Gases notes

MDCAT Chemistry

This chapter explains the motion of gas particles, gas pressure, temperature, volume and the gas laws. It also discusses absolute zero, the ideal gas equation, kinetic energy, root mean square velocity, and the differences between ideal and real gases.

States of Matter and Kinetic Molecular Theory

Matter exists mainly as solids, liquids and gases. A fourth state, plasma, is formed when a gas is supplied with very high energy and becomes ionized. The particles in all states are in motion, but the type and freedom of motion are different.

Kinetic Molecular Theory explains the behaviour of particles of matter in motion. The temperature of a substance is related to the average kinetic energy of its particles. As temperature increases, particle motion becomes faster.

The theory that explains the behaviour of particles of matter in motion is called Kinetic Molecular Theory.
Solid particles are closely packed and mainly possess vibrational motion about fixed positions.
Liquid particles possess vibrational, rotational and translational motion, but their movement is limited by nearby particles.
Gas particles have considerable translational, rotational and vibrational motion.
Gas particles are far apart compared with their size, so most of the volume of a gas is empty space.
Plasma contains positive ions and free electrons. It is electrically conducting and is found in stars, lightning and some artificial sources.
In solids, temperature is a measure of the average vibrational kinetic energy of particles.
For a gas, temperature is related to the average translational kinetic energy of its particles.

Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory gives an idealized model of gases. It assumes that gas molecules are very small, move continuously and randomly, and collide with one another and with the walls of the container.

Gas pressure is produced because moving molecules strike the walls of the container. These collisions change the momentum of the molecules and exert force on the walls.

Gas molecules move continuously in straight-line paths between collisions.
Molecules change direction when they collide with one another or with the walls of the container.
Collisions between ideal gas molecules are perfectly elastic, so there is no net loss of kinetic energy.
The time of a collision is negligible compared with the time between collisions.
There are no significant attractive or repulsive forces between molecules of an ideal gas.
The actual volume of gas molecules is considered negligible compared with the volume occupied by the gas.
At the same temperature, all gases have the same average kinetic energy, regardless of their molar masses.
Heating a gas increases the average kinetic energy and usually increases the speed of its particles.

Gas Pressure, Temperature and Kinetic Energy

Pressure is the force exerted per unit area. Gas pressure results from collisions of gas molecules with the walls of a container. It is commonly measured in pascal, atmosphere, millimetre of mercury or torr.

The Kelvin scale is used in gas laws because gas volume and pressure are related to absolute temperature. Kelvin temperature is obtained by adding 273 to the Celsius temperature, or more accurately 273.15 when required.

Pressure is given by P = F/A, where F is force and A is area.
1 atmosphere is approximately equal to 101325 Pa and 760 mmHg.
Temperature in kelvin = temperature in degree Celsius + 273.15.
At a fixed temperature, increasing the number of gas molecules in a container increases pressure.
At a fixed volume, heating a gas increases the average kinetic energy of molecules and increases pressure.
If the temperature of a gas changes from 300 K to 600 K in a closed vessel of constant volume, its average kinetic energy becomes double.
For one molecule, average translational kinetic energy is proportional to absolute temperature.
The Boltzmann constant is k = 1.38 x 10^-23 J K^-1.

Standard Temperature and Pressure and Absolute Zero

Standard Temperature and Pressure is a reference condition used to compare gases. In many FSc calculations, STP is taken as 273 K or 273.15 K and 1 atm pressure. At this condition, one mole of an ideal gas occupies approximately 22.4 L.

Absolute zero is the lowest theoretical temperature. It is 0 K, equal to about -273.15 degree Celsius. At absolute zero, the ideal gas equation predicts zero pressure for a fixed amount of gas at finite volume, although an actual gas cannot be cooled to this point.

The value commonly used for STP is 273.15 K and 1 atm.
The molar volume of an ideal gas at STP is approximately 22.4 L mol^-1.
Absolute zero is 0 K or -273.15 degree Celsius.
At -273 degree Celsius, the ideal gas pressure is taken as P = 0 atm when volume and amount of gas remain fixed.
Absolute zero is unattainable in practice because removing the final amount of thermal energy becomes increasingly difficult.
Experimental temperatures as low as about 10^-5 K have been achieved, but they are still above absolute zero.
Kelvin temperature cannot be negative in ordinary gas-law calculations.
At absolute zero, the classical prediction is that molecular translational kinetic energy becomes zero.

Boyle's Law

Boyle's Law describes the relationship between pressure and volume for a fixed mass of gas at constant temperature. When volume decreases, molecules strike the walls more frequently, so pressure increases.

Robert Boyle stated this law in 1662. It is an inverse relationship, not a direct relationship.

Boyle's Law: at constant temperature, pressure is inversely proportional to volume.
Mathematically, P is proportional to 1/V.
The equation is PV = constant.
For two conditions, P1V1 = P2V2.
If the pressure is reduced to half at constant temperature, the volume becomes double.
If the volume is reduced to half at constant temperature, the pressure becomes double.
A graph of P against V is a rectangular hyperbola.
A graph of P against 1/V is a straight line passing through the origin, when other conditions remain constant.

Charles's Law and Absolute Temperature

Charles's Law describes the relationship between the volume and temperature of a fixed mass of gas at constant pressure. On heating, gas molecules move faster and the gas expands if the pressure remains constant.

The relationship must be written using kelvin temperatures. Celsius values cannot be used directly in the gas-law equation because the Celsius scale does not begin at absolute zero.

Charles's Law: at constant pressure, volume is directly proportional to absolute temperature.
The equation is V/T = constant.
For two conditions, V1/T1 = V2/T2.
A gas expands by approximately 1/273 of its volume at 0 degree Celsius for each 1 degree Celsius rise in temperature, when pressure remains constant.
If a gas is warmed by 1 degree Celsius, it expands by about 1/273 of its original volume at 0 degree Celsius.
A gas at 0 degree Celsius has a temperature of 273 K.
To double the volume of a gas whose initial temperature is 0 degree Celsius, the final temperature is 546 K.
A graph of volume against kelvin temperature is a straight line passing through the origin for an ideal gas.

Ideal Gas Equation and Gas Density

Boyle's Law and Charles's Law can be combined into one equation. The combined gas law is useful when pressure, volume and temperature all change. For a specified amount of gas, the amount of gas remains constant.

The ideal gas equation also includes the number of moles. It is used for calculations involving pressure, volume, temperature and molar amount.

The combined gas law is P1V1/T1 = P2V2/T2 for a fixed mass of gas.
The ideal gas equation is PV = nRT.
P is pressure, V is volume, n is number of moles, R is the gas constant and T is absolute temperature.
The value of R is 0.0821 L atm mol^-1 K^-1 when pressure is in atm and volume is in litres.
The value of R is 8.314 J mol^-1 K^-1 when pressure is in pascal and volume is in cubic metres.
One mole of an ideal gas at STP occupies approximately 22.4 L.
Gas density is d = m/V, and for an ideal gas d = PM/RT, where M is molar mass.
At constant pressure and molar mass, gas density is maximum at low temperature. At constant temperature, it is maximum at high pressure.
Hydrogen has the greatest molecular speed among common gases at the same temperature because it has the smallest molar mass.

Root Mean Square Velocity and Molecular Motion

Gas molecules do not all move at exactly the same speed. Their speeds have a distribution. Root mean square velocity is a useful average speed related to the kinetic energy of gas molecules.

At the same temperature, lighter molecules move faster than heavier molecules. This is why hydrogen has a greater root mean square velocity than chlorine.

The root mean square velocity is represented by urms.
The equation is urms = square root of (3RT/M), where M is molar mass in kg mol^-1.
At constant temperature, urms is inversely proportional to the square root of molar mass.
The ratio is u1/u2 = square root of (M2/M1).
At the same temperature, hydrogen has a greater root mean square velocity than all gases with higher molar mass.
Among gases such as H2, N2, O2 and Cl2 at 25 degree Celsius, Cl2 has the lowest root mean square velocity because it has the greatest molar mass.
Increasing temperature increases the root mean square velocity of a gas.
Root mean square velocity is not the same as the ordinary average velocity, because the average velocity of randomly moving molecules can be zero.

Ideal and Real Gases

An ideal gas is a theoretical gas that follows all gas laws under all conditions. Real gases contain molecules with their own volume and intermolecular forces, so they do not behave ideally under every condition.

Real gases approach ideal behaviour when their molecules are far apart and their intermolecular attractions have little effect.

Ideal gas molecules have negligible volume and no intermolecular forces.
Real gas molecules have definite volume and exert intermolecular attractions and repulsions.
Real gases behave most nearly ideally at high temperature and low pressure.
At low pressure, gas molecules are far apart, so intermolecular forces become less significant.
At high temperature, molecules have greater kinetic energy and can overcome attractive forces more easily.
Intermolecular forces become significant at low temperature and high pressure.
A real gas deviates from ideal behaviour when it is compressed strongly or cooled greatly.
The compressibility factor is Z = PV/RT for 1 mole of gas.
For an ideal gas, Z = 1. If Z is greater than 1, repulsive effects or molecular volume are significant.
If Z is greater than 1 at 1 atm and 273.15 K, the molar volume is greater than 22.4 L because V = ZRT/P.
A real gas can be liquefied by lowering temperature and increasing pressure, but an ideal gas cannot be liquefied in the ideal model.

Related Chemical Examples and Environmental Point

The properties of gases also help explain the behaviour of molecules in compounds and the atmosphere. Carbon dioxide is a stable molecule because its atoms are joined by strong covalent bonds and it has a stable electronic arrangement.

Some gases and volatile compounds affect the atmosphere. Chlorofluorocarbons release chlorine radicals in the upper atmosphere, which can catalytically destroy ozone.

CO2 is a covalent molecule containing carbon and oxygen atoms joined by covalent bonds.
Covalent bonds are formed by sharing of electrons between atoms.
CFCs are chlorofluorocarbons that can destroy ozone in the stratosphere.
Ozone is O3, while ordinary oxygen gas is O2.
CFCs are broken down by ultraviolet radiation and release chlorine species that participate in ozone destruction.
The stability of CO2 as a molecule should not be confused with the stability of its atmospheric concentration or its environmental effects.

Key terms

Kinetic Molecular Theory: A theory that explains matter and gas behaviour in terms of the continuous motion of particles.
Pressure: Force exerted per unit area, produced by gas molecules colliding with container walls.
Absolute temperature: Temperature measured on the Kelvin scale, beginning at 0 K.
Standard Temperature and Pressure: A reference condition commonly taken as 273.15 K and 1 atm.
Absolute zero: The theoretical lowest temperature, equal to 0 K or about -273.15 degree Celsius.
Boyle's Law: At constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume.
Charles's Law: At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature.
Ideal gas: A theoretical gas with negligible molecular volume and no intermolecular forces.
Real gas: An actual gas whose molecules have volume and intermolecular forces.
Ideal gas equation: The equation PV = nRT relating pressure, volume, amount and absolute temperature.
Molar volume: The volume occupied by one mole of a substance under specified conditions.
Root mean square velocity: A speed measure related to the average kinetic energy of gas molecules.
Boltzmann constant: The constant k equal to 1.38 x 10^-23 J K^-1, relating molecular energy to temperature.
Compressibility factor: The quantity Z = PV/RT for one mole of gas, used to measure deviation from ideal behaviour.
Intermolecular forces: Attractive or repulsive forces acting between molecules.
Plasma: An ionized state of matter containing charged particles, including free electrons and positive ions.

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Chemistry shortcuts

Finding the limiting reactant and percentage composition

Convert every given mass or volume into moles first. The reactant that produces the least amount of the required product is the limiting reactant.

Write the balanced equation and calculate moles using n = mass/Mr.
Use the mole ratio to calculate the product. For percentage composition, use percentage = mass of element in one mole of compound divided by molar mass, multiplied by 100.
Example: Percentage of nitrogen in KNO3 = 14/101 × 100 = 13.86%.
Answer: 13.86% nitrogen.

Use gas volume at molar volume only when the gas conditions are stated or are standard conditions.

Using gas volume, pressure and temperature relations

At the same temperature and pressure, gas volume is directly proportional to the number of molecules. For changing conditions, use P1V1/T1 = P2V2/T2.

At constant temperature and pressure, divide or multiply the volume in the same ratio as the number of molecules.
Example: 10 mL H2 contains 2 × 10^3 molecules. Oxygen in 200 mL contains 20 × 2 × 10^3 = 4 × 10^4 molecules.
Answer: 4 × 10^4 molecules.
For a rigid container, increasing temperature increases molecular speed and mean free path if the gas remains in the same phase.

The direct volume to molecule ratio does not apply when temperature or pressure changes.

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