Introduction to Gas Laws and Properties

1. Gas particles are in constant, random motion.
2. Particles have negligible volume (they are treated as point masses).
3. There are no attractive or repulsive interactions between particles.
4. Collisions between particles and container walls are perfectly elastic.
5. The average kinetic energy of the particles is directly proportional to the absolute temperature.

While KMT describes "ideal" gases, real gases deviate from these assumptions, particularly at high pressures (where molecular volume becomes significant) or low temperatures (where intermolecular forces cause liquefaction).

Fundamental Gas Laws

The interactions between $P$, $V$, $n$, and $T$ are described by several empirical laws:

• Boyle’s Law: At constant $n$ and $T$, volume is inversely proportional to pressure ($V \propto \frac{1}{P}$ or $PV = k$).
• Charles’ Law: At constant $n$ and $P$, volume is directly proportional to temperature ($V \propto T$ or $\frac{V}{T} = k'$).
• Avogadro’s Law: At constant $T$ and $P$, volume is directly proportional to the number of moles ($V \propto n$ or $V = k''n$).

The Ideal Gas Law

By combining these individual relationships, we derive the Ideal Gas Law, which serves as the foundation for gas stoichiometry: $PV = nRT$

In this equation, $R$ is the Ideal Gas Constant. Its value depends on the units used:

• $R = 0.08314\text{ L bar mol}^{-1}\text{ K}^{-1}$
• $R = 8.314\text{ J mol}^{-1}\text{ K}^{-1}$

Gas Dynamics: Speed, Diffusion, and Effusion

Because gas molecules move at high velocities, we can study how they move through space and escape containers.

Molecular Speed and Mean Free Path

The speed of a gas molecule depends on its temperature and molar mass ($M$). A simplified relationship for speed ($v$) is: $v = \sqrt{\frac{3RT}{M}}$ This explains why lighter gases, like Hydrogen ($H_2$), move much faster than heavier gases like Oxygen ($O_2$).

The Mean Free Path ($l$) is the average distance a molecule travels before colliding with another. This distance decreases as pressure increases or as the "size" of the molecule increases.

Effusion and Diffusion

• Effusion is the process where gas particles escape through a tiny opening into a vacuum. Graham's Law states that the rate of effusion is inversely proportional to the square root of the molar mass: $\frac{\text{rate}_1}{\text{rate}_2} = \sqrt{\frac{M_2}{M_1}}$
• Diffusion is the gradual dispersion of one substance through another (e.g., a gas spreading through a room).

Chemistry of the Atmosphere

The atmosphere is a complex mixture of gases, primarily Nitrogen ($N_2, 78.1\%$) and Oxygen ($O_2, 21.0\%$). The chemical behavior of these gases has significant environmental implications.

The Ozone Layer

Ozone ($O_3$) is created in the stratosphere through the Chapman Cycle, where oxygen molecules are photolyzed by UV light to create free oxygen atoms that then react with $O_2$. However, Chlorofluorocarbons (CFCs) can destroy this layer. When CFCs reach the stratosphere, light breaks them down to release Chlorine atoms, which act as catalysts in a cycle that destroys ozone.

Atmospheric Warming and Smog

• Greenhouse Effect: Gases like $CO_2$ absorb infrared light, contributing to atmospheric warming. This occurs because the molecular vibrations (stretching and bending) allow the molecule to absorb specific wavelengths of energy.
• Smog: Urban smog is a mixture of oxidants, hydrocarbons, and nitrogen oxides ($NO_x$). It is often exacerbated by sunlight and temperature inversions, where a layer of warm air traps pollutants near the ground.
• Acid Rain: This is caused by the oxidation of sulfur dioxide ($SO_2$) into sulfur trioxide ($SO_3$), which then reacts with water to form sulfuric acid ($H_2SO_4$).

img-8.jpeg Figure 4: 1990 Annual Wet Sulfate Deposition