Question

A compound of iron and chlorine is soluble in water. An excess of silver nitrate was added to precipitate the chloride ion as silver chloride. If a 134.8 -mg sample of the compound gave \(304.8 \mathrm{mg} \mathrm{AgCl}\), what is the formula of the compound?

Short answer

The formula of the compound is \( \text{FeCl}_2 \).

Step-by-step solution

Determine Moles of AgCl

Convert the mass of AgCl to moles using its molecular weight. The molecular weight of AgCl is 143.32 g/mol. First, convert the mass from mg to g:\[ 304.8 \, \text{mg} = 0.3048 \, \text{g} \]Then, calculate the moles of AgCl:\[ \text{Moles of AgCl} = \frac{0.3048 \, \text{g}}{143.32 \, \text{g/mol}} \approx 0.00213 \, \text{mol} \]

Determine Moles of Chloride Ions

Since each molecule of AgCl contains one chloride ion, the moles of chloride ions are equal to the moles of AgCl precipitated:\[ \text{Moles of Cl} = 0.00213 \, \text{mol} \]

Convert Moles of Chloride to Mass

Find the mass of chloride using its molar mass (35.45 g/mol):\[ \text{Mass of Cl} = 0.00213 \, \text{mol} \times 35.45 \, \text{g/mol} \approx 0.0755 \, \text{g} = 75.5 \, \text{mg} \]

Determine Mass of Iron in Compound

Subtract the mass of chloride from the total mass of the compound to find the mass of iron:\[ \text{Mass of Fe} = 134.8 \, \text{mg} - 75.5 \, \text{mg} = 59.3 \, \text{mg} \]

Convert Mass of Iron to Moles

Use the atomic mass of iron (55.85 g/mol) to find moles of iron:\[ \text{Moles of Fe} = \frac{59.3 \, \text{mg}}{55.85 \, \text{g/mol}} = \frac{0.0593 \, \text{g}}{55.85 \, \text{g/mol}} \approx 0.00106 \, \text{mol} \]

Determine Formula of the Compound

Find the ratio of moles of Cl to moles of Fe:\[ \text{Ratio of Cl to Fe} = \frac{0.00213 \, \text{mol of Cl}}{0.00106 \, \text{mol of Fe}} \approx 2 \]Therefore, the formula of the compound is \( \text{FeCl}_2 \).

Key concepts

Molar Mass Calculation

Understanding molar mass calculation is essential in stoichiometry because it links mass, moles, and atoms of a substance. Molecules are composed of atoms, each with a specific atomic mass. The molar mass is the mass of one mole of a substance, expressed in grams per mole (\( ext{g/mol} \)). For example, to calculate the molar mass of AgCl (Silver Chloride), we add the atomic masses of silver (\( 107.87 \, \text{g/mol} \)) and chlorine (\( 35.45 \, \text{g/mol} \)), resulting in a total molar mass of (\( 143.32 \, \text{g/mol} \)). This allows us to convert between grams and moles of AgCl using the formula:

• \( \text{Moles} = \frac{\text{Mass in grams}}{\text{Molar Mass}} \)

This conversion is vital when analyzing reactions to determine the amount of reactants and products.

Chemical Formula Determination

Determining a chemical formula requires understanding the composition of elements in a compound. We use molar mass calculations to find out the amount of each constituent element. For our exercise, we find how much chloride and iron are in the compound.
We first use the given reaction to convert between the compounds formed (like AgCl) and our unknown compound (iron chloride). By knowing the amount of chloride from AgCl, we determine the remaining substance is iron. The number of moles of each element helps calculate the simplest whole number ratio of atoms (moles of Cl to moles of Fe). This is how chemists deduce that the empirical formula of the compound is \( \text{FeCl}_2 \), showing us there's one iron atom for every two chlorine atoms.

Precipitation Reaction

Precipitation reactions occur when two soluble substances react and form an insoluble product, known as a precipitate. These types of reactions are common in chemistry to isolate elements for analysis. In our case, a precipitation reaction occurs when silver nitrate (AgNO₃) is added to the compound containing chloride ions (Cl⁻).
This reaction forms silver chloride (AgCl), a solid that doesn't dissolve in water, thus precipitating from the solution. The balanced chemical equation for this reaction is:

• \( \text{AgNO}_3 + \text{Cl}^- \rightarrow \text{AgCl (s)} + \text{NO}_3^- \)

The amount of the precipitate (AgCl) gives insight into the chloride content of the original compound, crucial for determining the chemical formula.

Iron Chloride

Iron chloride, with various forms like \( \text{FeCl}_2 \) or \( \text{FeCl}_3 \), is a compound comprised of iron and chlorine. These are typically used in industrial applications and chemical synthesis.
The specific form of iron chloride depends on the oxidation state of iron and the molecular interactions that occur during its formation.
In our exercise, the analysis leads to an empirical formula of \( \text{FeCl}_2 \), commonly known as ferrous chloride. This form contains iron in the +2 oxidation state, and is essential in understanding the stoichiometry of the reaction as each compound's stability and reactivity vary with its form.