Question

The maximum number of molecules is present in:
A. 15L of ${{\text{H}}_{\text{2}}}$ gas at STP
B. 5L of ${{\text{N}}_{\text{2}}}$ gas at STP
C. 0.5g of ${{\text{H}}_{\text{2}}}$ gas
D. 10g of ${{\text{O}}_{\text{2}}}$ gas

Answer 1

The different types of the gases have the same number of the molecules in them if they have the same number of moles which is directly proportional or equal to the Avogadro number. So we find the number of moles by just dividing the mass of the substance given by the molar mass of that substance. And we can also find the number of moles by dividing the given volume by 22.4L as 1 mole is equal to the 22.4 L.

Complete step by step answer:
So as I told you that to find the number of molecules we need to find the number of moles in the substance given. As the number of moles is directly proportional to the number of molecules. As we know to calculate the moles we need to divide the given volume by 22.4L. so let us do it first for 15L of hydrogen gas.
So the given volume is 15L and the formula we will be using is the following:
Moles = $\dfrac{{{\text{given volume}}}}{{{\text{22}}{\text{.4L}}}}$
Now substituting the value we get,
Moles=$\dfrac{{15L}}{{{\text{22}}{\text{.4L}}}}$=0.669 moles
Now for 5L of nitrogen of volume given to us we will substitute it in the formula above we get,
Moles= $\dfrac{{5L}}{{{\text{22}}{\text{.4L}}}}$=0.223 moles
Now for the option c 0.5 g of hydrogen we need to calculate the number of moles. So we need to divide the given mass by the molar mass. So the molar mass of the hydrogen is 2$gmo{l^{ - 1}}$. The formula we will be using is the following:
Moles=$\dfrac{{{\text{given mass}}}}{{{\text{molar mass}}}}$
Now substituting the values we get,
Moles =$\dfrac{{0.5}}{2}$=0.25 moles
Now the molar mass of oxygen is 32$gmo{l^{ - 1}}$. So the moles of it for 10g of oxygen will be the following:
Moles= $\dfrac{{10}}{{32}}$=0.3125 moles
So as I told you, the number of moles is directly proportional to the number of molecules so the substance with the largest number of moles has the maximum molecules and that is 15L of hydrogen gas at STP which is option a.

So, the correct answer is Option A.

Note: The term of the mole concept was given to us by Wilhelm Ostwald. We use the concept of moles for measuring the smallest particles such as that of atoms. So for converting the number of moles into the number of molecules we need to multiply it by the Avogadro number.