Question

Which contains more molecules: \(2.5 \mathrm{~mol}\) of \(\mathrm{H}_{2} \mathrm{O}\) or \(2.5 \mathrm{~mol}\) of \(\mathrm{H}_{2}\) ? Which contains more atoms? Which weighs more?

Short answer

\(2.5 \text{mol}\) of \(H_2O\) and \(2.5 \text{mol}\) of \(H_2\) contain the same number of molecules. \(H_2O\) contains more atoms. \(H_2O\) also weighs more than \(H_2\).

Step-by-step solution

Understanding the concept of a mole

A mole is a unit that measures the amount of substance. One mole contains Avogadro's number of entities (\(6.022 \times 10^{23}\) entities/mol). Regardless of the type of substance, one mole of any substance contains the same number of entities, which is Avogadro's number.

Comparing the number of molecules

Since both \(2.5 \text{mol}\) of \(H_2O\) and \(2.5 \text{mol}\) of \(H_2\) represent the same number of moles, they contain the same number of molecules. Each contains \(2.5 \times 6.022 \times 10^{23}\) molecules.

Determining the number of atoms in each compound

\(H_2O\) has 3 atoms per molecule (2 hydrogen and 1 oxygen), and \(H_2\) has 2 atoms per molecule (2 hydrogen). To calculate the total number of atoms, multiply the number of molecules by the number of atoms per molecule. \(2.5 \text{mol}\) of \(H_2O\) has \(2.5 \times 3 \times 6.022 \times 10^{23}\) atoms, and \(2.5 \text{mol}\) of \(H_2\) has \(2.5 \times 2 \times 6.022 \times 10^{23}\) atoms. Clearly, \(H_2O\) contains more atoms.

Calculating the mass of each substance

The molar mass of \(H_2O\) (18.015 g/mol) is higher than that of \(H_2\) (2.016 g/mol). To find the mass, multiply the molar mass by the number of moles. \(2.5 \text{mol} \times 18.015 \text{g/mol} = 45.0375 \text{g}\) of \(H_2O\), and \(2.5 \text{mol} \times 2.016 \text{g/mol} = 5.04 \text{g}\) of \(H_2\). \(H_2O\) weighs more than \(H_2\).

Key concepts

Avogadro's Number

Avogadro's number, named after the scientist Amedeo Avogadro, is a fundamental constant that is essential to understanding the mole concept in chemistry. It is defined as the number of atoms, ions, or molecules that are contained in one mole of a substance.

The exact value is defined as approximately \(6.022 \times 10^{23}\) entities per mole. This number helps chemists convert between the microscopic world of atoms and molecules to the macroscopic world of grams and liters that we interact with daily. For instance, if we have \(2.5 \text{mol}\) of any substance, be it \(\mathrm{H}_2\mathrm{O}\) or \(\mathrm{H}_2\), the total number of molecules can be calculated by multiplying the amount in moles by Avogadro's number, giving \(2.5 \times 6.022 \times 10^{23}\) molecules. This fundamental concept demystifies how scientists can measure and work with incredibly large numbers of microscopic particles.

Molecular Mass

Molecular mass (also known as molecular weight) is the sum of the masses of all the atoms in a molecule. It is measured in atomic mass units (amu), where one atomic mass unit is \(1/12\) the mass of a carbon-12 atom.

In practical terms, molecular mass allows chemists to find out how much a certain number of molecules of a substance would weigh. For example, the molecular mass of water (\(\mathrm{H}_2\mathrm{O}\)) is calculated by adding the masses of two hydrogen atoms (approximately \(1\) amu each) and one oxygen atom (approximately \(16\) amu), resulting in a molecular mass of approximately \(18\) amu.

Relating Molecular Mass to Molar Mass

In the context of molar mass, which is the mass of one mole of a substance measured in grams, we find that the molar mass numerically equals the molecular mass but changes the unit to grams per mole (g/mol). This molar mass is what allows us to convert between moles and mass efficiently.

Comparing Molecules and Atoms

Comparing molecules and atoms involves understanding the basic structures of substances and the interrelations of their numbers and masses. A molecule is a group of atoms bonded together, representing the smallest unit of a chemical compound that can take part in a chemical reaction. Atoms, on the other hand, are the smallest constituent units of ordinary matter that form chemical elements.

When we compare \(2.5 \text{mol}\) of \(\mathrm{H}_2\mathrm{O}\) and \(\mathrm{H}_2\), though they both have the same number of molecules due to Avogadro's number, the actual number of atoms in each substance differs. \(\mathrm{H}_2\mathrm{O}\) molecules each contain three atoms (two hydrogens and one oxygen), while each \(\mathrm{H}_2\) molecule contains only two hydrogen atoms. Consequently, \(\mathrm{H}_2\mathrm{O}\) holds more atoms in total, given the same number of moles.

Real-world Implications

This comparison is not just theoretical; it has practical implications in calculations involving chemical reactions, where knowing the precise number of atoms present is crucial for determining reaction stoichiometry. Thus, understanding the differences and relationships between molecules and atoms is key to mastering the mole concept in chemistry.