Question

How many \(\mathrm{O}\) atoms of mass 15.99 amu are in \(15.99 \mathrm{~g}\) of oxygen?

Short answer

There are \(6.022 \times 10^{23}\) oxygen atoms in \(15.99 \, \text{g}\) of oxygen.

Step-by-step solution

Identify the Known Values

We are given that the mass of an oxygen atom is \(15.99\) amu and we need to find out how many atoms of this mass are present in \(15.99 \, \text{g}\) of oxygen.

Convert Grams to Moles

To find out how many atoms are present, we first need to convert grams of oxygen to moles. The molar mass of oxygen is \(15.99 \, \text{g/mol}\), so the number of moles in \(15.99 \, \text{g}\) is calculated as follows: \[\text{moles of oxygen} = \frac{15.99 \, \text{g}}{15.99 \, \text{g/mol}} = 1 \, \text{mol}\]

Use Avogadro's Number

Avogadro's number tells us that one mole of any element contains \(6.022 \times 10^{23}\) atoms. Since we have \(1\) mole of oxygen, we multiply it by Avogadro's number: \[\text{Number of oxygen atoms} = 1 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 6.022 \times 10^{23} \, \text{atoms}\]

Key concepts

Molar Mass

The molar mass is a crucial concept in chemistry when dealing with substances at a macroscopic scale. It describes the mass of one mole of a substance, which is important because it provides a bridge between the atom and the bulk material. In the context of oxygen (O), the molar mass is expressed in grams per mole (g/mol). For example, a single atom of oxygen has a mass of approximately 15.99 atomic mass units (amu), which translates to the molar mass of 15.99 g/mol.
Understanding molar mass allows us to convert between the mass of a substance and the number of moles, enabling calculations on how many particles are present in a given amount of material. The molar mass is the mass of Avogadro's number of atoms, which simplifies many practical laboratory calculations.

Avogadro's Number

Avogadro's number is one of chemistry's most fundamental constants. It tells us how many individual units, such as atoms, molecules, or ions, are contained in one mole of a substance. This constant is universally accepted to be approximately \(6.022 \times 10^{23}\).
This number is incredibly large because atoms and molecules are extraordinarily small. The concept of a mole, paired with Avogadro's number, simplifies calculations by allowing chemists to deal directly with measurable amounts of a substance. For instance, if we have one mole of oxygen, that means we have \(6.022 \times 10^{23}\) atoms of oxygen. This conversion is key in understanding the relationships in chemical reactions, stoichiometry, and material composition.
Overall, Avogadro's number bridges the gap between the atomic world and the macroscopic world, helping us to measure tiny particles in larger quantities.

Atomic Mass Unit

The atomic mass unit (amu) is a unit of mass used to express atomic and molecular weights. It is defined as one twelfth the mass of a single carbon-12 atom, which ensures consistency and accuracy in mass measurements across different atoms and molecules. Each element's atomic mass is usually close to a whole number and is expressed using the amu.
For example, oxygen has an atomic mass close to 15.99 amu. This tells us that a single oxygen atom is approximately 15.99 times heavier than 1/12th of a carbon-12 atom. The atomic mass unit allows us to compare the relative masses of different atoms and molecules effectively, which is critical for understanding chemical reactions and stoichiometry.

• 1 amu is a very small mass, suitable for individual atoms or small molecules.
• This unit is essential for precise scientific communication and understanding across different chemical disciplines.