Question

How many grams of Ne are in $ 1.44 \times {10^{24}} $ atoms of Ne?

Answer 1

Hint :The molar mass in $ {\text{g/mol}} $ of an element is numerically equal to the element’s atomic mass in $ amu $ . The atomic mass of Ne is $ 20.18{\text{ }}amu $ . The number of particles in one mole of a substance is $ 6.022 \times {10^{23}} $ (Avogadro’s number).
 $ {\text{No of moles = }}\dfrac{{{\text{No of atoms}}}}{{6.022 \times {{10}^{23}}{\text{ atoms/mol}}}} $
 $ {\text{Mass of substance = No of moles of substance }} \times {\text{ Molar mass}} $

Complete Step By Step Answer:
Here the number of atoms of Ne in a particular sample are given. And we are asked to find the mass of that sample in grams. We know that the mass of $ 1{\text{ mole}} $ of any substance is its molar mass. And the molar mass of an element is equal to its atomic mass. So, the molar mass of Ne is $ 20.18{\text{ g/mol}} $ .
Also, we know that there are $ 6.022 \times {10^{23}}{\text{ atoms/mol}} $ in $ 1{\text{ mole}} $ of any substance. So, we will first use this to find the number of moles of Ne in the given sample then multiply it with the molar mass of Ne to get the mass of the sample in grams.
We know that, $ {\text{No of moles = }}\dfrac{{{\text{No of atoms}}}}{{6.022 \times {{10}^{23}}{\text{ atoms/mol}}}} $
 $ \Rightarrow {\text{No of moles of Ne = }}\dfrac{{1.44 \times {{10}^{24}}{\text{ atoms}}}}{{6.022 \times {{10}^{23}}{\text{ atoms/mol}}}} $
 $ \Rightarrow {\text{No of moles of Ne = }}2.391{\text{ moles}} $
So, there are $ 2.391{\text{ moles}} $ of Ne in the given sample.
Now, we will use the relation between the number of moles and mass of a substance.
We know that, $ {\text{Mass of substance = No of moles of substance }} \times {\text{ Molar mass}} $
 $ \Rightarrow {\text{Mass of Ne = 2}}{\text{.391 mol }} \times 20.18{\text{ g/mol}} $
 $ \Rightarrow {\text{Mass of Ne = 48}}{\text{.25 g}} $
So, the mass of Ne in the sample is $ {\text{48}}{\text{.25 g}} $ .
Hence, the mass of $ 1.44 \times {10^{24}} $ atoms of Ne is $ {\text{48}}{\text{.25 g}} $ .

Note :
It is important to know the atomic mass of elements to solve questions of these types. Sometimes the atomic mass is given in the question. But it is better to remember it. A simple rule is to double the atomic number to get the atomic mass of the first twenty elements. But it does not always work.