Molecular Mass and Average Molecular Weight

About

Molecular Mass

Molecular mass is the total mass of a single molecule, calculated as the sum of the atomic masses of all the atoms that make up the molecule. It is typically expressed in atomic mass units (amu) or Daltons (Da), where:

• 1 amu (or 1 Dalton) = $1.66053906660 \times 10^{-24}$ grams.

Formula for Molecular Mass:

The molecular mass is calculated by adding the masses of each atom in the molecule according to its chemical formula. For a molecule with $n_i$ atoms of element $i$, the molecular mass is:

$M_{\text{molecule}} = \sum_{i} n_i \times m_i$

Where:

• $m_i$ is the atomic mass of the element $i$,

• $n_i$ is the number of atoms of element $i$ in the molecule.

Example:

For water (H₂O):

• Hydrogen (H) atomic mass ≈ 1.008 amu,

• Oxygen (O) atomic mass ≈ 16.00 amu.

The molecular mass of water is: $M_{\text{H₂O}} = (2 \times 1.008) + (1 \times 16.00) = 18.016 \text{amu}$

Average Molecular Weight (Molar Mass)

The average molecular weight (or molar mass) is the weighted average mass of a molecule based on the natural abundance of isotopes of its constituent elements. It represents the mass of one mole of molecules of the substance and is expressed in grams per mole (g/mol).

Since many elements have isotopes with different atomic masses, the average molecular weight accounts for these variations. The molar mass is typically used when converting between the mass of a substance and the number of moles in a sample.

Calculation of Average Molecular Weight:

To calculate the average molecular weight, the atomic masses used are the weighted averages based on the natural isotopic distribution of each element.

For an element with isotopes, the atomic mass $m_i$ is calculated as: $\text{Average Atomic Mass} = \sum_{j} (p_j \times m_{j})$

Where:

• $p_j$ is the natural abundance of isotope $j$,

• $m_{j}$ is the mass of isotope $j$.

For a molecule, the average molecular weight is the sum of the average atomic masses of its constituent atoms.

Example:

For chlorine (Cl), which has two main isotopes:

• $^{35}\text{Cl}$ with atomic mass 34.97 amu (75.77% abundance),

• $^{37}\text{Cl}$ with atomic mass 36.97 amu (24.23% abundance).

The average atomic mass of chlorine is:

$M_{\text{Cl}} = (0.7577 \times 34.97) + (0.2423 \times 36.97) = 35.45 \text{amu}$

For a molecule like hydrochloric acid (HCl), the average molecular weight is:

$M_{\text{HCl}} = (1.008) + (35.45) = 36.458 \text{amu} \text{ or } 36.458 \text{g/mol}$

Key Differences:

1. Molecular Mass:

   • Refers to the exact mass of a specific molecule (using exact isotopic masses).

   • Expressed in amu (atomic mass units).

2. Average Molecular Weight (Molar Mass):

   • Refers to the average mass of a mole of molecules considering natural isotope abundances.

   • Expressed in g/mol and commonly used in macroscopic calculations like stoichiometry.

Applications:

• Molecular Mass is useful in precise studies like mass spectrometry where individual molecules and their isotopes are measured.

• Average Molecular Weight is used in chemistry for calculating the amount of substance in reactions, determining concentrations, and converting between mass and moles.

Method

These are calculated based on the above definitions for Molecular Mass and Average Molecular Weight

Find

The Molecular Mass and Average Molecular Weight can be found in the Global property table.