Question

Find the number of atoms in $48\,g$ of ozone at NTP.

Answer 1

Here we are going to find the number of atoms for a given quantity of ozone at NTP. Ozone is having a molecular formula of ${O_3}$. And NTP stands for Normal Temperature and pressure which means that the conditions are the same as room conditions.

Complete step by step answer:
Let’s start with discussing the NTP for better understanding of the question. NTP stands for normal temperature and pressure, it is a term which is used to define air at ${25^o}C$ and $1$ atm pressure. We can see the difference of this term with respect to STP, that is, standard temperature and pressure which stands for ${0^o}C$ temperature and $1$ bar pressure.
In the question we are given $48\,g$ of Ozone, Ozone is having the molecular formula of ${O_3}$.
The molecular weight of ozone is $48\,g$. Hence the moles of ozone given to us can be calculated using
${\text{Moles}} = \dfrac{{{\text{Given Mass}}}}{{{\text{Molecular Mass}}}} = \dfrac{{48}}{{48}} = 1$ Mole of Ozone.
According to Avagadro’s number $1$ mole of a molecule contains $6.022 \times {10^{23}}$ molecules.
Hence, $1$ mole contains $6.022 \times {10^{23}}$ molecules.
Similarly each molecule of ozone contain $3$ oxygen atoms, hence
The number of oxygen atoms in $48\,g$ of ozone,
$\Rightarrow 3{\text{ }}X{\text{ }}6.022{\text{ }}X{\text{ }}{10^{23}}$ atoms of oxygen
$\Rightarrow 1.81{\text{ }}X{\text{ }}{10^{24}}$ atoms of oxygen.
Hence,
$\therefore$ The answer to this question is $1.81 \times {10^{24}}$ atoms.

Note:
In many of the questions instead of grams the volume of gas is given along with the volume of the gas. In this usually STP conditions are provided which are ${0^o}C$ temperature and $1$ bar pressure. At this condition it is to be noted that the volume of one mole of gas is $22.4{\text{ L}}$ and using this you can get your answer.