How Many Molecules Are There in 24 Grams of FeF₃?
Understanding the number of molecules in a given mass of a compound is a fundamental concept in chemistry, essential for solving stoichiometric problems and grasping the microscopic world of matter. Consider this: when dealing with a compound like iron(III) fluoride (FeF₃), determining the number of molecules requires a systematic approach involving molar mass calculations and Avogadro's number. This article will guide you through the process step-by-step, explain the underlying scientific principles, and highlight practical applications of such calculations in real-world scenarios.
Introduction to Moles and Molecules
Before diving into the calculation, don't forget to understand two key concepts: moles and Avogadro's number. A mole is a unit that represents a specific quantity of particles, such as atoms, molecules, or ions. Because of that, one mole of any substance contains approximately 6. 022 × 10²³ particles, a value known as Avogadro's number. This constant bridges the gap between the macroscopic scale (grams) and the microscopic scale (molecules), enabling chemists to work with manageable numbers in laboratory settings.
Step 1: Calculating the Molar Mass of FeF₃
To determine the number of molecules in 24 grams of FeF₃, we first need to calculate its molar mass. The molar mass is the sum of the atomic masses of all the atoms in a molecule, expressed in grams per mole (g/mol). Here's how to compute it:
- Iron (Fe): The atomic mass of iron is approximately 55.85 g/mol.
- Fluorine (F): Each fluorine atom has an atomic mass of 19.00 g/mol, and there are three fluorine atoms in FeF₃.
Adding these values together: [ \text{Molar mass of FeF₃} = 55.00) = 55.In practice, 85 + 57. Here's the thing — 85 + (3 \times 19. 00 = 112.
Step 2: Converting Grams to Moles
Once the molar mass is known, we can convert the given mass (24 grams) into moles using the formula: [ \text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}} ] Substituting the values: [ \text{Moles of FeF₃} = \frac{24}{112.85} \approx 0.2127 , \text{mol} ]
This means 24 grams of FeF₃ correspond to approximately 0.2127 moles of the compound.
Step 3: Using Avogadro's Number to Find Molecules
With the number of moles calculated, we can now determine the number of molecules by multiplying by Avogadro's number: [ \text{Number of molecules} = \text{Moles} \times \text{Avogadro's number} ] [ \text{Number of molecules} = 0.212
