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Chapter 4: Problem 52

Consider the reaction below. \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \longrightarrow \mathrm{CaCl}_{2}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) (a) How many grams of \(\mathrm{Ca}(\mathrm{OH})_{2}\) are required to react completely with \(415 \mathrm{mL}\) of \(0.477 \mathrm{M} \mathrm{HCl} ?\) (b) How many kilograms of \(\mathrm{Ca}(\mathrm{OH})_{2}\) are required to react with 324 L of a HCl solution that is 24.28\% HCl by mass, and has a density of \(1.12 \mathrm{g} / \mathrm{mL} ?\)

Short Answer

Expert verified
a) 7.33 grams of Ca(OH)2 are needed to react completely with 415 ml of 0.477 M HCl. b) 8.90 kilograms of Ca(OH)2 are required to react with 324 L of a HCl solution that is 24.28% HCl by mass, and has a density of 1.12 g/mL.

Step by step solution

01

Determine the reactant moles from the given volume and molarity

From the molarity and volume of the HCl solution, calculate the moles. Molarity = moles/volume. So, moles of HCl = Molarity * Volume = 0.477 M * 0.415 L = 0.19785 moles.
02

Use stoichiometry to find the moles of Ca(OH)2

From the reaction, 1 mole of Ca(OH)2 reacts with 2 moles of HCl. Hence moles of Ca(OH)2 = 0.19785 moles / 2 = 0.098925 moles.
03

Convert moles to grams

Convert the moles of Ca(OH)2 to grams using its molar mass (Molar mass of Ca(OH)2 = 74.093 g/mol). Grams = moles * Molar mass = 0.098925 moles * 74.093 g/mol = 7.33 g.
04

Determine the mass of HCl from the given solution volume and density

The solution volume is given, and the percentage composition by mass and density of the solution is known. The mass of the HCl in the solution is thus = Volume of solution * Density * (percentage composition / 100) = 324 L * (1.12 g/mL) * (24.28 / 100) = 8766.7712 g or 8.77 kg.
05

Convert mass to moles

Convert the mass of HCl to moles using its molar mass (Molar mass of HCl = 36.461 g/mol). Moles of HCl = Mass / Molar Mass = 8766.7712 g / 36.461 g/mol = 240.409 moles.
06

Use stoichiometry to find the moles of Ca(OH)2

Using the stoichiometric coefficients from the balanced chemical equation, find the moles of Ca(OH)2. Moles of Ca(OH)2 = Moles of HCl / 2 = 240.409 moles / 2 = 120.205 moles.
07

Convert moles to kilograms

Convert the moles of Ca(OH)2 to kilograms using its molar mass. Kilograms of Ca(OH)2 = Moles * Molar mass / 1000 = 120.205 moles * 74.093 g/mol / 1000 = 8.90 kg.

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