moles of NaOH used to reach the first equivalence point: \( \text{moles of NaOH} = 0.100 \, \text{M} \times 88.0 \, \text{mL} \times \frac{1 \, \text{L}}{1000 \, \text{mL}} \).

Determine the moles of HCl and the first proton of H3PO4 neutralized by the NaOH at the first equivalence point.

Use the stoichiometry of the reaction to find the concentration of \( \text{H}_3\text{O}^+ \) at the first equivalence point.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Titration and Equivalence Points

Titration is a quantitative analytical method used to determine the concentration of a solute in a solution. The equivalence point in a titration occurs when the amount of titrant added is stoichiometrically equivalent to the amount of substance in the sample. In this case, the first equivalence point indicates that all the strong acid (HCl) has reacted with NaOH, allowing for the calculation of the concentration of H3O+ ions present.

Strong vs. Weak Acids

Strong acids, like HCl, completely dissociate in water, producing a high concentration of H3O+ ions. In contrast, weak acids, such as H3PO4, do not fully dissociate, leading to a lower concentration of H3O+ ions. Understanding the behavior of these acids during titration is crucial for determining the concentration of H3O+ at the equivalence points.

Concentration Calculations

Concentration is defined as the amount of solute per unit volume of solution, typically expressed in moles per liter (M). To find the concentration of H3O+ at the first equivalence point, one must use the volume of NaOH added and its molarity to calculate the moles of NaOH, which corresponds to the moles of HCl initially present, and then relate this to the total volume of the solution to find the concentration of H3O+.

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Textbook Question

Ethylenediamine (NH2CH2CH2NH2, abbreviated en) is an organic base that can accept two protons: (a) Consider the titration of 30.0 mL of 0.100 M ethylenediamine with 0.100 M HCl. Calculate the pH after the addition of the following volumes of acid, and construct a qualitative plot of pH versus milliliters of HCl added: (i) 0.0 mL (ii) 15.0 mL (iii) 30.0 mL (iv) 45.0 mL (v) 60.0 mL (vi) 75.0 mL

Textbook Question

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?

Textbook Question

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. (c) What percent of the HCl is neutralized at the first equivalence point?

Textbook Question

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. (f) What indicators would you select to signal the equivalence points?

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. (a) What is the concentration of H3O+ at the first equivalence point?

Verified video answer for a similar problem:

Key Concepts

Titration and Equivalence Points

Strong vs. Weak Acids

Concentration Calculations

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. (a) What is the concentration of H₃O⁺ at the first equivalence point?