Question

Calculate the number of molecules in 11 gram of carbon dioxide​.

Answer 1

Hint: The mole concept is very significant and useful in chemistry. It is actually the base of stoichiometry and it provides the best option to express the amounts of reactants as well as products that are consumed and formed during a chemical reaction.

Complete step by step solution:
To calculate the number of moles, we generally use the following formula:
 $ Number{\text{ }}of{\text{ }}moles = \dfrac{{Given{\text{ }}mass{\text{ }}}}{{molecular{\text{ }}mass{\text{ }}of{\text{ }}the{\text{ }}given{\text{ }}species}} $
We know that 1 mole of any substance contains $ 6.023 \times {10^{23}}molecules $
Thus, the number of molecules of any substance can be identified by multiplying the number of moles with Avogadro's number i.e. $ 6.023 \times {10^{23}} $ . We can say:
 $ Number{\text{ }}of{\text{ }}molecules = number{\text{ }}of{\text{ }}moles \times 6.023 \times {10^{23}} $
We know that the molecular mass of any compound can be found out by adding the relative atomic masses of each element present in that particular compound. The chemical formula of carbon dioxide is $ C{O_2} $ . It is clear that carbon dioxide contains one atom of carbon and two atom of oxygen and thus its molecular mass can be calculated by adding the mass of one carbon atom and two oxygen atom as shown below:
 $ Molecular{\text{ }}mass{\text{ }}of{\text{ C}}{{\text{O}}_2} = (1 \times C) + (2 \times O) = (1 \times 12) + (2 \times 16) = 44u $
Mass of $ C{O_2} $ $ = 11g $ (Given)
Substituting the values, we will calculate the number of moles as shown below:
 $ Number{\text{ }}of{\text{ }}moles{\text{ }}of{\text{ }}C{O_2} = \dfrac{{{\text{11 }}}}{{{\text{44}}}} = 0.25 $
Now, using the number of moles of $ C{O_2} $ , we will calculate the number of molecules in 11 gram of carbon dioxide as stated below:
 $ Number{\text{ }}of{\text{ }}molecules = 0.25 \times 6.023 \times {10^{23}} = 1.505 \times {10^{23}} $
Hence, the number of molecules in 11 gram of carbon dioxide is $ 1.505 \times {10^{23}} $ .

Note:
Avogadro's number was actually obtained by dividing charge of one mole of electrons by the charge of one single electron that equals $ 6.02214154 \times {10^{23}}\; $ particles per mole. In order to convert moles into atoms, we can multiply the moles with Avogadro's number and if we want to convert atoms into moles, divide the number of atoms by Avogadro's number.