Problem 37 - Chemistry for Allied Health

Question

How many atoms of carbon are in \(0.75\) moles of \(\mathrm{CCl}_{4}\) ? How many atoms of chlorine?

Step-by-Step Solution

Answer

Carbon: 4.517 x 10^23 atoms, Chlorine: 1.807 x 10^24 atoms.

Step 1: Understanding Moles

One mole of any substance contains Avogadro's number of particles, which is approximately 6.022 x 10^23 particles per mole. This number represents the number of atoms or molecules in one mole.

Step 2: Identifying Components in the Compound

The compound \( ext{CCl}_4\) contains one carbon atom and four chlorine atoms per molecule. Therefore, we need to calculate the number of atoms for both elements separately.

Step 3: Calculating Carbon Atoms

Since there is one carbon atom per \( ext{CCl}_4\) molecule, the number of carbon atoms in 0.75 moles of \( ext{CCl}_4\) is simply 0.75 times Avogadro's number:\[ 0.75 imes 6.022 imes 10^{23} = 4.517 imes 10^{23} \] carbon atoms.

Step 4: Calculating Chlorine Atoms

Each \( ext{CCl}_4\) molecule contains four chlorine atoms. Therefore, for 0.75 moles, we calculate:\[ 0.75 imes 4 imes 6.022 imes 10^{23} = 1.807 imes 10^{24} \] chlorine atoms.

Key Concepts

Avogadro's number

Avogadro's number is a fundamental constant in chemistry that helps us understand the quantity of particles, such as atoms or molecules, present in a substance. Its value is approximately \( 6.022 \times 10^{23} \), meaning that one mole of any substance contains this specific number of particles.
Avogadro's number provides a bridge between the macroscopic and microscopic worlds, allowing chemists to count atoms and molecules by weighing them, which is much more practical. If you're trying to imagine just how large Avogadro's number is, think of it as the number of stars in a couple of hundred galaxies combined!

• It's essential for converting moles to particles (atoms, molecules, ions) and vice versa.
• Ensures consistency across scientific disciplines by standardizing the amount of substance.

Understanding Avogadro's number is crucial because it underpins a multitude of calculations in chemistry, enabling us to determine how much of a substance is involved in a reaction.

carbon atoms calculation

When calculating the number of carbon atoms in a chemical substance like \(\mathrm{CCl}_4\) (carbon tetrachloride), it's important to identify how many carbon atoms are present per molecule. In the molecule \(\mathrm{CCl}_4\), there is exactly one carbon atom per molecule.
To find out the total number of carbon atoms in a specific amount of \(\mathrm{CCl}_4\), you multiply the number of moles by Avogadro's number:
For example, with \(0.75\) moles of \(\mathrm{CCl}_4\):

• Calculate the number of carbon atoms as follows: \[0.75 \times 6.022 \times 10^{23} = 4.517 \times 10^{23}\]

This calculation means there are \(4.517 \times 10^{23}\) carbon atoms in \(0.75\) moles of \(\mathrm{CCl}_4\).
Knowing how to calculate the number of atoms is essential because it allows chemists to understand and predict the outcomes of chemical reactions and processes.

chlorine atoms calculation

Calculating the number of chlorine atoms in \(\mathrm{CCl}_4\) involves a similar process to that of carbon, but with an additional step due to its structure.
Each molecule of \(\mathrm{CCl}_4\) contains four chlorine atoms. So, you need to account for this when calculating the total number of chlorine atoms in a given amount of \(\mathrm{CCl}_4\).
For \(0.75\) moles of \(\mathrm{CCl}_4\):

• Calculate the number of chlorine atoms as follows: \[0.75 \times 4 \times 6.022 \times 10^{23} = 1.807 \times 10^{24}\]

This result shows there are \(1.807 \times 10^{24}\) chlorine atoms in \(0.75\) moles of \(\mathrm{CCl}_4\).
Understanding how to calculate the number of a particular type of atom in a substance is valuable, as it helps in preparing chemical equations and understanding reaction mechanics accurately.