Question

The density of gas was found to be 3.43g/l at 300K at $1.00atm$. Calculate the molar mass.

Answer 1

The molar mass of a gas can be derived from the ideal gas law,$PV=nRT$, by using the definition of molar mass to replace n , the number of moles. Molar mass is the mass of a substance that has $6.022\times 1023$ particles (Avogadro's number). The mass number of a component is equivalent to the molar mass of the component. The molar mass of a substance compound is the mass when the compound has $6.022\times 1023$ particles.

Complete step by step solution:
To solve this question. First we need to clear the concepts mentioned in the question.
Density is characterized as its mass per unit volume. Put another way, Density is the ration among mass and volume or mass per unit volume.
Molar mass is the mass of all the atoms of a molecule in grams for each mole. Molar mass can be utilized to figure the mass of a compound and to change moles to grams.

Mathematically, Density $=\dfrac{mass}{volume}...........(1)$
And, Number of moles $=\dfrac{mass}{molar mass}...........(2)$
Now, equating the equations (1) and (2) we get the following:
$V=\dfrac{n\times M}{d}........(3)$
And, the equation for ideal gas is
$PV=nRT$
Therefore inserting the given values and using equation (3)
$PV=nRT$
$\Rightarrow P\dfrac{n\times M}{d}=nRT$

$$\Rightarrow P\dfrac{M}{d}=RT \\\ \Rightarrow 1atm\times \dfrac{M}{3.43gm/{{l}^{3}}}=0.0821atmL/molK\times 300K \\\ \Rightarrow M=84.48g/{{l}^{2}} \\\$$

Hence, the molar mass is $84.48g/{{l}^{2}}$.

Note: A gas is viewed as ideal if its particles are so far separated that they don't apply any attractive forces upon each other. In actuality, there is nothing of the sort as a really ideal gas, however at high temperatures and low pressure (conditions in which individual particles will be moving rapidly and be exceptionally far separated from each other so their association is right around zero), gases act near to ideally; this is the reason the Ideal Gas Law is such a valuable estimation.