Gram Atomic and Gram Molecular Mass

Avogadro’s number is critical to understanding the structure of molecules as well as their interactions and combinations. e.g. because one atom of oxygen will combine with two atoms of hydrogen to form one molecule of water (H₂O), one mole of oxygen (6.022 × 10²³ of O atoms) will mix with two moles of hydrogen (2 × 6.022 × 10²³ of H atoms) to form one mole of H₂O. Another feature of Avogadro’s number is that the mass of one mole of material equals the molecular weight of that substance. Water, for example, has a mean molecular weight of 18.015 a.m.u. implying that one mole of water weighs 18.015 grams. Many chemical computations are made easier by this feature. 

Now let’s discuss some important concepts before understanding the gram atomic mass and gram molecular mass.

• 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. e.g. 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. e.g. 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. The term ‘Avogadro’s Constant’ is termed after the great pioneer Amedeo Avogadro. 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. For example, the gram atomic mass of helium is 4 g. Similarly, 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. If we wish to write a substance’s gram atomic mass, we first write its atomic mass, then subtract the atomic mass unit u and add grams to the numerical value of the atomic mass. That is,

Mass of the element (in g) = Number of gram atoms / 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). 

How to find the Gram Molecular Mass?

1. To determine the mass, use the molecular formula.
2. Look up each element’s relative atomic mass in the formula.
3. 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.
4. To get the gram molecular mass, add all of the numbers together.

The gram molecular mass of a substance is the amount of that substance in grams that is numerically equivalent to its molecular mass. To write a substance’s gram molecular mass, first, write its molecular mass, then subtract the molecular mass unit u and add grams to the numerical value of the molecular mass. For example, the gram molecular mass of oxygen gas (O₂) is 32 g.

Number of gram molecules = Mass of the substance (in g) / Molecular mass of the substance (in g)

The mass of one molecule of material in grams should not be confused with the mass of one molecule of the substance in grams. The real mass or molecular mass of a material is the mass of one molecule.

Sample Problems

Problem 1: What is Avogadro’s Constant?

Solution:

Avogadro’s number is critical to understanding the structure of molecules as well as their interactions and combinations. e.g. because one atom of oxygen will combine with two atoms of hydrogen to form one molecule of water (H₂O), one mole of oxygen (6.022 × 10²³ of O atoms) will mix with two moles of hydrogen (2 × 6.022 × 10²³ of H atoms) to form one mole of H₂O. 

Problem 2: Why are the gram atomic mass and gram molecular mass of all elemental substances are same?

Solution:

The mass of a grams of a molecule. a mass in grams equal to a substance’s molecular weight or the sum of all the atomic weights in its molecular formula

The mass in grams of one mole of atoms in a monatomic chemical element is known as gram atomic mass. It is the same as the relative atomic mass (or atomic weight) in grams. Only Nobel gases exist in a monotonic state. Hence, the gram atomic mass and gram molecular mass of all elemental substances are same.

Problem 3: Calculate the number of atoms present in 4 moles of hydrogen gas.

Solution:

1 molecule of hydrogen gas has 2 atoms

1 mole of hydrogen gas has N_A molecules ⇒ 1 mole of hydrogen gas has 2 × N_A atoms

Therefore, 4 moles hydrogen gas has 4 × 2 × N_A atoms i.e. 8 × N_A atoms

Problem 4: What is a mole?

Solution:

A mole is the unit of amount of substance. The number of entities present in a mole is equal to Avogadro’s Constant. Mole is the former term used for the term ‘ one gram atom’.

Problem 5: How many moles of oxygen gas are required to produce 3 moles of CO₂?

Solution:

Chemical reaction for the formation of carbon dioxide is

C +O₂ ⇢ CO₂

The above equation is balanced. Hence we can say that

1 mole of carbon and 1 mole of oxygen gas combine to form 1 mole of carbon dioxide.

Therefore, for the formation of 3 moles of carbon dioxide there will be requirement of 3 moles of oxygen gas.