Question

What is the mass of carbon dioxide which contains the same number of molecules as are contained in 40 g of oxygen?
(A) 40 g
(B) 55 g
(C) 44 g
(D) 32 g

Answer 1

Hint: A mole of any substance contains Avogadro’s number of molecules. Avogadro’s number of molecules is \[6.023 \times {10^{23}}{\text{ molecules/mol}}\] . The mass of one mole of a substance is equal to its molecular weight.

Complete step by step answer:
The chemical formulae of carbon dioxide gas and oxygen gas are \[{\text{C}}{{\text{O}}_{\text{2}}}\] and \[{{\text{O}}_{\text{2}}}\] respectively. The atomic weights of carbon and oxygen are \[{\text{12 g/mol}}\] and \[{\text{16 g/mol}}\] respectively.
Calculate the molecular weight of \[{{\text{O}}_{\text{2}}}\]
16 g/mol + 16 g/mol = 32 g/mol
Calculate the molecular weight of \[{\text{C}}{{\text{O}}_{\text{2}}}\]
12 g/mol + 16 g/mol + 16 g/mol = 44 g/mol
The number of molecules of oxygen present in \[{\text{40 g}}\] are \[\dfrac{{40}}{{32}} \times {{\text{N}}_{\text{A}}}\].
Here, \[{{\text{N}}_{\text{A}}}\] is Avogadro's number.
There are same number of molecules of carbon dioxide,
The number of molecules of carbon dioxide present are \[\dfrac{{40}}{{32}} \times {{\text{N}}_{\text{A}}}\].
But the number of molecules of carbon dioxide present are \[\dfrac{m}{{44}} \times {{\text{N}}_{\text{A}}}\].
Here, m represents the mass of carbon dioxide gas.
Hence,
\[\dfrac{m}{{44}} \times {{\text{N}}_{\text{A}}} = \dfrac{{40}}{{32}} \times {{\text{N}}_{\text{A}}} \\
m = \dfrac{{44 \times 40}}{{32}} \\
= 55{\text{ g}}\]
Thus, the mass of carbon dioxide which contains the same number of molecules as are contained in 40 g of oxygen is 55 g.

Hence, the option (B) is the correct answer.

Note: You can obtain the number of moles of a substance by dividing its mass with its molecular mass. You can convert the number of moles of a substance into the number of molecules by multiplying with Avogadro’s number. When two substances have equal numbers of molecules, they have the same number of moles.