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Chapter 4: Problem 102

A 0.8870 -g sample of a mixture of \(\mathrm{NaCl}\) and \(\mathrm{KCl}\) is dissolved in water, and the solution is then treated with an excess of \(\mathrm{AgNO}_{3}\) to yield \(1.913 \mathrm{~g}\) of \(\mathrm{AgCl}\). Calculate the percent by mass of each compound in the mixture.

Short Answer

Expert verified
To find the exact values, each of these steps must be followed to calculate the % mass of NaCl and KCl in the given mixture.

Step by step solution

01

Calculate the moles of AgCl formed

A chemical reaction between the NaCl, KCl, and AgNO3 takes place resulting in the formation of AgCl, which can be precipitated out from the solution. This enables us to connect the AgCl formed with the Chlorine that was in our original mixture of NaCl and KCl. The molar mass of \( \mathrm{AgCl} \) is 143.32 g/mol. The moles of AgCl formed can be calculated using the formula: Moles = mass / molar mass, i.e. \( \text{Moles of AgCl} = \frac{1.913}{143.32} \) .
02

Calculate the mass of Cl in the mixture

The moles of AgCl formed equals the moles of Cl in the mixture, because one molecule of AgCl contains one atom of Cl. The atomic mass of Cl is 35.45 g/mol, so the mass of Cl in the mixture can be calculated by multiplying the moles of Cl by its atomic weight: \( \text{Mass of Cl} = \text{Moles of Cl} \times \text{Molar mass of Cl} \).
03

Calculate the mass of NaCl and KCl

Since NaCl and KCl are the only two compounds in the mixture, and they both contain Cl, the masses of NaCl and KCl in the mixture can be calculated knowing the mass of Cl in the original mixture and the atomic masses of Na (22.99 g/mol) and K (39.10 g/mol). Therefore, we get the following formulas: \( \text{Mass of NaCl} = \text{Mass of Cl} + \text{Mass of Na} = \text{Mass of Cl} + (\text{Moles of Cl} \times \text{Molar mass of Na}) \) and \( \text{Mass of KCl} = \text{Mass of mixture} - \text{Mass of NaCl} \).
04

Calculate the percent by mass of each compound

Percent by mass is characterized as the mass of a particular substance (NaCl and KCl in this case) divided by the total mass of the mixture, multiplied by 100. Therefore: \( \text{% Mass of NaCl} = (\frac{\text{Mass of NaCl}}{0.887)} \times 100 \) and \( \text{% Mass of KCl} = (\frac{\text{Mass of KCl}}{0.887)} \times 100 \).

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Most popular questions from this chapter

Identify each of the following substances as a strong electrolyte, weak electrolyte, or nonelectrolyte: (a) \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\) (b) Ne, (c) \(\mathrm{NH}_{3}\) (d) \(\mathrm{NaOH}\).

A 325-mL sample of solution contains \(25.3 \mathrm{~g}\) of \(\mathrm{CaCl}_{2}\). (a) Calculate the molar concentration of \(\mathrm{Cl}^{-}\) in this solution. (b) How many grams of \(\mathrm{Cl}^{-}\) are in \(0.100 \mathrm{~L}\) of this solution?

A \(35.2-\mathrm{mL}, 1.66 \mathrm{M} \mathrm{KMnO}_{4}\) solution is mixed with \(16.7 \mathrm{~mL}\) of \(0.892 \mathrm{M} \mathrm{KMnO}_{4}\) solution. Calculate the concentration of the final solution.

How many grams of \(\mathrm{KOH}\) are present in \(35.0 \mathrm{~mL}\) of a \(5.50 \mathrm{M}\) solution?

This "cycle of copper" experiment is performed in some general chemistry laboratories. The series of reactions starts with copper and ends with metallic copper. The steps are: (1) A piece of copper wire of known mass is allowed to react with concentrated nitric acid [the products are copper(II) nitrate, nitrogen dioxide, and water]. (2) The copper(II) nitrate is treated with a sodium hydroxide solution to form copper(II) hydroxide precipitate. (3) On heating, copper(II) hydroxide decomposes to yield copper(II) oxide. (4) The copper(II) oxide is reacted with concentrated sulfuric acid to yield copper(II) sulfate. (5) Copper(II) sulfate is treated with an excess of zinc metal to form metallic copper. (6) The remaining zinc metal is removed by treatment with hydrochloric acid, and metallic copper is filtered, dried, and weighed. (a) Write a balanced equation for each step and classify the reactions. (b) Assuming that a student started with \(65.6 \mathrm{~g}\) of copper, calculate the theoretical yield at each step. (c) Considering the nature of the steps, comment on why it is possible to recover most of the copper used at the start.
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