Question

How many formula units are present in 500.0 g of lead(II) chloride?

Short answer

There are approximately \(1.08 \times 10^{24}\) formula units of lead(II) chloride in 500.0 g of the compound.

Step-by-step solution

Determine the molar mass of lead(II) chloride (PbCl₂)

Look up the atomic masses of lead (Pb) and chlorine (Cl) on the periodic table. The atomic mass of Pb is approximately 207.2 g/mol and that of Cl is approximately 35.45 g/mol. Calculate the molar mass of PbCl₂ by adding the atomic masses of its component elements: Molar mass of PbCl₂ = (mass of Pb) + 2 × (mass of Cl) = 207.2 g/mol + 2 × 35.45 g/mol = 207.2 g/mol + 70.90 g/mol = 278.1 g/mol

Convert the mass of lead(II) chloride to moles using the molar mass

Use the mass of PbCl₂ (500.0 g) and the molar mass calculated in step 1 to convert grams to moles: moles of PbCl₂ = (mass of PbCl₂) / (molar mass of PbCl₂) = 500.0 g / 278.1 g/mol = 1.798 moles

Calculate the number of formula units using Avogadro's number

Now that we have the number of moles of PbCl₂, we can determine the number of formula units by multiplying the number of moles by Avogadro's number: number of formula units = (moles of PbCl₂) × (Avogadro's number) = 1.798 moles × 6.022 × 10²³ formula units/mole = \(1.08 \times 10^{24}\) formula units There are approximately \(1.08 \times 10^{24}\) formula units of lead(II) chloride in 500.0 g of the compound.

Key concepts

Understanding Molar Mass

Molar mass is a fundamental concept in chemistry which allows us to connect the mass of a substance to the number of molecules or atoms it contains. It is essentially the mass of one mole of a substance, usually measured in grams per mole (g/mol).
To find the molar mass, you need to add up the atomic masses of all the atoms in a molecule, using the periodic table.
For example, in the case of lead(II) chloride (PbCl₂), you'd locate the atomic masses of lead (Pb) and chlorine (Cl). Lead has an atomic mass of approximately 207.2 g/mol, while chlorine's is about 35.45 g/mol. Since PbCl₂ consists of one lead atom and two chlorine atoms, you'd calculate its molar mass like this:

• Molar mass of PbCl₂ = Atomic mass of Pb + 2 × Atomic mass of Cl
• = 207.2 g/mol + 2 × 35.45 g/mol
• = 207.2 g/mol + 70.90 g/mol = 278.1 g/mol

This confirms that one mole of lead(II) chloride weighs 278.1 grams. Understanding molar mass is crucial as it serves as the bridge between the mass we measure and the number of particles involved.

Avogadro's Number Explained

Avogadro's number is a cornerstone of chemistry, providing a link between the macroscopic and microscopic worlds. It is defined as the number of particles, usually atoms or molecules, in one mole of a substance. This number is very large: approximately 6.022 × 10²³.
Why is it so important? Well, by knowing Avogadro's number, chemists can translate what they see in the lab (grams and liters) to actual numbers of molecules or atoms (the microscopic scale).
In practice, this means that if you know the number of moles of a substance, you can easily calculate how many formula units (or molecules) you have, simply by multiplying the number of moles by Avogadro's number:

• Number of formula units = Moles × Avogadro's number

In our example with lead(II) chloride, we calculated 1.798 moles of PbCl₂. By multiplying this by Avogadro's number, we get approximately 1.08 × 10²⁴ formula units.
This powerful understanding allows us to perform mass-to-particle and particle-to-mass calculations effortlessly.

Chemical Formula Calculation Mastery

Calculating quantities based on chemical formulas involves a systematic approach that maximizes the utility of the mole concept.
The first step is always to find the molar mass, which helps convert between grams and moles, the central bridge of chemical calculations.
For lead(II) chloride in our exercise:

• The molar mass was found to be 278.1 g/mol.
• Next, use the given mass (500.0 g) to find the number of moles: Moles = Mass / Molar Mass = 500.0 g / 278.1 g/mol ≈ 1.798 moles.

After finding the moles, Avogadro's number is used to switch from moles to formula units.
This step-by-step method ensures accuracy as it transitions from the known (mass) to the desired (formula units).
By mastering these calculations, you can solve a variety of chemistry problems, enhancing both your understanding and your ability to apply chemical concepts in practical scenarios.