Assume that you dissolve 10.0 g of a mixture of NaOH and Ba(OH)2 in 250.0 mL of water and titrate with 1.50 M hydrochloric acid. The titration is complete after 108.9 mL of the acid has been added. What is the mass in grams of each substance in the mixture?

검증된 단계별 안내

Determine the total moles of HCl used in the titration. Since the concentration of HCl is given as 1.50 M, and the volume used is 108.9 mL, convert the volume from mL to L and use the formula: Moles of HCl = Molarity of HCl × Volume of HCl in liters.

Write the balanced chemical equations for the reaction of HCl with NaOH and Ba(OH)2. For NaOH: HCl + NaOH → NaCl + H2O. For Ba(OH)2: 2 HCl + Ba(OH)2 → BaCl2 + 2 H2O.

Set up the stoichiometry based on the balanced equations. Since each mole of NaOH reacts with 1 mole of HCl and each mole of Ba(OH)2 reacts with 2 moles of HCl, use these ratios to express the moles of NaOH and Ba(OH)2 in terms of the moles of HCl.

Let x be the moles of NaOH and y be the moles of Ba(OH)2 in the mixture. Set up the equation x + 2y = total moles of HCl (from step 1) to account for all the HCl reacted.

Use the mass of the mixture (10.0 g) and the molar masses of NaOH and Ba(OH)2 to set up another equation: (Molar mass of NaOH) × x + (Molar mass of Ba(OH)2) × y = 10.0 g. Solve the system of equations from steps 4 and 5 to find the values of x and y, and then convert these moles back to grams to find the mass of each substance in the mixture.

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주요 개념

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Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the relationships between the amounts of substances consumed and produced. In this question, stoichiometry will help relate the moles of hydrochloric acid used in the titration to the moles of NaOH and Ba(OH)2 in the mixture.

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 (in this case, hydrochloric acid) to a solution until the reaction reaches completion, indicated by a color change or a specific endpoint. Understanding the titration process is essential for calculating the amounts of NaOH and Ba(OH)2 in the mixture based on the volume and concentration of the acid used.

Molarity and Moles

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. To solve the problem, it is necessary to convert the volume of hydrochloric acid used in the titration into moles, which can then be used to find the moles of NaOH and Ba(OH)2. This concept is crucial for determining the mass of each component in the original mixture.