Question

It was found that 380 mL of a gas at 27 and 800mm of Hg weighed \[0.455\] g. Find the molecular weight of the gas.

Answer 1

Hint: We will use the ideal gas equation here. All the other variables are given to us. Number of moles is mass divided by molar mass. We shall calculate the moles of gas present and then its molecular mass using the mass of gas formed.

Formula used:
\[{\text{PV}} = {\text{nRT}}\]
where P is pressure of the gas, V is the volume of gas, n is number of moles of the gas, R is universal gas constant and T is the temperature.
Number of moles can be given as: \[{\text{moles}} = \dfrac{{{\text{mass}}\left( {{\text{gram}}} \right)}}{{{\text{molar mass}}\left( {{\text{g}}/{\text{mol}}} \right)}}\],
universal gas constant is given as: \[{\text{R}} = 8.31\dfrac{{{\text{joule}}}}{{{\text{mole}} - {\text{K}}}} = 2\dfrac{{{\text{Cal}}}}{{{\text{mole}} - {\text{K}}}} = 0.082\dfrac{{{\text{L}} - {\text{atm}}}}{{{\text{mole}} - {\text{K}}}}\].

Complete step by step solution:
According to given data in question;
Volume of gas is 380mL or \[0.380\] L because \[\left( {1{\text{L}} = 1000{\text{mL}}} \right)\] ,
Temperature is 27 \[^\circ {\text{C}}\] or 300K because \[\left( {^\circ {\text{C}} = {\text{K}} + 273} \right)\]
Pressure of gas is 800mm of Hg or \[1.052{\text{atm}}\] because \[\left( {1{\text{atm}} = 760{\text{mmHg}}} \right)\]
\[{\text{R}} = 0.082\dfrac{{{\text{L}} - {\text{atm}}}}{{{\text{mole}} - {\text{K}}}}\]
As we have used volume in liters and pressure in atm.
In order to find molar mass or molecular weight of gas, we need to first find the number of moles of gas by using the ideal gas equation.
Applying ideal gas equation to get number of moles of gas:
\[{\text{n}} = \dfrac{{1.052 \times 0.380}}{{0.082 \times 300}} = 0.0162\]
As given mass of the gas is \[0.455\] g.
Thus molecular weight or molar mass can be given as; molar mass \[ = \dfrac{{{\text{mass}}}}{{{\text{no of moles}}}}\]
Thereby molar mass \[ = \dfrac{{0.455}}{{0.0162}} = 28.08\dfrac{{\text{g}}}{{{\text{mol}}}}\]
For real gas or Van der waal gas equation is used; \[\left( {{\text{P}} + {{\text{n}}^2}\dfrac{{\text{a}}}{{{{\text{V}}^2}}}} \right)\left( {{\text{V}} - {\text{nb}}} \right) = {\text{nRT}}\] .

Note: A gas which follows all gas laws and gas equation at every possible temperature and pressure is known as ideal or perfect gas. Potential energy of an ideal gas is taken to be zero. Its internal energy is directly proportional to absolute temperature. All real gas behaves as ideal gas at high temperature and low pressure. Internal energy of real gas depends upon temperature, pressure and volume.