Question

Suppose \(1.01 \mathrm{g}\) of \(\mathrm{FeCl}_{3}\) is placed in a 10.0 -mL volumetric flask, water is added, the mixture is shaken to dissolve the solid, and then water is added to the calibration mark of the flask. Calculate the molarity of each ion present in the solution.

Short answer

The molarities of the ions in the \(FeCl_{3}\) solution are 0.624 M for \(Fe^{3+}\) and 1.872 M for \(Cl^{-}\).

Step-by-step solution

Calculate the number of moles of FeCl3

To find the moles of FeCl3 in 1.01g, we need the molar mass of FeCl3. The molar mass of Fe is 55.85g/mol, Cl is 35.45g/mol, so the molar mass of FeCl3 is: \(Molar\ mass\ of\ FeCl_{3} = Fe + 3Cl = 55.85 + 3(35.45) = 161.70\ g/mol\) Next, we'll use the mass given and the molar mass to find the number of moles of FeCl3. \(Moles\ of\ FeCl_{3} = \frac{mass}{molar\ mass} = \frac{1.01 g}{161.70 g/mol} = 0.00624\ mol\)

Determine the number of moles of each ion in the solution

When FeCl3 dissolves in water, it dissociates into Fe3+ and Cl- ions. The balanced dissociation equation is: \(FeCl_{3}(aq) \rightarrow Fe^{3+}(aq) + 3Cl^{-}(aq)\) From the balanced equation, we can see that each mole of FeCl3 dissociates into 1 mole of Fe3+ and 3 moles of Cl-. Therefore, we have: Moles of \(Fe^{3+} = 1 \times 0.00624\ mol = 0.00624\ mol\) Moles of \(Cl^{-} = 3 \times 0.00624\ mol = 0.01872\ mol\)

Calculate the molarity of each ion

Now that we have the number of moles of each ion, we can find their molarity by dividing by the volume of the solution in liters. The volume of the solution is given as 10.0 mL, which is equal to 0.010 L. Molarity of \(Fe^{3+} = \frac{0.00624\ mol}{0.010\ L} = 0.624\ M\) Molarity of \(Cl^{-} = \frac{0.01872\ mol}{0.010\ L} = 1.872\ M\) Therefore, the molarities of the ions in the solution are 0.624 M for Fe3+ and 1.872 M for Cl-.

Key concepts

Ionic Dissociation

Ionic dissociation is a fundamental concept in chemistry, especially when dealing with ionic compounds in solutions. When an ionic compound like \( ext{FeCl}_3\) is dissolved in water, it separates into its constituent ions. In this case, \( ext{FeCl}_3\) undergoes dissociation to form \( ext{Fe}^{3+}\) and \( ext{Cl}^-\) ions. This process can be represented by a balanced chemical equation: \( \text{FeCl}_3(aq) \rightarrow \text{Fe}^{3+}(aq) + 3\text{Cl}^-(aq) \). Understanding ionic dissociation is crucial for predicting the behavior of solutions, as dissociation determines the concentration and properties of ions in a solution. Moreover, knowing the dissociation equation helps in calculating the concentration of each ion present once the compound has dissolved. In this exercise, we acknowledge that 1 mole of \( ext{FeCl}_3\) produces 1 mole of \( ext{Fe}^{3+}\) and 3 moles of \( ext{Cl}^-\). This stoichiometric ratio is essential for further molarity calculations.

Moles Calculation

Moles calculation is a critical step in chemistry that allows us to determine the amount of a substance present in a sample. For the compound \( ext{FeCl}_3\), the number of moles can be calculated by using the mass of the sample and its molar mass. To calculate moles, use the formula: \[ \text{Moles} = \frac{\text{mass}}{\text{molar mass}} \] In our example, we found the molar mass of \( ext{FeCl}_3\) to be 161.70 \(\text{g/mol}\). Using this, we can determine the moles of \( ext{FeCl}_3\) in a sample weighing 1.01g: \[ \text{Moles of FeCl}_3 = \frac{1.01\, \text{g}}{161.70\, \text{g/mol}} = 0.00624\, \text{mol} \] This result is helpful because it gives us a clear amount of the compound present, which is necessary for finding out the number of ions formed upon dissociation.

Volumetric Analysis

Volumetric analysis is a technique that involves measuring the volume of a solution to ascertain the concentration of solutes within. For this problem, the final solution volume is crucial for determining ion molarity. Here, the volume of the solution was noted as 10.0 mL, which is equivalent to 0.010 L. This conversion from milliliters to liters is vital since molarity calculations need the volume in liters.Once you have the moles of each ion, molarity can be calculated as follows: - Molarity \(M\) is calculated by dividing the number of moles of solute by the volume of the solution in liters: \[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \] For the \(\text{Fe}^{3+}\) ion, with 0.00624 moles, the molarity is \[ M = \frac{0.00624\, \text{mol}}{0.010\, \text{L}} = 0.624\, \text{M} \] For the \(\text{Cl}^-\) ion, with 0.01872 moles, the molarity is \[ M = \frac{0.01872\, \text{mol}}{0.010\, \text{L}} = 1.872\, \text{M} \] This step ties together moles and volumetric analysis to yield the final concentrations needed.

Chemical Equations

Chemical equations are a concise way to represent chemical reactions. They reveal important information about the reactants and products involved. In our solution, \(\text{FeCl}_3\) dissociates into ions following the chemical equation: \( \text{FeCl}_3(aq) \rightarrow \text{Fe}^{3+}(aq) + 3\text{Cl}^-(aq) \).Such equations offer insights into the stoichiometry, the quantitative relationship between reactants and products. From this equation, we see each mole of \(\text{FeCl}_3\) yields one mole of \(\text{Fe}^{3+}\) and three moles of \(\text{Cl}^-\) ions.Chemical equations also reflect mass conservation and charge balance, ensuring the total mass and charge are identical on both sides of the equation. In practical calculations, such equations allow us to anticipate and compute the number of ions resulting from a chemical reaction, providing a roadmap for solving exercises like determining ion molarity in solution. By correctly balancing equations, chemists can predict product formation and analyze reaction pathways.