Gram Atomic and Gram Molecular Mass

Avogadro's number is essential for relating the number of particles in a substance to the amount of substance in moles. For example, one mole of oxygen atoms reacts with two moles of hydrogen atoms to form one mole of water molecules (H₂O).

• It helps calculate the number of atoms, molecules, or ions in a substance.
• It is used to determine stoichiometric relationships in chemical reactions.
• The molar mass (g/mol) of a substance is numerically equal to its relative atomic or molecular mass (u). For example, one mole of water has a mass of 18.015 g.

Important Terms:

• Atomic Mass: Atomic mass is the mass of an atom of the given element. The unit of atomic mass is a.m.u. often denoted as u. One atomic mass unit (a.m.u.) is said to be exactly equal to the 1/12 the ratio of the mass of 1 mole of C-12 atoms to Avogadro's Constant (N_A).

• Molecular Mass: Molecular Mass is the sum of the mass of the atoms present in a molecule of the given substance. Its unit is also a.m.u.

Example: The molecular mass of NH₃ = 14 + 1 × 3 = 17 a.m.u.

• Molar Mass: The mass of the 1 mole of a given substance is known as molar mass. The SI unit of molar mass is kg/mol however g/mol is the usually used unit. Molar mass can also be defined as the molecular mass of the given substance expressed in grams.

Example: 2 a.m.u. is the molecular mass of hydrogen gas therefore as per the definition the molar mass of hydrogen gas will be 2 g.

• Mole Concept: It is a concept revolving around 12 g of C-12 isotope containing atoms equal to Avogadro's Constant. Mole is actually an amount. The amount can be of atoms, molecules, ions, electrons, fruits, or books but our scope would be limited to chemical entities. What we actually do is calculate the mass of chemical entities in terms of mole. The value of Avogadro's Constant i.e. the value of 1 mole of a substance is 6.0221367 × 10²³.

• Mole: One mole is defined as the amount of the substance which contains as many entities as there are atoms in 12 g of C-12 isotope. As measured by mass spectrometer the mass of one atom of C-12 atom is found to be 1.992648 × 10^-23 g. Since 1 mole of C-12 atoms is 12g. Therefore, the number of atoms present in 1 mole = 12g / 1.992648*10^-23 g atom^-1 or 6.0221367 × 10²³ atoms. The value of 1 mole is known as Avogadro's Constant. It is denoted by the symbol N_A.

Gram Atomic Mass

• Gram atomic mass is the periodic table element's atomic weight in grams.
• The molar mass of an element is the mass of one mole in grams. 
• The mass of one mole of an element is defined as its gram atomic mass. 
• It is calculated by taking an element's atomic weight from the periodic table and converting it to grams.
• Thus, when the mass of an element is expressed in grams then it is known as gram atomic mass.

Example: Sodium (Na) has an atomic weight of 22.99 u and a gram atomic mass of 22.99 grams.

• So one mole of sodium atoms weighs 22.99 g.
• This implies that the quantity of the element of the given substance when weighs equal to its gram atomic mass is called one gram atom. 
• The gram atomic mass of a material is the amount of that substance in grams that is numerically equivalent to its atomic mass.

Mass of the element (in g) = \frac{\text{Mass of the element (in g)}}{\text{Atomic mass of the element (in g)}}

Gram Molecular Mass

• The mass in grams of one mole of a molecular material is known as the gram molecular mass.
• The molar mass and gram molecular mass are the same things.
• The main distinction is that gram molecular mass defines the mass unit.
• The gram molecular mass (g/mol) can be expressed in grams or grams per mole (g/mol). 

Find Gram Molecular Mass

• To determine the mass, use the molecular formula.
• Look up each element's relative atomic mass in the formula.
• Multiply the subscript following each element symbol (the number of atoms) by the atomic mass of that element.
• If there is no subscript, it implies that the molecule contains only one atom of that element.
• To get the gram molecular mass, add all of the numbers together.

Example: the gram molecular mass of oxygen gas (O₂) is 32 g.

• The gram molecular mass of a substance is the amount of that substance in grams that is numerically equivalent to its molecular mass.

Number of gram molecules = \frac{\text{Mass of the substance (in g)}}{\text{Molecular mass of the substance (in g)}}