Question

If you have $ 2.4\times {{10}^{24}} $ atoms of copper, how many moles of copper do you have?

Answer 1

Hint: $ 1 $ mole is defined as the quantity which contains Avogadro’s number $ \left( {{N}_{0}} \right) $ i.e. $ 6.022\times {{10}^{23}} $ particles in it, in case of elements one mole contains Avogadro’s number of atoms, Now using this knowledge we can easily calculate the number of moles of Copper if we know the number of Copper atoms present.

Complete step-by-step answer:
Copper is an element that belongs to the $ {{12}^{th}} $ group and $ {{4}^{th}} $ period i.e. it lies in the d-block of periodic table and also falls under the category of Transition Metals; It has an atomic mass of $ 63.546u $ . Now, knowing the number of moles of Copper present in the sample we can use its molar mass value in grams to get the mass of the whole sample provided. Thus, knowing the number of moles we can clearly get many more details on the sample.

In our question we are provided with the total number of Copper\[\left( Cu \right)\]atoms which is numerically equal to $ 2.4\times {{10}^{24}} $ atoms of copper.
One Mole of Copper $ \left( Cu \right) $ contains $ 6.022\times {{10}^{23}} $ atoms of Copper or,
 $ 6.022\times {{10}^{23}} $ Atoms of atom comprises of $ 1 $ mole of Copper,
Thus, $ 1 $ atom of Copper equals $ \dfrac{1}{6.022\times {{10}^{23}}} $ moles of copper
Therefore, $ 2.4\times {{10}^{23}} $ atoms of Copper equals $ \dfrac{2.4\times {{10}^{24}}}{6.022\times {{10}^{23}}}=\dfrac{24\times {{10}^{^{23}}}}{6.022\times {{10}^{23}}}=3.985387 $ moles of Copper or,
 $ 2.4\times {{10}^{23}} $

A copper atom approximately has $ 4 $ moles of Copper.

Note: It is to be noted that by knowing the molar mass of the elements in a compound, we can calculate the molar mass of the compound, by adding up the individual molar masses of the elements. For example, the molar mass of water is $ 2\times 1+16=18gmo{{l}^{-1}} $ .