Question

Mass of $200ml$ of gas at $1atm$ pressure and ${27^o}C$ is $0.2g$. Calculate the molar mass of the gas.

Answer 1

In chemistry, every atom, molecule, and ion has a specific mass. It can be calculated by its mass number, number of the atom, and by using gas law equations. In this, the mole concept plays a big role that is based on the Avogadro number.

Complete step by step answer:
Firstly, let's look at the mole and so on.
Mole - It is the unit that is used to measure the amount of substance. In chemistry, it is defined as $1mol = 6.00214076 \times {10^{23}}$ . It is the Avogadro number, using this we can calculate the molar mass.
Molar mass - it is the mass of any substance.
Using the ideal gas equation we can find the molar mass of gas. If we have pressure, temperature, volume, and mass.
ideal gas equation - $PV = nRT$.
Here, $P$ - pressure, $V$ - volume, $T$ - temperature, $n$ - amount of substance, $R$ - ideal gas constant.
We have to find the molar mass of gas, and we have all these things. So, apply the ideal gas equation to get the answer.
Given, $P$ - $1atm$
$V$ - $200ml = 0.2l$
$n$ - ?
$R$ - $0.0821latm/K - mole$
$T$ - ${27^o}c = 300K$
now, find the value of $n$
$n = \dfrac{{PV}}{{RT}} = (1 \times 0.2)/(0.0821 \times 300)mol$
$n = 0.2/24.63mol = 0.0081gm = 24.691gm$
So, the answer is $24.691gm$ .

Note: Isotopes play a big role in varying the mass of the substance. Isotopes - A element has the same number of the proton but a different number of the neutron that is known as isotopes. Avogadro number - when the numeric value of Avogadro constant is defined in a mole that is known as Avogadro number. The ideal gas equation was first given by Benoit Paul Emile Clapeyron in $1834$.