Question

Calculate each of the following: a. number of \(\mathrm{C}\) atoms in \(0.500\) mole of \(\mathrm{C}\) b. number of \(\mathrm{SO}_{2}\) molecules in \(1.28\) moles of \(\mathrm{SO}_{2}\) c. moles of \(\mathrm{Fe}\) in \(5.22 \times 10^{22}\) atoms of \(\mathrm{Fe}\) d. moles of \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\) in \(8.50 \times 10^{24}\) molecules of \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\)

Short answer

a. \mathrm{C} atoms: 3.011 \times 10^{23} atoms, b. \mathrm{SO}_{2} molecules: 7.70 \times 10^{23}, c. \mathrm{Fe} moles: 0.0867, d. \mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O} moles: 14.1

Step-by-step solution

Number of \mathrm{C} atoms in 0.500 mole of \mathrm{C}

To find the number of atoms, use Avogadro's number, which is \(6.022 \times 10^{23}////\) atoms/mole. Multiply the number of moles by Avogadro's number: \[\text{Number of } \mathrm{C} \text{ atoms} = 0.500 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} \]

Calculate the number of \mathrm{C} atoms

Perform the calculation: \[\text{Number of } \mathrm{C} \text{ atoms} = 3.011 \times 10^{23} \text{ atoms} \]

Number of \mathrm{SO}_{2} molecules in 1.28 moles of \mathrm{SO}_{2}

Multiply the number of moles by Avogadro's number: \[\text{Number of } \mathrm{SO}_{2} \text{ molecules} = 1.28 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \]

Calculate the number of \mathrm{SO}_{2} molecules

Perform the calculation: \[\text{Number of } \mathrm{SO}_{2} \text{ molecules} = 7.70 \times 10^{23} \text{ molecules} \]

Moles of \mathrm{Fe} in 5.22 \times 10^{22} atoms of \mathrm{Fe}

To find the number of moles, use Avogadro's number. Divide the number of atoms by Avogadro's number: \[\text{Moles of } \mathrm{Fe} = \frac{5.22 \times 10^{22} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mole}} \]

Calculate the moles of \mathrm{Fe}

Perform the calculation: \[\text{Moles of } \mathrm{Fe} = 0.0867 \text{ moles} \]

Moles of \mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O} in 8.50 \times 10^{24} molecules of \mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}

To find the number of moles, use Avogadro's number. Divide the number of molecules by Avogadro's number: \[\text{Moles of } \mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O} = \frac{8.50 \times 10^{24} \text{ molecules}}{6.022 \times 10^{23} \text{ molecules/mole}} \]

Calculate the moles of \mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}

Perform the calculation: \[\text{Moles of } \mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O} = 14.1 \text{ moles} \]

Key concepts

Avogadro's number

Avogadro's number is a fundamental constant in chemistry. It represents the number of atoms, ions, or molecules in one mole of a substance.
Avogadro's number is written as \( 6.022 \times 10^{23} \). This huge number helps chemists understand and calculate the number of particles in macroscopic samples.
Using Avogadro's number allows chemists to bridge the gap between the atomic scale and the scale of everyday measurements. For instance, one mole of carbon contains \( 6.022 \times 10^{23} \) carbon atoms.

Moles to atoms/molecules conversion

Converting moles to atoms or molecules is straightforward when you use Avogadro's number.
If you have the number of moles, you can find the number of particles by multiplying the moles by \( 6.022 \times 10^{23} \).
For example, to find the number of \( \text{SO}_2 \) molecules in 1.28 moles, you simply multiply:
\[ 1.28 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} = 7.70 \times 10^{23} \text{ molecules} \].
This way, you can easily determine the number of atoms or molecules from a given amount of substance.

Stoichiometry

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. This concept is crucial for predicting how much of each substance is consumed or produced.
Using stoichiometry, you can determine the amount of product formed from a given amount of reactant, or vice versa.
Key to stoichiometry is the balanced chemical equation, where the coefficients indicate the relative numbers of moles of each substance involved in the reaction.
For example, in the reaction \( 2H_2 + O_2 → 2H_2O \), two moles of hydrogen react with one mole of oxygen to produce two moles of water.

Chemical Quantities

Understanding chemical quantities is essential for handling substances in various chemical reactions.
Using Avogadro's number, you can convert between moles and the number of particles. You can also determine the mass of a certain number of moles using the molar mass.
Let's consider the calculation of moles of \( \text{Fe} \) in \( 5.22 \times 10^{22} \) atoms of \( \text{Fe} \).
Divide the number of atoms by Avogadro's number: \[ \text{Moles of } \text{Fe} = \frac{5.22 \times 10^{22} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mole}} = 0.0867 \text{ moles} \].
This ensures accurate and meaningful quantification in chemical calculations.