A 100.0 mL solution containing aqueous HCl and HBr was titrated with 0.1235 M NaOH. The volume of base required to neutralize the acid was 47.14 mL. Aqueous AgNO3 was then added to precipitate the Cl-and Br-ions as AgCl and AgBr. The mass of the silver halides obtained was 0.9974 g. What are the molarities of the HCl and HBr in the original solution?

Verified step by step guidance

1. Calculate the total moles of NaOH used in the titration by multiplying the concentration of NaOH by the volume used, converted to liters. Use the formula: \( \text{moles of NaOH} = M_{\text{NaOH}} \times V_{\text{NaOH}} \).
2. Recognize that NaOH neutralizes both HCl and HBr in a 1:1 molar ratio. Therefore, the total moles of NaOH used will equal the total moles of HCl and HBr combined.
3. Calculate the moles of AgCl and AgBr formed using the mass of the precipitate and the molar masses of AgCl (143.32 g/mol) and AgBr (187.77 g/mol). Assume x moles of AgCl and y moles of AgBr are formed, then solve the equation: \( 143.32x + 187.77y = 0.9974 \) g.
4. Use the stoichiometry of the reactions \( \text{Ag}^+ + \text{Cl}^- \rightarrow \text{AgCl} \) and \( \text{Ag}^+ + \text{Br}^- \rightarrow \text{AgBr} \) to relate the moles of AgCl and AgBr back to the moles of HCl and HBr, respectively. Since each mole of AgCl and AgBr comes from one mole of Cl- and Br-, respectively, the moles of HCl and HBr are equal to the moles of AgCl and AgBr.
5. Calculate the molarities of HCl and HBr by dividing their respective moles by the volume of the original solution in liters. Use the formulas: \( M_{\text{HCl}} = \frac{\text{moles of HCl}}{0.100} \) and \( M_{\text{HBr}} = \frac{\text{moles of HBr}}{0.100} \).

Key Concepts

Neutralization Reaction

A neutralization reaction occurs when an acid reacts with a base to produce water and a salt. In this case, HCl and HBr are strong acids that react with NaOH, a strong base, to form water and sodium chloride (NaCl) and sodium bromide (NaBr). The stoichiometry of the reaction is crucial for determining the amounts of acid present based on the volume and concentration of the base used.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. In this scenario, the stoichiometric coefficients from the balanced neutralization reaction allow us to relate the moles of NaOH used to the moles of HCl and HBr in the original solution. This relationship is essential for determining the molarity of each acid.

Precipitation Reaction

A precipitation reaction occurs when two soluble salts react to form an insoluble compound, which precipitates out of solution. In this case, AgNO3 is added to the solution to precipitate Cl- and Br- ions as AgCl and AgBr. The mass of the precipitate can be used to calculate the moles of halide ions present, which helps in determining the original concentrations of HCl and HBr.