States of Matter: Gases, Liquids, and Solids

• Matter exists in different states including gas, liquid, and solid.
• Gas consists of molecules widely separated in empty space and are free to move throughout a container.
• Liquids have molecules touching each other, allowing movement throughout the liquid due to intermolecular space.
• Solids have molecules, atoms, or ions arranged in a specific order in fixed positions within a crystal lattice, allowing them to vibrate but not move.
• Gases are the most studied and best understood state of matter compared to liquids and solids.

General Characteristics of Gases

• Gases have limitless expansibility and will expand to fill their entire vessel.
• Gases are easily compressed by applying pressure using a movable piston.
• Different gases can diffuse rapidly through each other, resulting in a homogenous mixture.
• Gases exert pressure on the walls of their container in all directions.
• When a gas confined in a vessel is heated, the pressure increases.
• When a gas in a vessel fitted with a piston is heated, the volume of the gas increases.

Parameters of Gas

• There are four measurable properties of gases: Temperature (T), Pressure (P), Volume (V), and number of Moles (n).

Volume, V

• The volume of a gas sample is the volume of its container.
• Volume is given in litres (L or l) or millilitres (mL or ml).
• 1 litre = 1000 ml and 1 ml = 10–3 litres.
• One millilitre is practically equal to one cubic centimetre (cc or cm³).
• 1 litre equals 1000.028 cc.
• The SI unit for volume is cubic metre (m³), and a smaller unit is decimeter³ (dm³).

Pressure, P

• Pressure of a gas is the force exerted by its molecules per unit surface area in contact.
• A mercury manometer measures the pressure of a gas sample.
• Atmospheric pressure is determined using a mercury barometer.
• Standard atmospheric pressure is the pressure that supports a 760 mm Hg column at sea level, also known as 1 atm.
• A unit of pressure, millimetre of mercury, is measured in torr.
• 1 atm = 760 mm Hg = 760 torr
• The SI unit of pressure is the Pascal (Pa).
• 1 atm = 760 torr = 1.013 × 105 Pa

Temperature, T

• Gas temperatures are measured in Centigrade degrees (°C) or Celsius degrees.
• The SI unit of temperature is Kelvin (K) or Absolute degree.
• Convert Centigrade to Kelvin using the equation: K = °C + 273
• Kelvin temperature (or absolute temperature) is always used in calculations of other parameters of gases.
• A degree sign (°) is not used with Kelvin.

Moles, n

• The number of moles (n) of a gas sample in a container is the mass (m) of the sample divided by the molar mass (M).
• n = m/M

Gas Laws

• Volume of a given gas sample depends on the temperature and pressure applied to it.
• Any change in temperature or pressure influences the volume of the gas.
• The relationships among pressure, temperature, and volume for a gas mass are termed gas laws, describing the general behaviour of gases.

Boyle's Law

• For a fixed mass of gas at constant temperature, the volume is inversely proportional to its pressure.

Charles' Law

• For a fixed mass of gas at constant pressure, volume is directly proportional to the Kelvin temperature (absolute temperature).

The Combined Gas Law

• Combines Boyle's and Charles' Laws to yield P1V1/T1 = P2V2/T2 when a fixed mass of gas changes from state 1 to state 2.

Gay Lussac's Law

• At constant volume, pressure of a fixed mass of gas is directly proportional to the Kelvin temperature: P1/T1 = P2/T2.

Avogadro's Law

• Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

Molar Gas Volume

• At a given temperature and pressure, one mole of any gas has the same fixed volume.
• Chemists use standard temperature and pressure (STP) as a fixed reference to compare the molar volumes of gases.
• At STP, standard temperature = 273 K (0°C) and standard pressure = 1 atm (760 mm Hg).
• One mole of any gas occupies a volume of 22.4 litres at STP.

Ideal Gas Law

• The volume of a given amount of gas is directly proportional to the number of moles (n) and temperature (T), and inversely proportional to the pressure (P): V ∝ nT/P
• The ideal gas law applies to all gases exhibiting ideal behaviour, i.e. gases that perfectly obey the gas laws.

Ideal Gas Equation

• Incorporates gas constant R into the ideal gas law: V = R(nT/P) or PV = nRT
• The ideal gas equation holds accurately for all gases at low pressures.
• The ideal-gas equation is the Equation of State for a gas because it contains all variables (T, P, V and n), to describe the condition or state of the gas sample.

Numerical Value of the Gas Constant, R

• From the ideal gas equation: R = PV/nT
• 1 mole of a gas at STP occupies 22.4 litres.
• R is expressed in work or energy units per degree per mole and depends on the units of P and V used in calculation.
• Values of R in different units include 0.0821 litre-atm K-1 mol-1, 82.1 ml-atm K-¹ mol-1, 62.3 litre-mm Hg K¯¹ mol−1

Dalton's Law of Partial Pressures

• In a gas mixture, each component gas exerts a pressure as if it were alone.
• The partial pressure is the individual pressure of each gas within the mixture.
• A mixture of gases' total pressure is equal to the sum of partial pressures of all gases present.
• The total pressure is determined by the total number of moles, whether of one gas or a gas mixture.

Graham's Law of Diffusion

• Under the same temperature and pressure conditions, the rates of diffusion of different gases are inversely proportional to the square roots of their molecular masses.

Diffusion

• Diffusion: the mixing of gas molecules thru random motion under conditions where molecular collisions occur.

Effusion

• Effusion: the escape of gas thru a pinhole without molecular collisions.
• For effusion, the hole's diameter must be smaller than the molecules' mean free path.

Kinetic Molecular Theory (KMT) of Gases

• KMT explains the behaviour of gases and the gas laws; it builds on the idea that gas is made of many perpetual moving molecules.

Assumptions of KMT of Gases

• A gas consists of molecules of mass m in ceaseless random motion obeying classical mechanics.
• Molecules are negligible in size, and their diameters are much smaller than the separation between collisions.
• Molecules interact only through brief elastic collisions, meaning total translational kinetic energy is conserved.

Explanation to Kinetic Molecular Theory of Gases

• The molecules have physical properties of mass, momentum, and energy.
• Density of a gas is the sum of the mass of molecules divided by the volume the gas occupies.
• Pressure of a gas is a measure of the linear momentum of the molecules.
• Gas molecules collide with a container's walls, imparting momentum and measured force. The resultant, force over area, defines pressure.
• Temperature of a gas measures the mean kinetic energy of the gas.
• Gas molecules in constant random motion possess energy, influenced by molecule velocity.

Ideal Gas vs Real Gas

• An ideal gas follows the kinetic theory assumptions, and obeys basic gas laws under all conditions.
• A real gas, such as hydrogen, oxygen or nitrogen, opposes the assumptions of kinetic theory.
• Molecular collisions of ideal gas are elastic, whereas real gas collisions are not always.
• There are no attractive forces among molecules in an ideal gas, though they exist in a real gas.

Deviation from Ideal Gas

• Actual volume of molecules is negligible in ideal gas, but it is appreciable in real gases.

Compressibility Factor

• How much real gases deviate from ideal behaviour is termed compressibility factor.

van der Waals Equation

• Attempts to explain real gases’ deviation from ideal behaviour by attributing those to ideal gas molecules existing as point masses with no volume & lacking intermolecular attractions.

van der Waals Equation: Volume Correction

• The actual volume of gases is the ideal volume minus the volume occupied by the gas molecules.

van der Waals Equation Volume

• Excluded volume is four times the actual volume of gas molecules.

Waals Equation: Pressure Correction

• The van der Waals equation corrects pressure to account for intermolecular attractions, subtracting a term proportional to the inverse square of the volume (an²/V²).
• The ideal pressure is determined by the force of attraction between molecules.

Liquefaction of Gases

• The critical temperature is the temperature above which a gas cannot be liquefied, regardless of the pressure applied.
• Critical pressure is the minimum pressure required to liquefy a gas at its critical temperature.
• Critical volume is the volume one mole occupies at the critical temperature and pressure.
• Critical constants refers to the Critical temperature, pressure, and volume.
• A critical state is when the temperature and pressure meet the same identical liquid, merging smoothly with one another.
• This merging is also known as the critical phenomenon.

Law of Corresponding States

• Equations can be organized through reduced pressure, volume and temperature.