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If the \(\mathrm{Cl}^{-}\) ion concentration in a solution is \(2.61 \mathrm{M}\), what is the concentration of \(\mathrm{FeCl}_{3}\) ?

Short Answer

Expert verified
The concentration of FeCl鈧 is approximately 0.87 M.

Step by step solution

01

Understand the Dissociation of FeCl3

FeCl鈧 dissociates in water to form 1 Fe鲁鈦 ion and 3 Cl鈦 ions. The chemical equation for this dissociation is: \[ \mathrm{FeCl}_3 \rightarrow \mathrm{Fe}^{3+} + 3\mathrm{Cl}^{-} \] This means for every mole of FeCl鈧 dissolved, 3 moles of Cl鈦 ions are produced.
02

Utilize the Given Cl- Ion Concentration

We are provided with the concentration of Cl鈦 ions as 2.61 M. Knowing from the dissolution equation, the number of moles of Cl鈦 ions is three times the number of moles of FeCl鈧.
03

Calculate the Concentration of FeCl3

Since 3 moles of Cl鈦 ions are produced from every mole of FeCl鈧, we find the concentration of FeCl鈧 by dividing the concentration of Cl鈦 ions by 3:\[ \text{Concentration of } \mathrm{FeCl}_3 = \frac{2.61 \, \mathrm{M}}{3} \approx 0.87 \, \mathrm{M} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Dissociation of Compounds
Dissociation is an important chemical process where a compound breaks down into simpler constituents (usually ions) when dissolved in a solution like water. Let's consider how this works by using iron(III) chloride, FeCl鈧, as an example. In water, FeCl鈧 dissociates into one ferric ion (Fe鲁鈦) and three chloride ions (Cl鈦). This can be represented by the chemical equation: \[ \mathrm{FeCl}_3 \rightarrow \mathrm{Fe}^{3+} + 3\mathrm{Cl}^-\] Such dissociation is governed by inter-ionic forces that are greater in solids but weaken when the compound is placed in a polar solvent like water. The number of ions produced from each formula unit is crucial in determining the solution's ionic concentration and helps explain the direct link between the amount of FeCl鈧 dissolved and the resulting concentration of Cl鈦 ions.
Molar Concentration
The concept of molar concentration is essential when discussing solutions and their compositions. It represents the number of moles of a solute present in one liter of solution. In our exercise, the solution contains Cl鈦 ions, which are given at 2.61 M (mol/L). Molarity tells us precisely how concentrated a particular ion or molecule is within the solution, thereby allowing us to predict the outcomes of reactions or other concentration-dependent processes. To clarify:
  • A 1 M solution contains exactly one mole of solute per liter of solution.
  • Molar concentration is represented as \( \text{M} = \frac{\text{moles of solute}}{\text{liters of solution}} \).
This concept is useful in stoichiometry to understand how substances will react or dissociate in a given volume of solvent, tying it directly to both the dissolution process and reaction calculations.
Stoichiometry
Stoichiometry is like a bridge between the theoretical chemistry and practical calculations involving chemical reactions and equations. It helps in determining how much of reactants are needed to form specific amounts of products, or vice versa. Stoichiometry is based on balanced chemical equations, which maintain mass and charge conservation. For our exercise, stoichiometry was indispensable to determine the concentration of FeCl鈧. Given the dissociation equation, 1 mole of FeCl鈧 results in 3 moles of Cl鈦 ions. By knowing the concentration of Cl鈦, we can backtrack using stoichiometry to find the concentration of FeCl鈧: \[ \text{Concentration of } \mathrm{FeCl}_3 = \frac{2.61 \, \text{M of } \mathrm{Cl}^-}{3} \approx 0.87 \, \text{M} \] This calculation shows stoichiometry's power in solving real-life chemistry problems and underlines its importance as a tool in interpreting compound interactions and reactions.

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