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Chapter 4: Problem 118

A mixture contains only sodium chloride and potassium chloride. A \(0.1586-\mathrm{g}\) sample of the mixture was dissolved in water. It took \(22.90 \mathrm{~mL}\) of \(0.1000 \mathrm{M} \mathrm{AgNO}_{3}\) to completely precipitate all the chloride present. What is the composition (by mass percent) of the mixture?

Short Answer

Expert verified
The composition of the mixture is approximately 21.4% sodium chloride (\(NaCl\)) and 78.6% potassium chloride (\(KCl\)).

Step by step solution

01

Calculate the mols of silver nitrate

Find the moles of silver nitrate that reacted with the chloride mixture using the given volume and concentration: Moles of AgNO3 = (volume) × (concentration) Moles of AgNO3 = (22.90 ml) × (0.1000 mol/L) Note that we need to convert the volume from ml to L: Moles of AgNO3 = (0.0229 L) × (0.1000 mol/L) Moles of AgNO3 = 0.00229 mol
02

Calculate the mols of chloride ions

Calculate the moles of both chloride ions, as silver nitrate reacts equally with chloride ions from sodium chloride and potassium chloride. Moles of chloride ions = moles of AgNO3 = 0.00229 mol
03

Assign variables and write an equation

Assign variable x to moles of NaCl and y to moles of KCl in the mixture. Then, write an equation for total mass of the mixture sample. 0.1586 g = (x × 58.44 g/mol) + (y × 74.55 g/mol) We also know that the total moles of chloride equal the moles of AgNO₃: x + y = 0.00229
04

Solve the equations

Solve the two equations in step 3 simultaneously: x = 0.00229 - y Substitute x in the first equation: 0.1586 = ((0.00229 - y) × 58.44) + (y × 74.55) Now, solve for y: y ≈ 0.00171 mol Substitute y in the equation x = 0.00229 - y to find x: x ≈ 0.00058 mol
05

Calculate mass of NaCl and KCl

Use the molar masses of NaCl and KCl to find their masses in the 0.1586 g mixture: Mass of NaCl = x × molar mass of NaCl = 0.00058 mol × 58.44 g/mol ≈ 0.0339 g Mass of KCl = y × molar mass of KCl = 0.00171 mol × 74.55 g/mol ≈ 0.127 g
06

Calculate the mass percent of each compound

Now, calculate the mass percent of NaCl and KCl in the mixture: Mass percent of NaCl = (mass of NaCl / total mass) × 100 Mass percent of NaCl = (0.0339 g / 0.1586 g) × 100 ≈ 21.4% Mass percent of KCl = (mass of KCl / total mass) × 100 Mass percent of KCl = (0.127 g / 0.1586 g) × 100 ≈ 78.6% The composition of the mixture is approximately 21.4% sodium chloride and 78.6% potassium chloride.

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