Question

What is the density of carbon dioxide at STP? (\[C = 12.01g/mol\],\[O = 16.00g/mol\])

Answer 1

Hint: For this, the first thing we need to know is that we can find the density of any compound if we know its volume and mass. This is because density is the quotient of mass and volume. So here is it the molar mass of this compound by its volume when there is standard temperature and pressure.

Complete step by step answer:
Let us note down what is given to find the density of $C{O_2}$;
Given that: atomic mass of each individual element here is;
$ \Rightarrow C = 12.01g/mol$, $ \Rightarrow O = 16g/mol$
Also since STP is mentioned, let us find out what standard temperature and pressure gives;
It gives the volume that the compound $C{O_2}$ here has $ \Rightarrow V = 22400c{m^3}$
Now we just need to calculate the required density of $C{O_2}$.
For this we can use the formula of density where;
$ Density = \dfrac{{mass}}{{volume}}$
$ $ $Density{\text{ }}of\;C{O_2} = \dfrac{{molar\;mass\;of\;C{O_2}}}{{Volume\;at\;S.T.P}}$
Now let us move on to finding the required substituents;
Molar mass of $C{O_2}$can be calculated as;
$ \Rightarrow Molar\;mass = (12.01 + 2 \times 16)\;g/mol$
Therefore molar mass of $C{O_2}$
$ \Rightarrow $\[Molar{\text{ }}mass{\text{ }}of\;C{O_2} = 44.01\;g/mol\]
Then we volume occupied by molar weight of $C{O_2}$;
$ \Rightarrow Volume = 22400\;c{m^3}$
Substituting the values of molar mass and volume in the formula for density of $C{O_2}$;
 $ \Rightarrow Density\;of\;C{O_2} = \dfrac{{44.01\;g/m}}{{22400\;c{m^3}}}$
Simplifying we get;
$ \Rightarrow Density\;of\;C{O_2} = 0.00195\;g/c{m^3}$
Therefore at standard temperature and pressure, the density of carbon dioxide will be $0.00195\;g/c{m^3}$.

Note:
Since density is dependent on the volume and mass of the compound, when changes happen to them we need to remember that the density will not remain constant. The relation will be in this manner; if we reduce the volume of the compound then it will result in an increase in the density. Also as the molar mass of the compound goes higher the density of such a compound will also be quite high.