Question

Is the number of molecules in $1kg$of ${H_2}$ and $1kg$ of ${O_2}$ the same? What is the ratio of weights of ${H_2}$ and ${O_2}$ , the mixture of which contains an equal number of molecules of each gas?

Answer 1

The number of molecules can be calculated by multiplying the Avogadro’s number with the number of moles. The moles can be calculated from weight of substance and molar mass of substance. The molar mass of oxygen gas is $32$ atomic mass units and mass of hydrogen gas is $2$ atomic mass units.

Complete answer:
Given that the weight of hydrogen gas and oxygen gas is one kilogram. One kilogram is equal to $1000$ grams. The molar mass of hydrogen gas is $2$ atomic mass units and the molar mass of oxygen gas is $32$ atomic mass units.
Though the weight is same, the number of moles was different which leads to the difference in the number of molecules.
Thus, the number of molecules in $1kg$of ${H_2}$ and $1kg$ of ${O_2}$ were not the same.
The weight of hydrogen gas and oxygen gas are the product of molar mass and number of moles.
Given that the mixture contains an equal number of molecules of each gas which means the same number of moles.
Thus, the ratio of weights of ${H_2}$ and ${O_2}$ will be ratio of molar mass of ${H_2}$ and ${O_2}$ which is $2:32$On simplification, we will get $1:16$.

Note:
The number of moles were the quantity used to express the amount of substance. The number of molecules, atoms or ions present in one mole is equal to $6.023 \times {10^{23}}$ , this number can be called Avogadro's number which is the value of one mole.