Gases with a lighter molecular weight will travel faster than gases with a heavier molecular weight. A container with a mixture of hydrogen gas, helium gas, and oxygen gas in equal amounts has a hole poked in it, allowing the gases to escape. Which of the following is true? A. After 1 minute, more oxygen will have escaped than helium or hydrogen. B. After 30 seconds, more helium will have escaped than oxygen or hydrogen. C. After 3 minutes, there will be less hydrogen in the container than either oxygen or helium. D. All three gases will escape from the container in equal amounts.

Effusion is the process where gas molecules escape through a tiny hole into a vacuum or less pressurized space. Graham's Law of Diffusion tells us that lighter gases effuse faster than heavier ones. According to this law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Mathematically, Graham's Law is expressed as:


where:
rate_1:
The effusion rate of gas 1
\(M_1\) = The molar mass of gas 1
This means you simply divide rate_1 by rate_2 to get their ratio, which is the square root of this ratio of molar masses.
Since lighter gases effuse faster, they leave a container more quickly than heavier gases. This is why, in the given problem, hydrogen (the lightest gas in the mixture) effuses faster than helium and oxygen.

Understanding Graham's Law helps us predict which gas will be more abundant in a container after some of it has effused.

Molecular weight, or molar mass, is a measure of the mass of one mole of a substance. It is usually expressed in grams per mole (g/mol). For our problem, we have three gases: hydrogen (H2), helium (He), and oxygen (O2).

• The molecular weight of hydrogen (H2) is approximately 2 g/mol.
• The molecular weight of helium (He) is around 4 g/mol.
• The molecular weight of oxygen (O2) is roughly 32 g/mol.

With this information, we know hydrogen is the lightest gas, and oxygen is the heaviest among the three. This matters because it affects the effusion rate according to Graham's Law.
By understanding these molecular weights, we can apply Graham's Law and predict which gas will effuse and leave the container fastest.

Gases behave uniquely compared to solids and liquids. One such behavior is known as effusion. As per Graham's Law, lighter gases effuse faster than heavier ones. In a mixture containing gases with different molecular weights, the lighter gas molecules escape quicker.
For instance:

• Hydrogen, due to its tiny molecular weight, effuses very fast.
• Helium, being heavier than hydrogen but lighter than oxygen, has a moderate effusion rate.
• Oxygen, the heaviest of the three, has the slowest effusion rate.

In the given exercise, we see this behavior play out. After 3 minutes, the lighter gases like hydrogen will have mostly escaped from the container, leaving more of the heavier oxygen and a moderate amount of helium inside.
Understanding this behavior allows us to predict which gases will remain in a container over time and highlights the practical use of Graham's Law in everyday situations where gas behavior is important.