Grade 11 → States of matter → Gas Laws ↓
Graham's law of spread
Graham's law of diffusion is a principle in chemistry that describes the behavior of gases. In simple terms, it tells us that lighter gases diffuse, or spread out, faster than heavier gases when they are allowed to mix. This behavior is based on the principle that gas molecules are in constant random motion. When gases meet, the molecules collide with each other and diffuse out. Understanding this law helps us understand how gases behave under different conditions and is a fundamental concept in chemistry.
Understanding the spread
Diffusion is the process by which molecules spread from areas of high concentration to areas of low concentration. In the context of gases, this means how gas molecules move and mix with each other. For example, when you open a bottle of perfume in a room, the scent quickly spreads throughout the space. This is due to diffusion.
Consider the above example. If each coloured circle represents a different gas molecule, diffusion represents how these coloured circles will spread out uniformly on the line given enough time. Initially, they are far apart, but through random motion, they will eventually fill the space uniformly.
Mathematical expression of Graham's law
Graham's Law provides a quantitative relationship between the rate of diffusion of gases and their molar masses. The mathematics behind Graham's Law can be described using the following equation:
rate of diffusion of gas 1 / rate of diffusion of gas 2 = sqrt(M₂ / M₁)
Here:
rate of diffusion of gas 1
is how fast the first gas diffuses.rate of diffusion of gas 2
is how quickly the second gas diffuses.M₁
is the molar mass of the first gas.M₂
is the molar mass of the second gas.
The equation tells us that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. This means that lighter gases diffuse faster than heavier gases.
Example calculation
Let's consider an example to illustrate Graham's law. Suppose we have two gases: hydrogen (H₂) and oxygen (O₂). The molar mass of hydrogen is about 2 g/mol
, and for oxygen, it is about 32 g/mol
. We want to know how fast hydrogen diffuses compared to oxygen.
rate of diffusion of H₂ / rate of diffusion of O₂ = sqrt(32 / 2) = sqrt(16) = 4
This calculation shows that hydrogen expands 4 times faster than oxygen. Since hydrogen is much lighter than oxygen, it expands more rapidly when the two gases are allowed to mix.
Visualization of spread rates
Consider a simple visualization of gas diffusion rates. Imagine two connected chambers with a barrier between them. Initially, one chamber is filled with hydrogen and the other with oxygen. When the barrier is removed, diffusion occurs.
Over time, hydrogen gas enters the oxygen chamber more rapidly than oxygen, allowing for a more uniform distribution of gases for hydrogen.
Applications of Graham's Law
Graham's Law has many practical applications. It is used in areas ranging from industrial processes to medical treatments. Some of the major applications include:
1. Separation of gases: Graham's law is used in processes such as gas chromatography, where different gases are separated based on their rate of diffusion.
2. Respiratory System: In human physiology, the diffusion of gases in the lungs follows Graham's law as oxygen and carbon dioxide are exchanged.
3. Effusion: This is a related concept where gas escapes through a small hole. Graham's law can predict the rate of effusion based on the molar mass of the gases.
Textual example of gas expansion
Consider a real-world scenario: You are in the kitchen with a pot of boiling water. As the water vapor (steam) rises, it mixes with the air in the kitchen, which is primarily nitrogen and oxygen. Because water vapor is relatively light, it spreads quickly through the kitchen air, creating a humid environment.
Let's apply Graham's Law here. Suppose you compare the diffusion rates of water vapor and carbon dioxide (CO₂). Water vapor has a molar mass of about 18 g/mol
while carbon dioxide has a molar mass of about 44 g/mol
. We can use Graham's Law to figure out how the diffusion rates of these gases compare.
rate of diffusion of H₂O / rate of diffusion of CO₂ = sqrt(44 / 18) = sqrt(2.44) = 1.56
This calculation shows that water vapor diffuses about 1.56 times faster than carbon dioxide under the same conditions.
Conclusion
Graham's diffusion law provides a fundamental understanding of how gases behave when they mix together. It is not only essential for theoretical chemistry, but also has practical implications in many fields. By investigating how the mass of gas molecules affects their diffusion rates, we gain deep insights into natural processes and can apply this knowledge to technological and industrial applications.