Question

Calculate the number of molecules and number of atoms present in 11.2 litres of $O_2$ at NTP.

Answer 1

NTP, or Normal Temperature and Pressure, conditions imply a temperature of ${20}^{\circ }$ C, or 293.15 K, and a pressure of 1 atm.
T = 293.15 K
P = 1 atm
Since you also know the volume the gas occupies under these conditions, you can easily solve for the number of moles present by using the ideal gas law equation,
PV = nRT.
Once you know how many moles of oxygen gas you have, you can calculate the number of oxygen molecules by using the fact that 1 mole of any substance contains
exactly ${\mathrm{6.022.10}}^{23}$ molecules of that substance - this is known as Avogadro's number.
So, start by figuring out he number of moles you have
$PV=nRT\Rightarrow n=\frac{PV}{RT}n=\frac{1\text{/}atm.11.2\text{/}L}{0.082(\text{/}L.\frac{\text{/}atm}{mol.\text{/}K}.293.15\text{/}K)}=0.4659$ moles $O_2$
This is equivalent to having
$0.4659\text{/}moles.\frac{{\mathrm{6.022.10}}^{23}molecules}{1\text{/}mole}={\mathrm{2.81.10}}^{23}$ molecules
Since oxygen is a diatomic molecule, i.e. it takes two oxygen atoms to make up an oxygen molecule, the number of oxygen atoms will be twice as big
${\mathrm{2.81.10}}^{23}\text{/}molecules.\frac{2atoms}{\text{/}1molecule}={\mathrm{5.62.10}}^{23}atoms$