Question

Calculate each of the following quantities in \(0.185\) mole of \(\mathrm{C}_{6} \mathrm{H}_{14} \mathrm{O}:\) a. moles of \(\mathrm{C}\) b. moles of \(\mathrm{O}\) c. atoms of \(\mathrm{H}\) d. atoms of \(\mathrm{C}\)

Short answer

a. 1.11 moles of \(\text{C}\) b. 0.185 moles of \(\text{O}\) c. 1.56 x 10^{24} atoms of \(\text{H}\) d. 6.68 x 10^{23} atoms of \(\text{C}\)

Step-by-step solution

Understand the molecular formula

The molecular formula of \(\text{C}_{6}\text{H}_{14}\text{O}\) indicates that each molecule of this compound contains 6 atoms of carbon (\text{C}), 14 atoms of hydrogen (\text{H}), and 1 atom of oxygen (\text{O}).

Calculate moles of carbon (\text{C})

To find the moles of carbon in 0.185 mole of \(\text{C}_{6}\text{H}_{14}\text{O}\), use the ratio of carbon atoms. Since there are 6 moles of carbon in 1 mole of \(\text{C}_{6}\text{H}_{14}\text{O}\), multiply 0.185 by 6. \[ 0.185 \times 6 = 1.11 \text{ moles of C} \]

Calculate moles of oxygen (\text{O})

There is 1 mole of oxygen in each mole of \(\text{C}_{6}\text{H}_{14}\text{O}\). Therefore, the moles of oxygen will be the same as the total moles of the compound. \[ 0.185 \text{ moles of } \text{O} \]

Calculate moles of hydrogen (\text{H})

To find the moles of hydrogen in 0.185 mole of \(\text{C}_{6}\text{H}_{14}\text{O}\), use the ratio of hydrogen atoms. Since there are 14 moles of hydrogen in 1 mole of \(\text{C}_{6}\text{H}_{14}\text{O}\), multiply 0.185 by 14. \[ 0.185 \times 14 = 2.59 \text{ moles of H} \]

Find the number of atoms of hydrogen (H)

Using Avogadro's number \(N_A = 6.022 \times 10^{23} \) atoms/mole, convert moles of hydrogen to atoms. Multiply 2.59 moles of hydrogen by Avogadro's number. \[ 2.59 \times 6.022 \times 10^{23} = 1.56 \times 10^{24} \text{ atoms of H} \]

Find the number of atoms of carbon (C)

Using Avogadro's number, convert moles of carbon to atoms. Multiply 1.11 moles of carbon by Avogadro's number \[ 1.11 \times 6.022 \times 10^{23} = 6.68 \times 10^{23} \text{ atoms of C} \]

Key concepts

Molecular Formula

The molecular formula is a key concept in chemistry. It tells you exactly how many atoms of each element are in a molecule. For example, in the molecular formula \(\text{C}_{6}\text{H}_{14}\text{O}\), there are 6 carbon (\text{C}) atoms, 14 hydrogen (\text{H}) atoms, and 1 oxygen (\text{O}) atom. This information is crucial for understanding the composition of a molecule and for mole calculations.

Moles

The mole is a fundamental unit in chemistry that measures the amount of substance. One mole corresponds to 6.022 x 10^{23} entities (atoms, molecules, etc.). This number is also known as Avogadro's number. In problems involving moles, we often convert between moles and the actual number of atoms or molecules.

For instance, if we have 0.185 moles of \(\text{C}_{6}\text{H}_{14}\text{O}\), we can find the moles of each element by using the ratios provided in the molecular formula.

Avogadro's Number

Avogadro's number is incredibly important in chemistry. It allows us to convert between the number of moles and the number of atoms or molecules. Avogadro's number is 6.022 x 10^{23}.

When you multiply the number of moles by Avogadro's number, you get the number of atoms or molecules. For example, to find the number of hydrogen atoms in 0.185 moles of \(\text{C}_{6}\text{H}_{14}\text{O}\), you would perform two steps:

1. Calculate the moles of hydrogen (0.185 moles \(\times\) 14 moles of H/mole of \(\text{C}_{6}\text{H}_{14}\text{O}\) = 2.59 moles of H).
2. Multiply by Avogadro's number (2.59 moles of H \(\times\) 6.022 x 10^{23} atoms/mole = 1.56 x 10^{24} atoms of H).

Atoms

Atoms are the smallest units of matter that retain the identity of an element. They are the building blocks of molecules, which are combinations of two or more atoms. Each atom consists of a nucleus (protons and neutrons) and electrons.

In mole calculations, understanding the atomic composition of a molecule enables us to determine the number of atoms from a given amount of moles.

For example, 0.185 moles of \(\text{C}_{6}\text{H}_{14}\text{O}\) contains a specific number of carbon, hydrogen, and oxygen atoms.

Stoichiometry

Stoichiometry is the area of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It involves mole ratios derived from the balanced chemical equation.

In stoichiometric calculations, you can determine the amounts of each substance involved, providing a deeper insight into chemical reactions.

In our example, stoichiometry helps us calculate how many moles of each element are in 0.185 moles of \(\text{C}_{6}\text{H}_{14}\text{O}\). By knowing the molecular formula, we can derive that there are 1.11 moles of carbon, 2.59 moles of hydrogen, and 0.185 moles of oxygen. Using Avogadro's number, these quantities can then be converted into atoms.