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Question: How many grams of Ne are in \( 1.44 \times {10^{24}} \) atoms of Ne?...

How many grams of Ne are in 1.44×10241.44 \times {10^{24}} atoms of Ne?

Explanation

Solution

Hint : The molar mass in g/mol{\text{g/mol}} of an element is numerically equal to the element’s atomic mass in amuamu . The atomic mass of Ne is 20.18 amu20.18{\text{ }}amu . The number of particles in one mole of a substance is 6.022×10236.022 \times {10^{23}} (Avogadro’s number).
No of moles = No of atoms6.022×1023 atoms/mol{\text{No of moles = }}\dfrac{{{\text{No of atoms}}}}{{6.022 \times {{10}^{23}}{\text{ atoms/mol}}}}
Mass of substance = No of moles of substance × Molar mass{\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 mole1{\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 g/mol20.18{\text{ g/mol}} .
Also, we know that there are 6.022×1023 atoms/mol6.022 \times {10^{23}}{\text{ atoms/mol}} in 1 mole1{\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, No of moles = No of atoms6.022×1023 atoms/mol{\text{No of moles = }}\dfrac{{{\text{No of atoms}}}}{{6.022 \times {{10}^{23}}{\text{ atoms/mol}}}}
⇒No of moles of Ne = 1.44×1024 atoms6.022×1023 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}}}}
⇒No of moles of Ne = 2.391 moles\Rightarrow {\text{No of moles of Ne = }}2.391{\text{ moles}}
So, there are 2.391 moles2.391{\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, Mass of substance = No of moles of substance × Molar mass{\text{Mass of substance = No of moles of substance }} \times {\text{ Molar mass}}
⇒Mass of Ne = 2.391 mol ×20.18 g/mol\Rightarrow {\text{Mass of Ne = 2}}{\text{.391 mol }} \times 20.18{\text{ g/mol}}
⇒Mass of Ne = 48.25 g\Rightarrow {\text{Mass of Ne = 48}}{\text{.25 g}}
So, the mass of Ne in the sample is 48.25 g{\text{48}}{\text{.25 g}} .
Hence, the mass of 1.44×10241.44 \times {10^{24}} atoms of Ne is 48.25 g{\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.