A volume of 18.72 mL of 0.1500 M K2Cr2O7 solution was required to titrate a sample of FeSO4 according to the equation in Problem 4.126. What is the mass of the sample?

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1. Identify the balanced chemical equation for the reaction between \( \text{K}_2\text{Cr}_2\text{O}_7 \) and \( \text{FeSO}_4 \). Typically, the reaction is: \[ \text{Cr}_2\text{O}_7^{2-} + 6\text{Fe}^{2+} + 14\text{H}^+ \rightarrow 2\text{Cr}^{3+} + 6\text{Fe}^{3+} + 7\text{H}_2\text{O} \]
2. Calculate the moles of \( \text{K}_2\text{Cr}_2\text{O}_7 \) used in the titration using the formula: \[ \text{moles} = \text{concentration} \times \text{volume} \]. Convert the volume from mL to L before using it in the calculation.
3. Use the stoichiometry of the balanced equation to find the moles of \( \text{FeSO}_4 \). According to the equation, 1 mole of \( \text{Cr}_2\text{O}_7^{2-} \) reacts with 6 moles of \( \text{Fe}^{2+} \).
4. Calculate the mass of \( \text{FeSO}_4 \) using the moles obtained and the molar mass of \( \text{FeSO}_4 \). The formula is: \[ \text{mass} = \text{moles} \times \text{molar mass} \].
5. Ensure all units are consistent and check calculations for accuracy.

Key Concepts

Titration

Titration is a quantitative analytical technique used to determine the concentration of a solute in a solution. It involves the gradual addition of a titrant of known concentration to a solution of the analyte until the reaction reaches its endpoint, which is often indicated by a color change. Understanding the stoichiometry of the reaction is crucial for calculating the amount of the analyte present.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows chemists to determine the relationships between the quantities of substances involved in a reaction. In this context, knowing the mole ratio between K2Cr2O7 and FeSO4 is essential for converting the volume and molarity of the titrant into moles of FeSO4, which can then be used to find the mass of the sample.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (M). In this problem, the molarity of the K2Cr2O7 solution is used to calculate the number of moles of the titrant that reacted with the FeSO4 sample, which is a critical step in determining the mass of the sample based on the stoichiometric relationships.