Understanding Atoms in One Mole of CH₃OH

This question asks about the total number of atoms present in one mole of methanol, which has the chemical formula CH₃OH.

What is a Mole?

In chemistry, a mole is a unit of amount of substance. It is defined as containing exactly $6.02214076 \times 10^{23}$ elementary entities (such as atoms, molecules, ions, or electrons). This number is known as Avogadro's number ($N_A$). For simplicity, we often use the rounded value $6.022 \times 10^{23}$.

Analyzing the CH₃OH Molecule

To find the total number of atoms in one mole of CH₃OH, we first need to determine how many atoms are in a single molecule of CH₃OH.

The chemical formula CH₃OH tells us the types and numbers of atoms in one molecule:

• Carbon (C): 1 atom
• Hydrogen (H) in CH₃ group: 3 atoms
• Oxygen (O): 1 atom
• Hydrogen (H) in OH group: 1 atom

Adding these up, the total number of atoms in one molecule of CH₃OH is:

Total atoms per molecule = 1 (C) + 3 (H) + 1 (O) + 1 (H) = 6 atoms.

Calculating Total Atoms in One Mole

One mole of CH₃OH contains Avogadro's number of CH₃OH molecules. Since each molecule contains 6 atoms, the total number of atoms in one mole of CH₃OH is the number of molecules multiplied by the number of atoms per molecule.

Total atoms in one mole = (Number of molecules in one mole) $\times$ (Number of atoms per molecule)

Total atoms in one mole = $N_A \times 6$

Using the approximate value for Avogadro's number ($6.022 \times 10^{23}$):

Total atoms in one mole $\approx 6.022 \times 10^{23} \times 6$

Total atoms in one mole $\approx 36.132 \times 10^{23}$

To express this in standard scientific notation, we move the decimal one place to the left and increase the exponent by one:

Total atoms in one mole $\approx 3.6132 \times 10^{24}$

When rounded to two significant figures, this value is $3.6 \times 10^{24}$.

Let's look at the given options:

• $6.0 \times 10^{23}$ (This is approximately the number of molecules, not atoms)
• $3.6 \times 10^{24}$ (This matches our calculation)
• $3.0 \times 10^{25}$ (This is too high)
• $3$ (This is just the number of carbon atoms or a very small number)

Therefore, the number of atoms in one mole of CH₃OH is approximately $3.6 \times 10^{24}$.

Revision Table: Key Concepts in Mole Calculations

Additional Information on Mole Calculations and Atoms

Calculations involving moles and atoms are fundamental in chemistry. Here are some related points:

• Molar Mass: The molar mass of CH₃OH can be calculated by summing the atomic masses of its constituent atoms (C: 12.01 g/mol, H: 1.01 g/mol, O: 16.00 g/mol). Molar mass of CH₃OH = 1(12.01) + 4(1.01) + 1(16.00) = 12.01 + 4.04 + 16.00 = 32.05 g/mol. This means one mole of CH₃OH weighs about 32.05 grams.
• Converting Mass to Moles: If you have a certain mass of a substance, you can convert it to moles by dividing the mass by the molar mass.
• Converting Moles to Entities: You can convert moles to the number of molecules (or atoms, ions, etc.) by multiplying the number of moles by Avogadro's number.
• Converting Entities to Atoms: If you know the number of molecules and the number of atoms per molecule, you can find the total number of atoms, as demonstrated in this problem.

Understanding the relationship between mass, moles, and the number of particles (atoms, molecules) is crucial for solving many chemistry problems, especially in stoichiometry.