 ## Introduction to Atomic Mass and Molecular Mass

Subject: Chemistry

#### Overview

An atomic number is a total number of protons present in the nucleus of an atom. The mass of $\frac{1}{12}$th of an atom of the C12 isotope is called one atomic mass unit (1 amu) is called Atomic mass unit (AMU).

### Atomic Mass and Molecular Mass

Some of The terms related to atom and molecule are introduced just in brief so that they might help to solve chemical arithmetic smoothly.

1. Atomic number: It is a total number of protons present in the nucleus of an atom e.g. carbon atom contains 6 protons; its atomic number is 6.
Atomic number is also the number of electrons present in the neutral atom.
2. Atomic mass number: It is the total number of protons and neutrons present in an atom of an element e.g. carbon contains 6 protons and 6 neutrons.
Therefore, \begin{align*}\text{the atomic mass number of carbon}&=No.\; of\; protons + No.\; of\; neutrons\;\\ &=6+6\\&=12\\ \end{align*}
A proton and a neutron have identical mass, so they are commonly called as nucleon. It means carbon contains twelve nucleons. Symbolically, the atomic number and atomic mass number of carbon are denoted as 12C6.
3. Isotopes: Different species of an element having the same atomic number and different atomic mass number are called isotopes. Isotopes are chemically identical but differ in their physical properties such as melting point, boiling point, density etc.
Isotopes of an element arise by the difference of the number of neutrons. Most of the elements have at least two isotopes e.g. H consists of three isotopes. Those are protium (1H1), deuterium(2H1) and tritium (3H1). The first two are stable isotopes but the third one is the radioactive isotope.
4. Isobars: They are the species having a different atomic number but the same atomic mass number.
e.g. 24Na11 and 24Mg12 called isobars.
5. Atomic mass unit (AMU): The mass of $\frac{1}{12}$th of an atom of C12isotope is called one atomic mass unit (1 amu). The mass of all atoms and molecules are expressed with reference to the mass of one amu.
$$The\; actual\; mass\; of\; 1 \;amu=\frac{1}{12} \times \frac{12}{6.023\times10^{23}}$$
=1.66$\times$10-24g
6. Average atomic mass (Atomic weight): It is defined as the average mass of an element with respect to the mass of $\frac{1}{12}$the of an atom of the C-12 isotope.
The average of an isotopic mass of all the isotopes present in the natural mixture is the atomic mass of an element.
Mathematically,
$$Atomic\; mass = \frac{Mass\; of\; 1 \;atom \;of\; the\; element}{\frac{1}{12} of \;mass \;of \;1\; atom\; of C^{12}}$$
$$= \frac{Mass\; of\; 1\; atom\; of\; the\; element}{Mass\; of\; 1\; atom\; of\; C^{12}}\times\;12$$
Atomic mass begins an average mass, it is fractional in number e.g. Two isotopes of chlorine have atomic masses 35 and 37 and are present in chlorine in the ratio of 3:1 respectively. The average relative weight of chlorine, therefore, would be = $\frac{35\times3+37}{4}$ =35.5 or $\frac{35\times\;75\;+\;37\;\times\;25}{100}$ = 35.5 amu
Hence, the fractional atomic mass of an element is due to the presence of different isotopes in natural mixture with a different percentage.
7. Gram-atom (Gram atomic mass): Atomic weight is simply a number, which does not have any unit of mass. The gram atomic weight or simply gram atom is the atomic weight expressed in terms of grams. Therefore, 1 gram atom of hydrogen weighs 1 gram. Similarly one gram atom of oxygen, sulphur and sodium weigh 16 g, 32 g, and 23 g respectively. Hydrogen and oxygen are molecular species. Their molecules are diatomic whereas carbon and sodium are atomic species. The molecules of carbon and sodium are monatomic. Therefore, when we say one gram molecule or gram mole of hydrogen, it is 2 g of hydrogen and one gram mole of oxygen means 32g of oxygen. Similarly one gram-mole of carbon dioxide is 44 gram (CO2 = 12+16$\times$ 2=44).
$$No.\; of\;gram\; atom\; of \;element =\left(\frac{Mass\; of\; element\; in\; gram}{Atomic\; mass\; of\; element}\right)$$
8. Molecular Mass or Molecular Weight: It is the mass of a molecule of a substance with respect to the mass of $\frac{1}{12}$thof an atom of C-12 isotope e.g. the molecular masses of H2O, CO2 and NaCl are 18, 44 and 58.5 amu respectively.
A molecular mass is calculated by the summation of atomic masses of all the atoms present in the given molecule e.g. molecular mass of C6H12O6 = 6*12+12*1+6*16 = 180 amu.
9. Gram Molecular Mass (g mole): The molecular mass is a relative term and it is a unitless number e.g. molecular mass of H2SO4 = 98. It means, the weight of 1 molecule of H2SO4 is 98 times heavier than the mass of $\frac{1}{12}$th of an atom of C-12 isotope (i.e. 1 amu). When the molecular mass of a substance is expressed in gram, it is called one gram molecular mass or 1 g mole.
For example:
Molecular mass of H2 = 2 amu and 2 g of H2 = 1 g mole of H2
Molecular mass of CO2 = 44 amu and 44 g of CO2 = 1 g mole of CO2
Mathematically, we have
$$No.\; of\; g\; mole = \frac{Mass\; in\; gram}{Molecular\; mass\; in\; g}$$ Bibliography

Pant, Manju, Bhoj Raj Bhattarai and Nab Raj Adhikari. Comprehensive Chemistry. 6th edition . Vol. 1 . Kathmandu: Heritage Publisher and Distributors Pvt. Ltd., 2072.

##### Things to remember
• $$The\; actual\; mass\; of\; 1 \;amu=\frac{1}{12} \times \frac{12}{6.023\times10^{23}}$$
• $$No.\; of\; g\; mole = \frac{Mass\; in\; gram}{Molecular\; mass\; in\; g}$$
• $$No.\; of\; g\; mole = \frac{Mass\; in\; gram}{Molecular\; mass\; in\; g}$$
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