Question

If 2.30 g occupies 0.870 L at 690 torr and 37 degrees C. How would you calculate the molar mass?

Answer 1

Hint: Calculate the number of moles of the substance by using the ideal gas equation, and then calculate the number of moles by using the formula $no\,of\,mole=\dfrac{given\,mass}{molar\,mass}$

Complete answer:
In order to answer the question, we need to know about moles and molar mass. Now, matter is made up of atoms, and as matter has mass, then the atoms should have an individual mass. Molar mass of an element or compound is the mass which houses $6\times {{10}^{23}}$ particles. For, example, the hydrogen molecule has a molar mass of 2 grams. This means 2 grams of hydrogen contains $6\times {{10}^{23}}$ atoms, and this number is also called the Avogadro’s number.
Number of moles of an element or a compound is the ratio of its given mass taken by the user, to its molar mass. More is the number of moles, more is the concentration of the substance. Now, let us come to the question.
We can use the formula for ideal gas law, by substituting the values given in the question. So, on substituting, we get:
\[\begin{align}
  & PV=nRT \\
 & \Rightarrow n=\dfrac{PV}{RT} \\
 & \Rightarrow n=\dfrac{\dfrac{600}{760}\times 0.87}{0.082\times (273.15+37)} \\
 & \Rightarrow n=0.03106mole \\
\end{align}\]
Now, we have successfully obtained the number of moles, and we have been also given the weight of the substance that is taken. The formula to calculate the number of moles is $no\,of\,mole=\dfrac{given\,mass}{molar\,mass}$, so by using this formula we get the molar mass. On calculating, we have:
\[\begin{align}
  & {{M}_{m}}=\dfrac{m}{n} \\
 & \Rightarrow {{M}_{m}}=\dfrac{2.30}{0.03106}=74.05g\,mo{{l}^{-1}} \\
\end{align}\]
This means that each mole of the substance weights 74.05 grams.

Note:
It is to be noted that 1 bar pressure is equal to 760 torr. So, while calculating, the pressure which was given to be 690 torr, was converted to bar, by dividing it with 760, in order to avoid error.