Question

How many molecules are present in $4.4$moles of ${\text{C}}{{\text{O}}_2}$gas?

Answer 1

Hint:To answer this question, you must recall Avogadro's number. The Avogadro’s constant or Avogadro’s number gives the number of molecules/ atoms/ ions present in one mole of a substance.

Complete answer:
The value of Avogadro’s constant is $6.023 \times {10^{23}}$.
1 mole of any substance contains $6.023 \times {10^{23}}$particles. Hence the molecules present in $4.4$moles of ${\text{C}}{{\text{O}}_2}$gas are given by
\[N = 4.4 \times 6.022 \times {10^{23}}\]
$\therefore N = 2.6501 \times {10^{24}}$molecules.

Additional information:
 Just like one mole of a substance contains a fixed amount of particles, similarly, one mole of a gas also occupies fixed volume at constant pressure and temperature. We can find the volume of one mole of gas at standard conditions using the Ideal Gas Equation (Assuming all gases to be ideal)
We know that the ideal gas law is given by the expression \[PV = nRT\]
STP (standard temperature and pressure) represents the conventional physical conditions set by IUPAC at which $T = 273K$ and $P = 1atm$
Also, we know that $R = 0.0821{\text{L}}{\text{.atm/(Kmol)}}$
Now, putting these values into the ideal gas equation, we can calculate the volume for 1 mole of gas as,
$PV = nRT$
$ \Rightarrow (1{\text{atm}})(V) = (1{\text{mol}})[0.0821{\text{L}}{\text{.atm/(Kmol)}}](273{\text{K}})$
$ \Rightarrow V \approx 22.4L$
Thus, we can conclude that volume occupied by one mole of a gas at standard conditions is found to be $22.4{\text{Litres}}$.

Note:
The value of the Avogadro constant is given in such a way so that the mass of one mole of any given chemical substance (in grams) has the same numerical value (for all practical purposes) as the mass of one molecule of the substance in terms of atomic mass units (amu). One atomic mass unit is $1/12th$ of the mass of one carbon- 12 atom. It is approximately equal to the mass of one proton or one neutron.