Question

State whether the following statements are true or false. \(1 \mathrm{~g}\) atom of nitrogen contains \(6.023 \times 10^{23}\) atoms of nitrogen.

Short answer

Answer: Yes, it is true that 1 gram atom of nitrogen contains \(6.023 \times 10^{23}\) atoms of nitrogen.

Step-by-step solution

Find the molar mass of nitrogen

To find out how many atoms are in 1 gram atom of nitrogen, we first need to know the molar mass of nitrogen. Nitrogen is a diatomic molecule with the formula N2. One atom of nitrogen has an atomic mass of 14.0067 u, so the molecular mass of N2 is twice the atomic mass of nitrogen: Molar mass of N2 = 2 × 14.0067 u = 28.0134 u

Convert 1 gram atom to moles

Next, we will convert the given 1 gram atom of nitrogen into moles. Since the molar mass of nitrogen is 28.0134 u: 1 gram atom of nitrogen = 1 × 28.0134 grams = 28.0134 grams Now, let's convert this mass into moles using the molar mass: Number of moles = (mass) / (molar mass) = (28.0134 grams) / (28.0134 g/mol) = 1 mole

Calculate the number of nitrogen atoms

Now that we have the number of moles, we can use Avogadro's number to find the number of nitrogen atoms: Number of nitrogen atoms = (number of moles) × (Avogadro's number) = (1 mole) × (\(6.023 \times 10^{23}\) atoms/mol) = \(6.023 \times 10^{23}\) atoms

Verify the statement

As we calculated, 1 gram atom of nitrogen contains \(6.023 \times 10^{23}\) atoms. Therefore, the given statement is true.

Key concepts

Atomic Mass

Atomic mass is the mass of a single atom, expressed in atomic mass units (u), where 1 u is defined as one twelfth of the mass of a carbon-12 atom. This number provides insight into the mass of different elements at the atomic level.
For example, nitrogen, which is a crucial component in our atmosphere, has an atomic mass of 14.0067 u per atom. This value is particularly important when calculating molecular weights or converting gram amounts to moles, as used in chemical equations.
To understand molecular weight, consider that atomic mass focuses on individual atoms. The atomic mass reflects isotopic distribution, but for calculations, the atomic weight given on the periodic table is generally employed. In essential chemistry, knowing the atomic mass helps in converting between different measurement units, essential for further calculations involving moles and molecules.

Avogadro's Number

Avogadro's number, which is approximately \(6.022 \times 10^{23}\), represents the quantity of atoms, molecules, or particles present in one mole of a substance. This large number is a fundamental constant essential for bridging the gap between the microscopic atomic scale and the macroscopic world we can measure.
Named after the Italian scientist Amedeo Avogadro, this number serves as a constant to convert moles into measurable entities. For example, in the case of nitrogen, when calculating how many atoms are present in one mole, Avogadro's number is instrumental.
Understanding Avogadro's number makes it possible to relate atomic-scale quantities to laboratory-scale quantities, crucial for calculations involving substances in real-world chemical reactions.

Molar Mass

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It is a direct application of atomic mass and Avogadro's number to convert atomic mass units to practical masses found in the lab.
For elemental nitrogen, which usually exists as molecules of two atoms (\(N_2\)), each nitrogen atom has an atomic mass of approximately 14.0067 u. The molar mass of nitrogen gas is therefore calculated as \(28.0134\) g/mol, with two nitrogen atoms in each molecule.
The importance of molar mass lies in its ability to allow chemists to weigh out amounts equivalent to the atomic scale, facilitating stoichiometry in chemical reactions. Having a foundational understanding of molar mass enables the conversion of mass to moles, helping determine how many molecules or atoms are present in a given sample.

Nitrogen Atom Calculations

Calculating the number of atoms in a sample involves several steps, which can seem complex but are manageable when broken down. Start by understanding the relationship between mass, moles, and molecules.
In the given scenario of 1 gram atom of nitrogen, you first multiply by the molar mass (28.0134 g/mol for \(N_2\)) to find the mass in grams. Then, convert this mass into moles, which was calculated as 1 mole of nitrogen here.
With the number of moles determined, Avogadro's number \(6.022 \times 10^{23}\) becomes essential. Multiplying the moles by this constant provides the total number of nitrogen atoms present.
Each of these steps interlinks to transform a measurement of mass into a detailed count of atoms, demonstrating how individual atoms constitute the substances we observe in chemistry.