Question

What is the mass, in grams, of $3.40\times {{10}^{22}}$ atoms He?

Answer 1

Hint: One mole of the substance contains $6.022\times {{10}^{23}}$ atoms and the mass of this amount of substance is known as its molar mass. The molar mass of helium is 4 grams that means 1 mole of helium weighs 4 grams.

Complete answer:
Avogadro’s number gives the number of particles of a substance present in 1 mole of that substance. These particles could be either electrons, atoms, or molecules. Its approximate value is $6.022\times {{10}^{23}}$.
So, 1 mole of Helium contains $6.022\times {{10}^{23}}$ atoms. So, the number of moles of helium present in $3.40\times {{10}^{22}}$ atoms:
\[\begin{align}
  & \because 6.022\times {{10}^{23}}\text{ atoms}\to \text{1 mole He} \\
 & \therefore 3.40\times {{10}^{22}}\text{ atoms}\to \dfrac{1}{6.022\times {{10}^{23}}}\times 3.40\times {{10}^{22}}=0.056\text{ moles He} \\
\end{align}\]
Since the molar mass of helium is 4 which means that one mole of He weighs 4 grams. Therefore, we can write it as:
\[\begin{align}
  & 1\text{ mole He}\to \text{4}\text{.00 grams} \\
 & \Rightarrow \text{0}\text{.056 moles He}\to \text{4}\text{.00}\times \text{0}\text{.056 grams}=0.224\text{ grams} \\
\end{align}\]
Hence, the mass, in grams, of $3.40\times {{10}^{22}}$ atoms helium is \[0.224\text{ grams}\].

Note:
The basic unit in which the atomic weight of elements is measured is known as an atomic mass unit. One atomic mass unit (amu) is defined as 1/12th mass of a carbon-12 atom. So, the atomic mass of helium is 4.0026 amu. The atomic mass unit can be converted to grams by the following relation:
\[1\text{ amu}=1.66\times {{10}^{-24}}\text{ g}\]
Using this we can calculate the mass of substances involved in a chemical reaction.