Question

A gas cylinder can hold 1 Kg of hydrogen at room temperature and pressure:
State the law that helped you to arrive at the above result.

Answer 1

Gas is a substance or matter in a state in which it will expand freely to fill the whole of a container, having no fixed shape (unlike a solid) and no fixed volume (unlike a liquid).

Complete Step by Step Solution:
Avogadro’s law helped us to arrive at the result a gas cylinder can hold 1 Kg of hydrogen at room temperature and pressure.
Avogadro’s law states that under the same conditions of temperature and pressure, equal volumes of different gases have the same number of molecules.
Volume ∝ number of molecules (Pressure and temperature constant).
A gas cylinder can hold 1 Kg of hydrogen at room temperature and pressure:
If the number of molecules of hydrogen in the cylinder is X molecules, then the number of $C{{O}_{2}}$ molecules in the cylinder under the same condition of temperature and pressure, will also be same. It will also be X.
From the ideal gas equation PV = nRT, when pressure, volume and temperature are constant, the number of moles of two gases will be same. Hence, the number of molecules of two gases will be same.
A gas cylinder can hold 1 kg.
The mass of hydrogen = $1kg\times 1000{g}/{kg}\;$ = 1000 g.
The molar mass of hydrogen is 2 g/mol.
The number of moles of hydrogen present $=\dfrac{mass}{molarmass}=\dfrac{1000}{2}=500mol$.
Hence, the number of moles of $C{{O}_{2}}$ = the number of moles of ${{H}_{2}}$ = 500 mol.
The number of molecules of $C{{O}_{2}}$ = $500mol\times 6.023\times {{10}^{23}}{molecules}/{mole}\;$
The number of molecules of $C{{O}_{2}}$ = $3.012\times {{10}^{26}}$ molecules.
Hence, A gas cylinder can hold 1 Kg of hydrogen at room temperature and pressure, Avogadro’s law, helped us to arrive at the above result.

Notes:
Always remember, Avogadro’s law states that under the same conditions of temperature and pressure, equal volumes of different gases have the same number of molecules.
Avogadro’s Number $({{N}_{A}})$ is the number of atoms or molecules in one mole of a substance, equal to $6.023\times {{10}^{23}}$