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Chapter 13: Problem 57

Brass is a substitutional alloy consisting of a solution of copper and zinc. A particular sample of red brass consisting of \(80.0 \% \mathrm{Cu}\) and \(20.0 \% \mathrm{Zn}\) by mass has a density of \(8750 \mathrm{~kg} / \mathrm{m}^{3} .\) (a) What is the molality of \(\mathrm{Zn}\) in the solid solution? (b) What is the molarity of \(\mathrm{Zn}\) in the solution?

Short Answer

Expert verified
The molality of Zn in the solid solution is \(3.825 \: \text{mol/kg}\), and the molarity of Zn in the solution is \(26.76 \: \text{mol/L}\).

Step by step solution

01

Convert percentages to masses

Assume we have 100 grams of brass. Since the sample is 80.0% Cu and 20.0% Zn by mass, we can calculate the masses of each element as follows: Mass of Cu = 80.0% × 100 grams = 80 grams Mass of Zn = 20.0% × 100 grams = 20 grams
02

Determine moles of Zn and Cu

Now, determine the moles of Zn and Cu in the brass by dividing their masses by their respective molar masses: Molar mass of Cu = 63.55 g/mol Molar mass of Zn = 65.38 g/mol Moles of Cu = (80 g)/(63.55 g/mol) = 1.259 mol Moles of Zn = (20 g)/(65.38 g/mol) = 0.306 mol
03

Find the mass and volume of the solution

Since we considered 100 grams of brass, the mass of the solution is 100 grams. Now, find the volume of the solution using the given density: Density = (Mass of solution) / (Volume of solution) 8750 kg/m^3 = (100 g) / (Volume of solution) Convert the density from kg/m^3 to g/cm^3: 8750 kg/m^3 × (1 kg/1000 g) × (100^3 cm^3/1 m^3) = 8.75 g/cm^3 Now, solve for the volume of the solution: Volume of solution = (100 g) / (8.75 g/cm^3) = 11.43 cm^3 (convert to L): 11.43 cm^3 × (1 L / 1000 cm^3) = 0.01143 L
04

Calculate molality and molarity of Zn

Now, we can calculate the molality and molarity of Zn in the solution: Molality(m) = (Moles of Zn) / (Mass of Cu in kg) = (0.306 mol) / (0.080 kg) = 3.825 mol/kg Molarity(M) = (Moles of Zn) / (Volume of solution in L) = (0.306 mol) / (0.01143 L) = 26.76 mol/L The molality of Zn in the solid solution is 3.825 mol/kg, and the molarity of Zn in the solution is 26.76 mol/L.

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Caffeine \(\left(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2}\right)\) is a stimulant found in coffee and tea. If a solution of caffeine in chloroform \(\left(\mathrm{CHCl}_{3}\right)\) as a solvent has a concentration of \(0.0500 \mathrm{~m}\), calculate (a) the percent caffeine by mass, (b) the mole fraction of caffeine.

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