Question

Number of molecules present in \[4.2g\] of \[{N_2}\] is \[x \times {10^{22}}\] . What is the value of \[x\] (round off to one digit)?

Answer 1

Hint: The number of molecules of any given element having a specific mass can be determined by finding out the amount of that element (number of moles). The mole concept relates the mass of any molecule with the number of molecules associated with it.

Complete answer:
Nitrogen is a diatomic gas consisting of two nitrogen atoms strongly and covalently bonded to each other. The triple bond formation between two nitrogen atoms in a molecule makes it inert (unreactive) at room temperature.
The number of moles of nitrogen molecules present in \[4.2g\] mass can be calculated using the ratio of the given mass and the molar mass of the nitrogen molecule.
The formula for calculating the number of moles is given as follows:
\[n = \dfrac{{{\text{given mass}}}}{{{\text{molar mass}}}}\]
The given mass of a nitrogen molecule is \[4.2g\] and the molar mass is \[28gmo{l^{ - 1}}\] . On inserting these values in the formula we get,
\[n = \dfrac{{4.2g}}{{28gmo{l^{ - 1}}}} = 0.15mol\]
Now, the number of moles can be used to determine the number of molecules by multiplying the number of moles with Avogadro's number. As one mole of any element or compound contains the number of atoms or molecules equal to the Avogadro’s number. The value of Avogadro’s number is \[6.022 \times {10^{23}}\]
Thus, the number molecules will be:
\[{\text{number of molecules}} = 0.15mol \times 6.022 \times {10^{23}} = 9.033 \times {10^{22}}\]
On comparing the number of molecules with a given value i.e. \[x \times {10^{22}}\] we get that the rounded off value of \[x\] is \[9\] .

Note:
The molar mass of a nitrogen molecule is numerically equal to its molecular mass but has different units. The molar mass can be calculated by multiplying the mass of one nitrogen atom by its stoichiometric number which is two as nitrogen is a diatomic molecule.