Question

A sample of carbon dioxide gas contains $6\times {{10}^{22}}$ molecules. How many moles of carbon dioxide does it represent?

Answer 1

This question is based on the concept of Avogadro number and number of moles. We know that atoms combine to make molecules and one mole of any substance contains many molecules. Here, we need to find out the number of moles of carbon dioxide which contains $6\times {{10}^{22}}$ molecules. For this we will use Avogadro number.

Complete step-by-step answer: We know that one mole of any substance at STP contains $6.0\times {{10}^{23}}$ atoms/molecules/constituents and 22.4 L of volume.
$6.02\times {{10}^{23}}$ is also known as Avogadro number denoted by ${{N}_{A}}$ in honour of Amedeo Avogadro.
From the above statement we can say that,
$6.02\times {{10}^{23}}$ molecules of substance make up one mole of that substance
Therefore, using unitary method, we can say that
1 molecule of a substance is made up of = $\dfrac{1}{6.02\times {{10}^{23}}}$ moles of that substance.
Here, we have to find out the number of moles of carbon dioxide
Therefore, $6\times {{10}^{22}}$ molecule of carbon dioxide is made up of = $\dfrac{1}{6.02\times {{10}^{23}}}\times 6\times {{10}^{22}}$ moles of it.
On solving we get,
$\Rightarrow \dfrac{1}{6.02\times {{10}^{23}}}\times 6\times {{10}^{22}}=\,0.099$ or $0.1000$ moles of carbon dioxide.

Hence, $6\times {{10}^{22}}$ molecules of carbon dioxide represent $0.1000$ moles of it.

Note: While solving the problems based on the mole concept and Avogadro number always determine the starting and ending step firstly, that what exactly is given to you and what you are asked to find. Then use a unitary method for deriving a relation and then solve the question by simply substituting the values in the relation.