Question

An evacuated glass vessel weighs $50g$ when empty, $148g$ when filled with a liquid density $0.98gm{l^{ - 1}}$ and $50.5g$ when filled with ideal gas at $760mmHg$ $300K$. Determine the molar mass of the gas. [Write your answer to the nearest integer]..

Answer 1

Hint: We know that the mass per unit volume is the density of a material and it is used to calculate the rigidity of the material.
${\text{Density}} = \dfrac{{{\text{Mass}}}}{{{\text{Volume}}}}$

Complete step by step answer:
Given,
The mass of an empty vessel is $50g$.
The mass of a vessel filled with gas is $50.5g$.
The mass of the liquid filled in the vessel is$148g$.
The density of the liquid is $0.98gm{l^{ - 1}}$
The pressure of the ideal gas is $760mmHg$.
The temperature is $300K$.
Now, calculate the mass of the ideal gas as,
${\text{Mass of ideal gas}} = 50.5 - 50 = 0.5g$
The mass of the liquid is calculated as,
${\text{Mass of liquid}} = 148 - 50 = 98g$
Let us calculate the volume using the density formula.
${\text{Volume}} = \dfrac{{{\text{Mass}}}}{{{\text{Density}}}}$
${\text{Volume}} = \dfrac{{98}}{{0.98}} = 100ml = 0.1L$
We can calculate the molar mass of a substance liberated from the ideal gas equation.
The ideal gas equation is,
$PV = nRT$
We know that, the amount of moles in given amount of any substance is equal to the grams of the substance divided by its molecular mass of the substance,
${\text{Moles}}\left( {\text{n}} \right) = \dfrac{{{\text{Mass}}\left( W \right)}}{{{\text{Molecular mass}}\left( M \right)}}$
Thus, the ideal gas equation becomes.
$PV = \dfrac{W}{M}RT$
$\left( {\dfrac{{760}}{{760}}} \right) \times 0.1 = \dfrac{{0.5}}{M}\left( {0.0821Latmmo{l^{ - 1}}{K^{ - 1}}} \right)\left( {300K} \right)$
The molar mass of substance = $123.15 \approx 123g$.

Note:
Now we can discuss about the details of molar mass as,
Molar mass of an element is defined as the atomic mass of an element present in Avogadro’s number of atoms. To find the molar mass, one must have to change the units of atomic mass from the atomic mass unit to grams.
For example, sulfur has an atomic mass of $32amu$ so one mole of sulfur has a molar mass of $32g$ and contains Avogadro’s number of atoms.
Remember to convert the pressure in millimeter mercury $\left( {mmHg} \right)$ to the standard atmosphere unit by dividing the given value by $760$.