Question

What volume will $454\,gms\,(1\,lb)$ of hydrogen occupy at $1.05\,atm\,$and ${25^ \circ }C$?

Answer 1

Hydrogen is the only gas which reacts or acts or behaves closely to any idea gas ever be theorised. All the other gases in actual and real conditions follow the real gas equation.

Complete answer:
The ideal gas is defined as $pV = nRT$
p is equal to the pressure, in units of atm.
V is the volume that the gas occupies and it is measured in litres,
N is the number of moles of the gas present and moles is unitless.
R is the universal gas constant,
T is the temperature of the gas in Kelvin.
First let's calculate the number of moles of Hydrogen present:
$moles = \dfrac{{given\,mass}}{{molecular\,mass}}$
Molecular mass of hydrogen atom is $2gm$
$moles\,of\,{H_2} = \dfrac{{454}}{2} \\\ \Rightarrow moles\,of\,{H_2} = 227\, \\\$
Given that the temperature is ${25^ \circ }C$, let convert it to kelvins for which we have to just add $273$ to the temperature i.e.
$temp\,in\,K = 25 + 273 = 298\,K$
Now we have various quantities for the hydrogen gas, we have the moles, we have the universal constant, temperature and the pressure of the gas and what we need to calculate is the volume.
As we know from the ideal gas equation $pV = nRT$
Then we can also say that $V = \dfrac{{nRT}}{p}$
Putting the values of moles, constant, temperature and the pressure.
$V = \dfrac{{nRT}}{p} \\\ \Rightarrow V = \dfrac{{227 \times 0.082057 \times 298}}{{1.05}} \\\ \Rightarrow V = 5286.8278\,L \\\$
As we can see the calculated $V = 5286.8278\,L$ when we put the values in the ideal gas equation.
The volume of the hydrogen gas is $V = 5286.8278\,L$.

Note:
Very few gases that are there that can act ideal but by tweaking the ideal gas equation we can obtain the real gas equation which also has the R constant.