A gas storage tank has a small leak the pressure in the tank drops more quickly if the gas is hydrogen than oxygen. Why?
H2 is a smaller molecule than O2; it effuses through a small hole faster than any other gas. Look up Grahams's Law for further information. The rate of effusion is indirectly proportional to the square root of the molar mass.
The drop in pressure is quicker for hydrogen gas compared to oxygen gas due to their respective molecular properties. To understand this difference, we need to consider the molecular weight, speed of molecules, and the size of the molecules.
Hydrogen gas (H2) has a lower molecular weight than oxygen gas (O2). The molecular weight of hydrogen is about 2 atomic mass units (AMU, also known as Da), while oxygen has a molecular weight of about 32 AMU. The lower molecular weight of hydrogen means that each hydrogen molecule is lighter compared to an oxygen molecule.
In a gas leak situation, the speed at which the gas molecules escape is primarily determined by their kinetic energy and velocity. According to the Kinetic Theory of Gases, the average kinetic energy of gas molecules is directly proportional to the temperature of the gas. Therefore, assuming the temperature is the same for both hydrogen and oxygen, both gases will have similar average kinetic energies.
However, lighter hydrogen molecules have higher average speeds compared to heavier oxygen molecules at the same temperature due to the lower molecular weight. This means that hydrogen molecules move faster and escape more quickly when a leak occurs, leading to a quicker drop in pressure compared to oxygen gas.
Additionally, the size of the gas molecules can also affect the rate of leakage. Oxygen molecules (O2) are larger in size compared to hydrogen molecules (H2). Due to their larger size, oxygen molecules may have a more challenging time squeezing through small openings, resulting in a slower leak compared to hydrogen gas.
In summary, the faster speed and smaller size of hydrogen molecules contribute to a quicker drop in pressure compared to oxygen gas when there is a small leak in a gas storage tank.