Question

A cylinder of argon gas contains $50.0L$ of $Ar$ at $18.4atm$ and ${127^\circ }C$. How many moles of argon are in the cylinder?

Answer 1

Hint: As we know the term mole which is given as the ratio of the given mass of any substance or compound to the molecular mass of the given substance or compound. We can calculate it by knowing the mass and molecular mass of the compound. We also know the moles are directly related to the number of atoms as well as molecules and volume of a substance.

Complete step-by-step answer:
As we already know the mole concept where a mole is defined when mass of a substance is divided by the molecular mass of that substance. Mole number is commonly expressed as shown below:
$\Rightarrow moles = \dfrac{{mass}}{{molecular\;mass}}$

Now, along with moles, we can also calculate the other parameters such as the volume of any substance at NTP or STP, number of atoms, number of molecules and many more in a given mass of any substance using the below formula:
$\Rightarrow moles = \dfrac{{mass}}{{molecular\;mass}} = \dfrac{{Vol.\;at\;STP}}{{22.4L}} = \dfrac{{no.of\;atoms\;or\;molecules}}{{{N_A}}}$

Now, we are given with the volume of Argon gas in a cylinder which is $50.0L$ and we also have the relation between moles and volume, so we will get the number of moles of argon as:
$\Rightarrow moles = \dfrac{{Vol.\;at\;STP}}{{22.4L}}$
$\Rightarrow moles = \dfrac{{50.0}}{{22.4}}$
$\Rightarrow moles = 2.23mol$

Therefore, the correct answer is $2.23mol$ are there in $50.0L$ of argon gas cylinder.

Note: Always remember that the ratio of mass to the molecular mass is equivalent to its number of moles which in turn is equivalent to the ratio of number of atoms or number of molecules to the Avogadro’s number. We can also calculate the volume of a substance at normal conditions of temperature and pressure as well as standard conditions if we know its number of moles.