Question

Which of the following is not correct? (a) Diffusion of gases occurs more rapidly at higher temperatures. (b) Effusion of \(\mathrm{H}_{2}\) is faster than effusion of He (assume similar conditions and a rate expressed in units of \(\mathrm{mol} / \mathrm{h})\) (c) Diffusion will occur faster at low pressure than at high pressure. (d) The rate of effusion of a gas \((\mathrm{mol} / \mathrm{h})\) is directly proportional to molar mass.

Short answer

Statement (d) is not correct.

Step-by-step solution

Understanding Diffusion and Effusion

Diffusion is the movement of particles from an area of higher concentration to one of lower concentration, while effusion is the escape of gas particles through a tiny hole into a vacuum. Both processes are influenced by temperature, pressure, and molar mass of the gas involved.

Analyzing Statement (a)

Statement (a) talks about diffusion of gases at higher temperatures. According to kinetic molecular theory, as temperature increases, the kinetic energy of gas molecules increases, making them move faster. Therefore, diffusion occurs more rapidly at higher temperatures. Hence, statement (a) is correct.

Analyzing Statement (b)

Statement (b) relates to the effusion rates of hydrogen and helium. Graham's law states that the rate of effusion is inversely proportional to the square root of its molar mass. Hydrogen has a smaller molar mass (2 g/mol) compared to helium (4 g/mol), so hydrogen effuses faster than helium. Thus, statement (b) is correct.

Analyzing Statement (c)

Statement (c) discusses the effect of pressure on diffusion. At lower pressures, a gas has fewer collisions and particles can spread out more easily, allowing faster diffusion. Hence, diffusion occurs faster at low pressure than high pressure, making statement (c) correct.

Analyzing Statement (d)

Statement (d) states that the rate of effusion is directly proportional to molar mass. According to Graham's law, effusion rate is inversely proportional to the square root of molar mass, not directly proportional. Therefore, statement (d) is incorrect.

Key concepts

Diffusion

Diffusion is a process where gas molecules spread out from an area of higher concentration to an area of lower concentration until equilibrium is achieved. This can be seen when you spray perfume in one corner of a room and eventually, the scent spreads throughout the entire space. The key factors influencing diffusion are the temperature and pressure.

At high temperatures, molecules move faster due to increased kinetic energy. This speeds up the diffusion process, allowing gases to mix quickly. Similarly, lower pressures mean fewer gas molecule collisions, facilitating a quicker spread through the available space. Hence, diffusion is generally faster at higher temperatures and lower pressures.

This concept is vital in many real-world applications, such as in respiratory systems where oxygen diffuses into blood or during the exchange of gases in leaves for photosynthesis.

Effusion

Effusion refers to the escape of gas molecules through a tiny hole into a vacuum or less-pressurized environment. Imagine a balloon with a pinhole; over time, the air particles inside will gradually seep out through the hole. Effusion is different from diffusion because it involves movement through a barrier.

The rate of effusion depends on the speed of the gas particles, which is influenced by two factors: the temperature and the particle's molar mass. Similar to diffusion, higher temperatures result in faster-moving molecules, enhancing the rate of effusion.

This process is crucial in situations like separating isotopes in nuclear processes or in gas masks where efficient filtering is required.

Graham's Law

Graham's Law provides a mathematical model to compare the rates of effusion or diffusion of gases. It states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, it's expressed as: \[\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}}\]where \(r_1\) and \(r_2\) are the rates of effusion for gases 1 and 2, and \(M_1\) and \(M_2\) are their respective molar masses.

This law explains why lighter gases, like hydrogen, effuse faster than heavier gases such as helium under similar conditions. Graham's Law is helpful when examining scenarios such as hydrogen leaks or evaluating the time required for gases to pass through porous materials.

Understanding this concept helps in accurate predictions and explanations regarding gas behavior in various fields, from chemistry to engineering.

Kinetic Molecular Theory

Kinetic Molecular Theory (KMT) is a model that helps explain the physical behavior of gases. It suggests that gas particles are in constant, random motion, and their speed increases with temperature. This theory is foundational in understanding how temperature, pressure, volume, and the number of particles relate to each other in a gas.

According to KMT, increasing temperature will boost the kinetic energy of particles, resulting in faster particle movement which impacts diffusion and effusion rates. Moreover, KMT underlines that gases behave ideally at low pressures and high temperatures, where interactions between molecules are negligible.

By applying KMT, we can predict how changes in environmental conditions might affect processes involving gases, and it serves as a critical tool for interpreting phenomena such as weather patterns, engine operations, and even breathing efficiency in different conditions.