Question

Explain how one is able to find molecular formula or the moles in a substance by the help of gas laws? That is, explain this equation: $ n = \dfrac{m}{M} $ .

Answer 1

Hint :We need to know what the ideal gas equation means or says, and depending on that a few laws were formulated which are today called the gas laws. The gas law we use here is called Ideal gas law that says that gas is something that has no volume and no attraction to its constituent particles. Remember that the way we can calculate the number of moles in a substance is by using its mass and molar mass, where molar mass is the $ grams/mol $ form of the atomic weight.

Complete Step By Step Answer:
Since we know what the ideal gas law says, we can see how it will help us to calculate molecular formula or number of moles. That helps us to find this formula.
Now let us proceed to how we can find the formula for number of moles:
Firstly from the question, we will be able to identify the empirical formula of the compound. From that we can automatically find molar mass. Lastly rearrange that equation to get the molecular formula or number of moles.
That in terms of equation looks like;
Molar mass $ M = \dfrac{m}{n} $ , where $ m $ is mass and $ n $ is number of moles
Then rearrange to get: $ n = \dfrac{m}{N} $
With an example we will understand this type of problem better;
Consider the empirical formula of cyclopropane: $ CH2 $ .
Given temperature as $ {50^ \circ }C $ , pressure $ 0.984\;atm $ , mass of $ 1.56g $ and volume of $ 1\;L $ . Give cyclopropane’s molecular formula.
Substitution values into the ideal gas law;
 $
  PV = nrT \\
    \\
   \Rightarrow n = \dfrac{{PV}}{{RT}} \\
    \\
   \Rightarrow n = \dfrac{{0.984 \times 1}}{{0.08206 \times 323.2}} \\
    \\
   \Rightarrow n = 0.0371\;mol \\
  $
And the molar mass is;
 $
   \Rightarrow M = \dfrac{m}{n} \\
    \\
   \Rightarrow M = \dfrac{{1.56}}{{0.0371}} \\
    \\
   \Rightarrow M = 42\;g/mol \\
  $
 $ CH_2 $ ’s empirical formula mass $
   = 12.01 + 2.016 \\
   = 14.03\;g/mol \\
  $
Therefore number of moles will be;
 $
   \Rightarrow n = \dfrac{m}{M} \\
    \\
   \Rightarrow n = \dfrac{{42}}{{14.03}} \\
    \\
   \Rightarrow n \approx 3 \\
    \\
  $
So molecular formula of $ CH_2 = (CH_2)_3 $

Note :
Ideal gas equation is as follows:
 $ PV = nRT $ , in words it says that the product of volume and pressure of gas is proportional to the temperature. Here $ P $ = pressure of ideal gas, $ V $ = volume of the same, $ T $ = temperature, $ n $ = gives number of moles of gas, $ R $ = universal gas constant.
The gas laws which are made are from this ideal gas equation, the few laws are named as Boyle’s law, Charles’ law, Avogadro’s law, Ideal gas law.