States of Matter and Gas Laws Explained

Scientific Prefixes and Submultiples

Understanding scientific prefixes is crucial for expressing very large or very small numbers concisely. Here are common prefixes and their factors:

• Giga (G): 10⁹
• Mega (M): 10⁶
• Micro (µ): 10^-6
• Nano (n): 10^-9
• Pico (p): 10^-12

Understanding Scientific Notation

Scientific notation is a way of writing numbers that are too large or too small to be conveniently written in decimal form. It is commonly used in science, where it is also called "standard form" or "standard index form."

Example: To express 38,000 meters with three significant figures:

38,000 m = 3.80 x 10⁴ m

Gas Volume Variation at Constant Pressure (Charles's Law)

When the temperature of a given mass of gas increases, if the pressure remains constant, the volume of that mass of gas increases. This relationship is known as Charles's Law.

Gas Pressure Variation at Constant Volume (Gay-Lussac's Law)

When a gas is heated in a closed container, the pressure exerted by the gas on the walls of the container increases. This principle is described by Gay-Lussac's Law.

Properties of Gases

• Gases have neither a definite shape nor a definite volume; they fill their container. The container must be closed because gases expand indefinitely.
• Gases are compressible, meaning their volume decreases when pressure is applied.
• Gases flow easily and can escape readily.

Properties of Liquids

• Liquids adapt to the shape of their container.
• Liquids are hardly compressible.
• Liquids and gases are collectively called fluids.

Properties of Solids

• Solids are rigid and have their own definite volume.
• Solids are hardly compressible.

Boyle's and Mariotte's Law

This law describes the inverse relationship between the pressure and volume of a gas at constant temperature.

If we reduce the volume by half without altering temperature, the pressure must double. If we reduce it to one-third, the pressure will be threefold. This behavior is the same for all gases.

This law, established by Robert Boyle in 1662 and independently by Edme Mariotte in 1676, states: For a fixed mass of gas at constant temperature, the product of its pressure and volume is constant.

Mathematically, this is expressed as:

P₁V₁ = P₂V₂ = P₃V₃ = constant

Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory (KMT) provides a microscopic explanation for the macroscopic properties of gases:

• Gases are formed by a large number of molecules that are in fast and incessant motion.
• The molecules collide with each other and against the walls of the container. They move in zigzag directions at various speeds.
• Not all molecules move at the same speed.
• The pressure exerted by the gas against the container walls is the result of these molecular collisions.
• These molecules are extremely small and are widely separated.
• The velocity of the particles depends on the gas temperature; the higher the temperature, the faster the particles move.
• When two gases are at the same temperature, the average kinetic energy of their molecules is the same.

Kinetic Molecular Theory Explains Gas Properties

KMT helps us understand why gases behave the way they do:

• If the volume of the container holding the gas decreases without varying the temperature, the frequency of molecular collisions against the walls increases, thus increasing the pressure.
• If a gas in a closed container has its temperature increased, the average kinetic energy of its molecules increases. This leads to more frequent and forceful collisions against the container walls, resulting in an increase in gas pressure.