Problem 95 - Chemistry Matter and Change

Question

What mass of iron(III) chloride is needed to prepare 1.00 L of a 0.255\(M\) solution? (Chapter 14)

Step-by-Step Solution

Answer

41.33 grams of iron(III) chloride is needed.

Step 1: Understand the Problem

We need to find the mass of iron(III) chloride (\( \text{FeCl}_3 \)) required to create 1.00 L of a 0.255\(M\) (molarity) solution. Molarity is the number of moles of solute per liter of solution.

Step 2: Calculate Moles of Solute

Using the definition of molarity (\(M\)), \[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]We have:\[ 0.255 = \frac{\text{moles of } \text{FeCl}_3}{1.00} \]Thus, the moles of \( \text{FeCl}_3 \) needed are 0.255 moles.

Step 3: Determine the Molar Mass of Iron(III) Chloride

The chemical formula for iron(III) chloride is \( \text{FeCl}_3 \), which consists of 1 iron (Fe) atom and 3 chlorine (Cl) atoms. The atomic masses are approximately 55.85 g/mol for Fe and 35.45 g/mol for Cl.Calculate the molar mass:\[ 55.85 + 3(35.45) = 55.85 + 106.35 = 162.20 \text{ g/mol} \]

Step 4: Calculate Mass of Iron(III) Chloride

Use the moles calculated in Step 2 and the molar mass from Step 3 to find the mass.\[ \text{Mass} = \text{moles} \times \text{molar mass} \]\[ \text{Mass} = 0.255 \text{ moles} \times 162.20 \text{ g/mol} \]\[ \text{Mass} = 41.331 \text{ grams} \]

Step 5: Final Answer

The mass of iron(III) chloride needed is approximately 41.33 grams.

Key Concepts

Molar Mass

Molar mass is an essential concept in chemistry. It refers to the mass of one mole of a given substance, typically measured in grams per mole (g/mol). Molar mass acts as a bridge between the macroscopic scale that you observe in the laboratory and the atomic scale that explains why things happen. The molar mass of a compound can be calculated using the periodic table, by summing the atomic masses of all atoms in a molecule.

For example, in the compound iron(III) chloride (\(\text{FeCl}_3\)), the molar mass is determined by adding the atomic mass of one iron (Fe) atom and three chlorine (Cl) atoms. With the atomic masses of Fe and Cl being approximately 55.85 g/mol and 35.45 g/mol respectively, the calculation is straightforward:

• \(\text{Molar mass of FeCl}_3 = 55.85 + 3 \times 35.45 = 162.20 \ \text{g/mol}\)

Molar mass helps in converting between the mass of a substance and the amount of substance in terms of moles. It's a fundamental concept for many calculations in chemistry.

Solution Preparation

Preparing a solution means dissolving a solute (solid, liquid, or gas) into a solvent, often water, to create a homogeneous mixture. The concentration of the solution tells you how much solute is present in a given volume of solvent. Molarity (\(M\)) is a common unit of concentration, indicating moles of solute per liter of solution.

To prepare a solution of a certain molarity, you need to calculate the amount of solute needed, which involves a few important steps:

• Choose the desired molarity and volume: Decide on the concentration you wish to achieve and the total volume of solution needed.
• Calculate moles of solute required: Using the molarity formula \(\left(M = \frac{\text{moles of solute}}{\text{liters of solution}}\right)\), you can find out how many moles are needed.
• Convert moles to mass: Use the molar mass of the solute to convert moles into grams, which is often more convenient for measurements.

Understanding these steps ensures that you can accurately prepare solutions for experiments and calculations.

Stoichiometry

Stoichiometry involves the study of the quantitative relationships between the amounts of reactants and products in chemical reactions. It is a crucial concept that helps predict how much product you will get from a certain amount of reactants. This involves using balanced chemical equations to make conversions between moles, mass, and volume.

Here's how stoichiometry can be seen through the lens of solution preparation:

• Convert initial measurements: Start with known quantities such as volume and molarity.
• Use mole ratios and molar mass: Apply the mole concept and molar mass from the periodic table to convert between different units.
• Predict quantities of products or reactants: Determine how much of each substance will react or be produced based on stoichiometric calculations.

A solid grasp of stoichiometry enables you to efficiently solve a wide variety of chemistry-related problems, from simple calculations to more complex reactions.

Iron(III) Chloride

Iron(III) chloride, or ferric chloride (\(\text{FeCl}_3\)), is a chemical compound comprising one iron atom and three chlorine atoms. It’s widely utilized in water treatment, etching, and as a catalyst in some organic reactions. Understanding its properties and uses can help in grasping the real-world applications of chemistry.

Here’s a bit more about iron(III) chloride:

• Physical Properties: It usually appears as a brownish-yellow solid and can be dissolved in water to form an acidic solution.
• Chemical Behavior: When dissolved, it can undergo hydrolysis, releasing hydrogen ions and resulting in a lowering of pH.
• Industrial Uses: Due to its ability to form complexes and react with other compounds, \(\text{FeCl}_3\) is critical in many industrial processes, making it a very functional substance beyond the classroom.

By understanding iron(III) chloride in this broader context, you see how the concepts of molarity, solution preparation, and stoichiometry are applied practically.