Question

3.16 gm of an ideal gas was injected into a bulb of the internal volume of 8L at pressure $ P $ atm and temp $ T $ K. The bulb was then placed in a thermostat maintained at $ \left( {T + 15} \right){\text{ K}} $ . $ 0.6 $ gm of the gas was let off to keep the original pressure.
Find $ P $ and $ T $ if the molecular weight of the gas is 44.
(A) $ P = 0.062{\text{ atm, }}T = 75{\text{K}} $
(B) $ P = 1.062{\text{ atm,}}T = 75{\text{K}} $
(C) $ P = 2.062{\text{ atm}},T = 55{\text{K}} $
(D) $ P = 3.062{\text{ atm}},T = 55{\text{K}} $

Answer 1

Hint: We need to find the pressure and temperature. We can simply use the ideal gas equation to find the required data. We are going to use the ideal gas equation:
 $ PV = nRT $
Here, $ P $ is the pressure of the gas
 $ V $ is the volume of the gas
 $ n $ is the number of moles
 $ R $ is the universal gas constant
 $ T $ is the temperature of the gas.

Complete step by step answer
We already know that the molecular weight of the gas is 44.
Amount of ideal gas given is 3.6gm.
Volume of ideal gas is 8L.
So, the initial moles, $ n = \dfrac{{3.6}}{{44}} $
Final moles $ n' = \dfrac{{3.6 - 0.6}}{{44}} = \dfrac{{3.0}}{{44}} $
Now pressure and volume are constant,
Using the ideal gas equation,
 $ {n_1}{T_1} = {n_2}{T_2} $
On putting the values,
 $ \dfrac{{3.6}}{{44}} \times T = \dfrac{{3.0}}{{44}} \times \left( {T + 15} \right) $
 $ T = 75K $
Again, applying the inert gas equation,
 $ P = \dfrac{{nRT}}{V} = \dfrac{{0.0818 \times 75 \times 0.0821}}{8} = 0.062{\text{atm}} $
Thus, pressure and temperature respectively are 0.062atm and 75K.
We need to select the correct option.
The correct option is A.

Note
The ideal gas law $ PV = nRT $ was discovered by physicist and engineer Clapeyron in 1834.The term ideal gas refers to a hypothetical gas composed of molecules which follow a few rules: Ideal gas molecules do not attract or repel each other. The only interaction between ideal gas molecules would be an elastic collision upon impact with each other or an elastic collision with the walls of the container.
The ideal gas law is a valuable tool in understanding state relationships in gaseous systems. For example, in a system of constant temperature and pressure, the addition of more gas molecules results in increased volume.
The real gas that acts most like an ideal gas is helium. This is because helium, unlike most gases, exists as a single atom, which makes the van der Waals dispersion forces as low as possible. Another factor is that helium, like other noble gases, has a completely filled outer electron shell.