Problem 143 - Chemistry Matter and Change

Question

What mass of iron(III) chloride contains \(2.35 \times 10^{23}\) chloride ions?

Step-by-Step Solution

Answer

The mass of iron(III) chloride needed is approximately 21.1 grams.

Step 1: Determine Moles of Chloride Ions

We start by using Avogadro's number which is \[6.022 \times 10^{23}\] ions/mol. Divide the given number of chloride ions by Avogadro's number to find the moles of chloride ions:\[\text{moles of chloride ions} = \frac{2.35 \times 10^{23}}{6.022 \times 10^{23}} \approx 0.39 \text{ moles}.\]

Step 2: Calculate Moles of Iron(III) Chloride

Iron(III) chloride, \(\text{FeCl}_3\), contains 3 chloride ions per formula unit. To find the moles of \(\text{FeCl}_3\), divide the moles of chloride ions by 3:\[\text{moles of FeCl}_3 = \frac{0.39}{3} \approx 0.13 \text{ moles}.\]

Step 3: Calculate Mass of Iron(III) Chloride

Next, we need the molar mass of \(\text{FeCl}_3\). The atomic masses are: Fe = 55.85 u and Cl = 35.45 u. Thus:\[\text{Molar mass of FeCl}_3 = 55.85 + 3 \times 35.45 = 162.2 \text{ g/mol}.\]Now, multiply the moles of \(\text{FeCl}_3\) by its molar mass to find the mass in grams:\[\text{mass of FeCl}_3 = 0.13 \times 162.2 \approx 21.1 \text{ grams}.\]

Key Concepts

The Mole Concept

The mole is a fundamental concept in chemistry that represents a specific number of entities, whether these are atoms, molecules, or ions. Think of it as a way of counting by weighing. Just like a dozen represents 12 items, a mole represents a much larger number: Avogadro's number. One mole of any substance contains exactly the same number of entities, which is hugely beneficial for solving problems in chemistry where we often deal with incredibly small particles like ions and atoms. By using the mole concept, chemists can convert between the mass of a substance and the number of atoms or molecules it contains. In our exercise, when we know the number of chloride ions, the mole concept allows us to find out how many moles those ions translate into.

Avogadro's Number

Avogadro's number is a key part of the stoichiometric landscape. It is defined as exactly 6.022 × 10^{23} entities per mole. This large number is used because atoms and molecules are extremely small, and we often deal with them in vast quantities. Avogadro’s number allows chemists to translate between microscopic-scale amounts into macroscopic-scale quantities that we can measure and understand, such as moles. In the problem at hand, Avogadro's number helps us convert a large number of chloride ions ( 2.35 × 10^{23} ) into a more manageable quantity of moles. This makes subsequent calculations much more straightforward.

Molar Mass

Molar mass is the bridge between moles and grams. It is defined as the mass of one mole of a given substance—measured in grams per mole (g/mol). Every element's atomic mass, which you can find on the periodic table, contributes to the molar mass of a compound. For example, FeCl_3 is composed of iron (Fe) and chlorine (Cl). The molar mass of FeCl_3 is calculated by adding the atomic masses of one iron atom and three chlorine atoms, resulting in 162.2 g/mol. Once we know how many moles of FeCl_3 we have from the earlier steps, we can easily convert this to a mass using its molar mass.

Chemical Calculations

Chemical calculations often involve conversions between different units. Here, we seamlessly moved from ions to moles, then from moles to mass. This is a typical sequence in stoichiometry, often requiring steps involving Avogadro’s number and molar mass. Here's a simplified breakdown of the calculation process used in our exercise:

• Determine moles from the number of entities using Avogadro's number.
• Account for the composition of the compound—in our case, three chloride ions per FeCl_3 unit.
• Use the molar mass to convert from moles to grams.

Being adept with these conversions is crucial for any chemistry student. Understanding the relationships between moles, Avogadro’s number, and molar mass allows for solving diverse problems effectively.