Question

Calculate the weight of (a) single atom of nitrogen (b) single atom of carbon (c) \(1.5 \times 10^{21}\) atoms of sodium (d) single molecule of carbon monoxide

Short answer

Question: Calculate the individual weights of the following elements and compounds: (a) a single atom of nitrogen (N) (b) a single atom of carbon (C) (c) the total weight of \(1.5 \times 10^{21}\) atoms of sodium (Na) (d) a single molecule of carbon monoxide (CO) Answer: (a) Weight of a single atom of nitrogen: \(\approx 2.32 \times 10^{-23}\) g (b) Weight of a single atom of carbon: \(\approx 1.99 \times 10^{-23}\) g (c) Weight of \(1.5 \times 10^{21}\) atoms of sodium: \(\approx 5.73\) g (d) Weight of a single molecule of carbon monoxide: \(\approx 4.65 \times 10^{-23}\) g

Step-by-step solution

Find the molar mass of nitrogen

Find the molar mass of nitrogen using the periodic table. The molar mass of nitrogen (N) is approximately 14 g/mol.

Calculate the weight of a single nitrogen atom

Using the formula mentioned in the analysis, the weight of a single nitrogen atom can be calculated as: Weight of a single nitrogen atom = (14 g/mol) / (\(6.022 \times 10^{23}\) atoms/mol)

Find the molar mass of carbon

Find the molar mass of carbon using the periodic table. The molar mass of carbon (C) is approximately 12 g/mol.

Calculate the weight of a single carbon atom

Using the formula mentioned in the analysis, the weight of a single carbon atom can be calculated as: Weight of a single carbon atom = (12 g/mol) / (\(6.022 \times 10^{23}\) atoms/mol)

Find the molar mass of sodium

Find the molar mass of sodium using the periodic table. The molar mass of sodium (Na) is approximately 23 g/mol.

Calculate the weight of \(1.5 \times 10^{21}\) sodium atoms

First, find the weight of a single sodium atom using the formula: Weight of a single sodium atom = (23 g/mol) / (\(6.022 \times 10^{23}\) atoms/mol) Now, multiply this weight by the number of sodium atoms given (\(1.5 \times 10^{21}\) atoms) to find the total weight: Total weight of \(1.5 \times 10^{21}\) sodium atoms = (Weight of a single sodium atom) * (\(1.5 \times 10^{21}\) atoms)

Find the molar mass of carbon monoxide

Carbon monoxide (CO) is a compound made up of one carbon atom and one oxygen atom. The molar mass of carbon monoxide is the sum of the molar masses of carbon and oxygen. Molar Mass of CO = Molar Mass of Carbon + Molar Mass of Oxygen Molar Mass of CO = 12 g/mol (carbon) + 16 g/mol (oxygen) = 28 g/mol

Calculate the weight of a single carbon monoxide molecule

Using the formula mentioned in the analysis, the weight of a single carbon monoxide molecule can be calculated as: Weight of a single carbon monoxide molecule = (28 g/mol) / (\(6.022 \times 10^{23}\) molecules/mol) After calculating the weights for each case, you will get the following results: (a) Weight of a single atom of nitrogen: \(\approx 2.32 \times 10^{-23}\) g (b) Weight of a single atom of carbon: \(\approx 1.99 \times 10^{-23}\) g (c) Weight of \(1.5 \times 10^{21}\) atoms of sodium: \(\approx 5.73\) g (d) Weight of a single molecule of carbon monoxide: \(\approx 4.65 \times 10^{-23}\) g

Key concepts

Molar Mass

When we talk about molar mass, we refer to the mass of one mole of a substance. It is an essential concept in chemistry because it bridges the gap between the atomic scale and the macroscopic scale we interact with daily. The unit for molar mass is grams per mole (g/mol). To find the molar mass of an element, you would look at the atomic weight listed on the periodic table. For elements, the atomic weight and molar mass are numerically the same, but their units differ; atomic weight is unitless, whereas molar mass is expressed in g/mol.

In practical terms, the molar mass lets us convert between the mass of a substance and the number of moles. For a compound like carbon dioxide, CO2, you would add the molar mass of one carbon (12 g/mol) and two oxygens (2 * 16 g/mol) to get a molar mass of 44 g/mol for the compound. This value means that one mole of carbon dioxide has a mass of 44 grams. Remembering that a mole contains Avogadro's number of particles will help us in calculations involving exact counts of molecules or atoms.

Avogadro's Number

Avogadro's number, also known critically as Avogadro's constant, is an integral part of chemistry that defines the number of particles in one mole of a substance. The accepted value is approximately \(6.022 \times 10^{23}\) entities per mole. This number may seem impossibly large, but it accurately represents the vast number of atoms or molecules even in a small sample of a substance.

When we deal with molar mass and want to determine the mass of a single atom or molecule, we divide the molar mass by Avogadro's number. So, if an atom of carbon has a molar mass of 12 g/mol, the mass of a single carbon atom would be \(12 \text{ g/mol} \div 6.022 \times 10^{23} \text{ atoms/mol} = 1.99 \times 10^{-23}\) grams. Avogadro's number is essential when translating between microscopic atomic scale quantities and quantities we can measure and work with in the laboratory.

Atomic Weight

Atomic weight is a dimensionless quantity (meaning it has no units) that reflects how heavy an atom is compared to a carbon-12 atom, which has been assigned the atomic weight of exactly 12. It’s an average weight of all the isotopes of an element, weighted by their natural abundance. Because atoms are so tiny, the atomic weight allows chemists to compare different atoms on a scale that's easy to understand.

For instance, the atomic weight of carbon is about 12.01, which accounts for the presence of carbon-12 and carbon-13 in nature. You can use atomic weight to track inter-element transitions that occur in various chemical reactions. In calculating the weight of single atoms or a specific number of atoms, we use the concept of atomic weight to arrive at the molar mass which is then applied alongside Avogadro’s number.

Molecular Weight

Molecular weight, sometimes referred to as molecular mass, is a measure that sums the atomic weights of the atoms in a molecule. Just like atomic weight helps us compare different atoms, molecular weight lets us compare different molecules. It is also dimensionless but is often practically used in the same numerical sense as the molar mass of the molecule.

For example, a molecule of water (H2O) has a molecular weight that equals the sum of the atomic weights of two hydrogen atoms and one oxygen atom. If we assume atomic weights of approximately 1 for hydrogen and 16 for oxygen, the molecular weight of water becomes approximately 18. When we say a mole of water weighs about 18 grams, we are using its molecular weight expressed in g/mol. This concept becomes especially useful when chemists have to work out the quantities required for chemical reactions, where balancing molecular weights is paramount.