Question

A gas cylinder can hold $\,1Kg\,$ of hydrogen at room temperature and pressure:
i.Find the number of moles of hydrogen present
ii.What weight of $\,C{O_{2\,}}$ can it hold under similar conditions of temperature and pressure. $\,(H = 1,C = 12,O = 16)\,$
iii.If the number of molecules in hydrogen of cylinder is $\,X\,$, calculate the number of $\,C{O_2}\,$ molecules under the same conditions of temperature and pressure
iv.State the law that helped you to arrive at the above results

Answer 1

One of the most impressive things about gases is that all the gases more or less follow the gas laws, despite large variations in chemical properties. In establishing the formulas for simple molecules at a time when the difference between atoms and molecules was not well known, finding that the volume of a gas was directly proportional to the number of particles it produced was a great help. In this question, all solutions belong to this concept.
Here, molecular mass of $\,C{O_2} = 44g\,$. Molecular mass of one hydrogen molecule$\,{H_2} = 2g\,$.

Complete answer:
Let us analyse each question one by one;
i.Mass of hydrogen in $\,grams = 1kg = 1000g\,$
Molar mass of hydrogen molecule$\, = 2g/mol\,$
Therefore,
$\,Number\,of\,moles\, = \dfrac{{Given\,weight}}{{Molecular\,mass}}\,$
$\, \Rightarrow \dfrac{{1000}}{2}\, = 500 mol\,$

ii.Here, it is given that temperature and pressure are constant and volume is also constant as it is in the cylinder itself, so the number of moles are also constant which means the number of moles of hydrogen is equal to the number of moles of carbon dioxide as well. From the ideal gas equation $\,PV = nRT\,$, the number of moles of two gases will be the same while pressure, volume and temperature are constant.
So, we have seen that the number of moles of hydrogen is equal to $\,500mol\,$. In order to find the weight of $\,C{O_2}\,$, here we can apply the same formula of number of moles by rearranging it as follows;
$\,Given\,weight = Number\,of\,moles \times Molecular\,mass\,$
$\, \Rightarrow 500 \times 44 = 22000g = 22Kg\,$

iii.The number of moles is constant here, then number of molecules are constant as well, since;
$\,Number\,of\,molecules = \,number\,of\,moles \times {N_A}\,$
The number of carbon dioxide molecules is therefore equal to $\,X\,$

iv.Avogadro’s law helped us to arrive at the outcomes above. It states that equivalent quantities of all gases produce an equivalent number of molecules at constant temperature and pressure;
$\,V \propto n\,$when temperature and pressure are constant;
$\,V = \,$Volume, $\,n = \,$number of molecules

Note:
Avogadro’s law provides a means for the volume of gas in a receptacle to be measured. The law is substantially valid for real gases at sufficiently low pressures and high temperatures. A perfect example of Avogadro 's law is the mechanism of respiration. The increase in the molar quantity of air in the lungs as humans inhale is followed by an increase in the volume of the lungs (lung expansion).