Question

Copper has compounds with copper(I) ion or copper(II) ion. A compound of copper and chlorine was treated with a solution of silver nitrate, \(\mathrm{AgNO}_{3},\) to convert the chloride ion in the compound to a precipitate of \(\mathrm{AgCl}\). A 59.40 -mg sample of the copper compound gave \(86.00 \mathrm{mg}\) AgCl. (a) Calculate the percentage of chlorine in the copper comnound (b) Decide whether the formula of the compound is \(\mathrm{CuCl}\) or \(\mathrm{CuCl}_{2}\)

Short answer

The compound is CuCl with 35.80% chlorine.

Step-by-step solution

Calculate the Moles of AgCl Formed

First, determine the number of moles of AgCl in the precipitate. Use the molar mass of AgCl, which is approximately 143.32 g/mol. Convert the mass of AgCl (86 mg) to grams:\[86 \text{ mg} = 0.086 \text{ g}\]Now, calculate the moles of AgCl:\[\text{Moles of AgCl} = \frac{0.086 \text{ g}}{143.32 \text{ g/mol}} \approx 0.000600 \text{ mol}\]

Determine Moles of Cl in AgCl

The chemical formula for silver chloride, AgCl, indicates that each mole of AgCl contains one mole of Cl. Therefore, the moles of Cl in the AgCl precipitate is equal to the moles of AgCl:\[\text{Moles of Cl} = 0.000600 \text{ mol}\]

Calculate Mass of Cl in the Compound

Use the moles of Cl to find its mass. The molar mass of Cl (chlorine) is approximately 35.45 g/mol. Multiply the moles of Cl by its molar mass:\[\text{Mass of Cl} = 0.000600 \text{ mol} \times 35.45 \text{ g/mol} = 0.02127 \text{ g} = 21.27 \text{ mg}\]

Calculate Percentage of Chlorine in the Copper Compound

Divide the mass of chlorine by the total mass of the copper compound sample, then multiply by 100 to get the percentage:\[\text{Percentage of Cl} = \left( \frac{21.27 \text{ mg}}{59.40 \text{ mg}} \right) \times 100 \approx 35.80\%\]

Compare with Theoretical Percentages for CuCl and CuCl2

Next, determine whether the percentage of chlorine aligns with the theoretical percentages in each possible compound:- For CuCl, the percentage of Cl is calculated as:\[\text{Molar mass of CuCl} = 63.55 \text{ g/mol (Cu)} + 35.45 \text{ g/mol (Cl)} = 98.00 \text{ g/mol}\]\[\% \text{ Cl in CuCl} = \left( \frac{35.45}{98.00} \right) \times 100 \approx 36.17t\%\]- For CuCl2, the percentage of Cl is:\[\text{Molar mass of CuCl}_2 = 63.55 \text{ g/mol} + 2 \times 35.45 \text{ g/mol} = 134.45 \text{ g/mol}\]\[\% \text{ Cl in CuCl}_2 = \left( \frac{70.90}{134.45} \right) \times 100 \approx 52.75\%\]The experimental chlorine percentage (35.80%) is closest to the theoretical percentage for CuCl (36.17%).

Key concepts

Stoichiometry

Stoichiometry is a key concept in chemistry that involves calculating the quantities of reactants and products in chemical reactions. It relies heavily on the concept of the mole, which is the standard unit of measurement for amount of substance in the International System of Units (SI). In this exercise, stoichiometry is used to determine the amount of chlorine present in a compound based on the amount of silver chloride formed during a precipitation reaction.

By converting the mass of silver chloride (AgCl) to moles using its molar mass, we can deduce the moles of chloride ions present, because AgCl contains equal moles of silver and chloride ions. This stoichiometric relationship allows us to find the mass of chlorine, and thereby calculate the percentage of chlorine in the original copper compound sample.

The concept of stoichiometry enables chemists to predict and verify the amounts of substances consumed and produced in a chemical reaction, making it crucial in chemical analysis and quantitative studies.

Copper Compounds

Copper compounds such as copper(I) chloride (CuCl) and copper(II) chloride (CuCl2) are commonly studied in chemistry due to their unique properties and reactions. Copper can form different types of compounds depending on its oxidation state, which is the measure of the degree of oxidation of an atom in a chemical compound.

In the given exercise, we explore copper(I) chloride and copper(II) chloride, which have different chlorine to copper ratios. Understanding the nature of copper compounds helps in determining their formulas through experimental data.

• Copper(I) Chloride (CuCl): Contains one copper atom per chlorine atom. It exhibits a 1:1 molar ratio of copper to chlorine.
• Copper(II) Chloride (CuCl2): Contains one copper atom and two chlorine atoms, resulting in a 1:2 molar ratio.

The correct identification of a copper compound depends on the experimental percentage of chlorine. By comparing this percentage with the theoretical calculations, one can determine the accurate formula of the copper compound.

Precipitation Reactions

Precipitation reactions are a type of chemical reaction where two solutions react to form an insoluble solid called a precipitate. These reactions are driven by the formation of a solid from two aqueous solutions. In our example, the chloride ions in the copper compound react with silver ions from the silver nitrate solution to produce silver chloride, which is insoluble in water and forms a solid precipitate.

The process is as follows: when a solution containing chloride ions is mixed with a solution that contains silver ions, a white precipitate of silver chloride (AgCl) forms almost immediately. The formation of a precipitate is a physical change that indicates a chemical reaction has occurred.

• Precipitation reactions are useful for detecting the presence of specific ions in solutions.
• The process also helps quantify certain ions based on the mass of the precipitate formed.

Understanding precipitation reactions is essential for chemical analysis, especially when determining the composition of unknown compounds. This methodology allows chemists to isolate and study specific elements within complex mixtures.