Question

How would you find the molecular weight of unknown gas?

Answer 1

Hint: To solve this question, first we will determine the mass of the fixed volume of a gas at given temperature and pressure and then we will apply the Ideal gas law equation which is a general gas equation to find the molecular weight of unknown gas. First list down the known quantities that are known like mass(\[{\text{m}}\]), volume (\[{\text{V}}\]), temperature (\[{\text{T}}\]), pressure(\[{\text{P}}\]) and universal gas constant (\[{\text{R}}\]), n is number of moles.

Complete step by step answer:
We know that ideal gas law is a mathematical relation between pressure, volume, number of moles,temperature and universal gas constant and it is written as
\[{\text{PV = nRT}}\]
By applying molar mass definition we can replace \[{\text{n}}\](i.e. number of moles) as,
We know that \[{\text{M = }}\dfrac{{\text{m}}}{{\text{n}}}\]
So we can write that \[{\text{n = }}\dfrac{{\text{m}}}{{\text{M}}}\].
Substituting the value of \[{\text{n}}\] in ideal gas law equation to calculate the molecular weight and it is,
\[{\text{PV = }}\dfrac{{\text{m}}}{{\text{M}}}{{ \times RT}}\]
\[{\text{M = }}\dfrac{{{\text{mRT}}}}{{{\text{PV}}}}\]
\[{\text{M = m}} \times \dfrac{{{\text{RT}}}}{{{\text{PV}}}}\]………………..\[i\]
For eg, an unknown gas with mass of \[200\]g has volume of \[20\]lts at standard temperature and pressure. Find out how to calculate molecular weight of gas. Putting all the values in equation \[i\], we get
\[{\text{M = 200}} \times \dfrac{{{\text{0}}{\text{.0821}} \times {\text{273}}}}{{1 \times 20}}\]
\[{\text{M = 200}} \times {\text{1}}{\text{.120}}\]
On simplification we get,
\[ \Rightarrow {\text{M = 224}}{\text{.13}}\]
In this way by using the equation \[i\] we can easily calculate the molecular weight of an unknown gas.

Note:
We need to remember that the molecular weight also known as molar mass is the mass of one mole of a substance. It is expressed in grams/mole. It should be noted that if we know the molecular weight or molar mass of a compound then we can easily balance the chemical reaction. Molar masses of different gases vary always but molar volumes of all gases are the same when measured at standard temperature and pressure conditions. Molecular weight can also help to find the molecular formula of a compound.