Question

Calculate the number of gram atoms present in 103 g of Barium (Ba-137.4)
A. 103
B. 0.4
C. 0.75
D. 0.3

Answer 1

Hint: The concept of moles and molar mass is used here. There is an equation that relates the number of moles, the molar mass and the given mass of the element or compound.

Complete Solution :
- In order to solve this question, we need to have an idea about the moles and molar mass of an element or compound. Before the advent of mass spectrometry for determining the atomic masses accurately, scientists were determining mass of one atom relative to another by experimental means. Hydrogen, being lightest atom arbitrarily assigned a mass of 1 (without any units) and other elements were assigned masses relative But in 1961, the International Union of chemists had chosen the most stable isotope of carbon (C-12 isotope) as the default mass for comparison of the atomic masses of various elements. In this system $^{12}C$ is assigned a mass of exactly 12 atomic mass units (amu) and masses of all other atoms are given relative to this standard One atomic mass unit is defined as a mass exactly equal to one-twelfth the mass of one carbon-12 atom. Now, the mass of the substance, be it any element or a compound which has an exact number of $6\times {{10}^{23}}$ particles in it is called the molar mass. Molar mass is different for different elements and compounds. The number of moles for a substance is given by the formula:
\[no\,of\,moles=\dfrac{given\,mass}{molar\,mass}\]

- However, we can also say that this number of moles represent the number of gram atoms present in a specific sample. In order to find the number of atoms, we have to just multiply the number of moles, with the Avogadro number. Now, let us come to the question. We have the given weight of Barium as 103g and the molar mass of Barium as 137.4g. So, using the formula we have the gram atoms of Ba as:
\[\begin{align}
  & gram\,ato{{m}_{Ba}}=\dfrac{given\,weigh{{t}_{Ba}}}{molar\,mas{{s}_{Ba}}}=\dfrac{103}{137.4}=0.749=0.75 \\
 & \\
\end{align}\]
 So, the number of gram atoms present in 103 g of Ba is 0.75.
So, the correct answer is “Option C”.

Note: It is to be noted that Barium is unimolecular, so its molar mass is 137.4. If we had oxygen which has molar mass 16, it would be actually $16\times 2 = 32g\,mo{{l}^{-1}}$ as oxygen exists as diatomic molecule ${{O}_{2}}$.