Question

How many milliliters of \(0.250 \mathrm{M} \mathrm{KMnO}_{4}\) are needed to react with \(3.55 \mathrm{~g}\) of iron(II) sulfate, \(\mathrm{FeSO}_{4}\) ? The reaction is as follows: $$ \begin{array}{r} 10 \mathrm{FeSO}_{4}(a q)+2 \mathrm{KMnO}_{4}(a q)+8 \mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \\ 5 \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}(a q)+2 \mathrm{MnSO}_{4}(a q)+\mathrm{K}_{2} \mathrm{SO}_{4}(a q)+ \\ 8 \mathrm{H}_{2} \mathrm{O}(l) \end{array} $$

Short answer

18.72 mL of 0.250 M KMnO₄ are needed.

Step-by-step solution

Calculate the Molar Mass of FeSO₄

To determine the number of moles of \ \ \( \text{FeSO}_4 \), calculate its molar mass. \ \ The molar mass of \ \( \text{FeSO}_4 \) is calculated by summing the atomic masses: \ \ \( \text{Fe} = 55.85 \, \text{g/mol} \), \ \( \text{S} = 32.07 \, \text{g/mol} \), \ \( \text{O}_4 = 4 \times 16.00 \, \text{g/mol} = 64.00 \, \text{g/mol} \). \ \ Therefore, the molar mass of \ \( \text{FeSO}_4 = 55.85 + 32.07 + 64.00 = 151.92 \, \text{g/mol} \).

Determine the Moles of FeSO₄

Calculate the moles of \ \( \text{FeSO}_4 \) using its mass and molar mass. \ \ \[ \text{Moles of \( \text{FeSO}_4 \)} = \frac{3.55 \, \text{g}}{151.92 \, \text{g/mol}} \approx 0.0234 \, \text{mol} \]

Use Stoichiometry of the Reaction

From the balanced equation, \ \(10 \text{FeSO}_4 \) reacts with \ \(2 \text{KMnO}_4 \). \ \ Thus, the moles of \( \text{KMnO}_4 \) needed to react with \ \(0.0234 \text{ mol} \) of \( \text{FeSO}_4 \) is calculated by: \ \ \[ 0.0234 \, \text{mol FeSO}_4 \times \frac{2 \, \text{mol KMnO}_4}{10 \, \text{mol FeSO}_4} = 0.00468 \, \text{mol KMnO}_4 \]

Convert Moles of KMnO₄ to Volume

Use the molarity of the KMnO₄ solution to find the required volume. \ \ Since \ \(0.250 \text{ M} \) is given as \ \( \text{moles/L} \), \ \ \[ \text{Volume of KMnO}_4 = \frac{0.00468 \, \text{mol}}{0.250 \, \text{mol/L}} = 0.01872 \, \text{L} = 18.72 \, \text{mL} \]

Conclusion

The volume of \(0.250 \, \text{M} \) \( \text{KMnO}_4 \) solution required is \(18.72 \text{ mL} \).

Key concepts

Molarity

Molarity is an essential concept in chemistry that helps us understand the concentration of a solution. It is defined as the number of moles of solute per liter of solution. To find the molarity, you use the formula:

• Molarity (M) = moles of solute / liters of solution

In the given problem, we're dealing with a solution of potassium permanganate (\( \mathrm{KMnO}_4 \)) that has a molarity of \( 0.250 \, \mathrm{M} \). This tells us that in one liter of this solution, there are \( 0.250 \) moles of \( \mathrm{KMnO}_4 \) present. This information is crucial for calculating the volume of solution needed to react with a specific amount of iron(II) sulfate in the exercise.

Moles

Understanding moles is key to mastering stoichiometry. A mole is a unit that measures an amount of substance. One mole contains exactly \( 6.022 \times 10^{23} \) entities (Avogadro's number) be it atoms, molecules, or ions. In context, moles allow us to use masses measured in grams to count molecules.In this exercise, you first calculate the moles of iron(II) sulfate (\( \mathrm{FeSO}_4 \)) using its mass and molar mass. The result is:

• Moles of \( \mathrm{FeSO}_4 \) = \( \frac{3.55 \, \mathrm{g}}{151.92 \, \mathrm{g/mol}} \approx 0.0234 \, \mathrm{mol} \)

This calculation tells you exactly how many moles of \( \mathrm{FeSO}_4 \) you are working with, which sets the stage for the subsequent stoichiometric calculations.

Balanced Chemical Equation

A balanced chemical equation is a representation of a chemical reaction that has the same number of each type of atom on both sides of the equation. This ensures the law of conservation of mass is followed.For the given reaction, you'll see:

• \( 10 \mathrm{FeSO}_4 (aq) + 2 \mathrm{KMnO}_4 (aq) + 8 \mathrm{H}_2 \mathrm{SO}_4 (aq) \rightarrow 5 \mathrm{Fe}_2 \left( \mathrm{SO}_4 \right)_3 (aq) + 2 \mathrm{MnSO}_4 (aq) + \mathrm{K}_2 \mathrm{SO}_4 (aq) + 8 \mathrm{H}_2 \mathrm{O} (l) \)

The balanced equation allows you to determine the relationship between the reactants and the products. In this scenario, it indicates that 10 moles of \( \mathrm{FeSO}_4 \) will react with 2 moles of \( \mathrm{KMnO}_4 \). Understanding this ratio is crucial for calculating the moles of \( \mathrm{KMnO}_4 \) needed based on the available \( \mathrm{FeSO}_4 \).

Molar Mass

Molar mass is the mass of one mole of a given substance. It is expressed in grams per mole (g/mol). Calculating molar mass involves adding the atomic masses of all the atoms in a molecule.For iron(II) sulfate, \( \mathrm{FeSO}_4 \), the calculation is as follows:

• Iron (\( \mathrm{Fe} \)): \( 55.85 \, \mathrm{g/mol} \)
• Sulfur (\( \mathrm{S} \)): \( 32.07 \, \mathrm{g/mol} \)
• Oxygen (\( \mathrm{O}_4 \)): \( 4 \times 16.00 \, \mathrm{g/mol} = 64.00 \, \mathrm{g/mol} \)

Adding these gives the molar mass of \( \mathrm{FeSO}_4 \) as \( 151.92 \, \mathrm{g/mol} \). This value is integral for converting the given mass of \( \mathrm{FeSO}_4 \) (3.55 g in this exercise) into moles, thereby enabling the stoichiometric calculations to proceed.