Question

How many molecules are present in 80L of $C{{O}_{2}}$ gas at STP?

Answer 1

Hint: Mole is not only related to mass but also to volume as any matter that has a certain mass will occupy a certain volume. 1 mole is the amount of molecules present in 22.4 litres of a gas calculated at standard temperature and pressure.

Complete step by step solution:
-Everything present in this universe is made up of atoms. The mass of an atom cannot be measured truly due to its very small size. So a relative term is used for it called relative atomic mass. It is based on the mass of 1 carbon-12 atom. It was adopted internationally in 1961 and according to it, relative atomic is given by
\[Relative\text{ }atomic\text{ }mass\text{ }=\text{ }\dfrac{mass\text{ of 1 atom of element}}{\dfrac{1}{12}\times \text{ mass of 1 C-12 atom}}\]
-Mole is the amount of substance that contains the atoms, molecules or other particles in an entity equal to the atoms present in 12 g of C-12 isotope. It defines the basis of physical chemistry and so its number is called Avogadro's number which is equal to 6.023x${{10}^{23}}$entities. It is denoted by the symbol ${{N}_{A}}$ .
-Some standard terms used in mole concept are
1 gram-atom = 1 mole atom
1 gram-molecule = 1 mole molecule
1 gram-ion = 1 mole ion
- Avogadro’s number is the number of molecules present in 1 mole which is equal to \[6.023\times {{10}^{23}}\] entities. It is denoted by the symbol ${{N}_{A}}$ . This value is directly used to find the number of atoms in certain different types of molecules which have different representational units.
-In the question, we need to find the number of molecules. We know that the number of molecules is related to the moles and is given by avogadro’s number. So we can have our answer if we find the moles of the gas.
-By simple mathematics, we see that 22.4L of a gas has 1 mole molecule in it. So, 1L of gas will have $\dfrac{1}{22.4}$ moles in it. Hence, 80L of the gas will have $\dfrac{1}{22.4}\times 80$ moles in it.
Thus the number of moles in 80L of gas is 3.57 moles.
-Now we know 1 mole has \[6.023\times {{10}^{23}}\] molecules in it which is given by avogadro’s number. So 3.57 moles will have \[3.57\times 6.023\times {{10}^{23}}\] molecules in it which is equal to \[21.5\text{ }\times \text{1}{{\text{0}}^{23}}\] molecules.

Therefore the correct answer is \[21.5\text{ }\times \text{1}{{\text{0}}^{23}}\]molecules.

Note: Before solving the question for finding the number of molecules when the volume is given and not the mass, always check if the value is asked at STP or not. The moles are linked with the volume of the gas only at STP. For other temperatures and pressures, we cannot directly solve for the number of molecules.