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Kinetic Theory of Gases

A theoretical model about the structure and motion of gases used to explain physical and chemical properties and behaviors.

Kinetic Theory Model 1

Gases are composed of particles that are in continuous random motion.

Kinetic Theory Model 2

Attraction and repulsion forces between gas particles are negligible.

Kinetic Theory Model 3

The particles of a gas possess kinetic energy calculated by $E_k = \frac{1}{2}mv^2$.

Kinetic Theory Model 4

The average kinetic energy of gas particles is directly proportional to absolute temperature and is identical for all gases at the same temperature.

Kinetic Theory Model 5

Collisions between gas particles and container walls are perfectly elastic.

Effect of increasing temperature on Maxwell-Boltzmann distribution curve

The peak of the curve lowers and shifts to the right (flattens), while the total area under the curve remains constant.

Gas property: Take the shape of their container / Low density

Particles show negligible forces of attraction and are in constant random motion

allows them to spread out as far as possible to occupy the container volume.

Gas property: Can be compressed

Gas particles have negligible volume and are widely spaced, providing space for them to be forced into a smaller volume.

Gas property: Readily diffuse through other gases

Particles are widely spaced

move randomly

experience negligible intermolecular forces

allowing for mixing between different gases.

Gas property: Exert pressure

Gas particles move in straight lines and collide with container walls; these collisions exert force per unit area on the walls.

Temp affect on pressure

Increasing gas temperature increases average kinetic energy and particle speed, leading to a higher frequency and greater force of wall collisions, raising pressure.

Amount of gas effect on pressure

Increasing the amount of gas increases the concentration of particles per volume

resulting in a higher frequency of wall collisions and higher pressure.

Volume of the container effect on pressure

Increasing container volume spreads particles further apart

increasing the travel distance before colliding with walls

reduces collision frequency and lowers pressure

Differences between an ideal gas and a real gas

An ideal gas assumes:

zero particle volume

no intermolecular forces,

perfectly elastic collisions;

In reality:

real gas particles occupy finite volume

experience intermolecular attractions/repulsions

non-ideal collisions.

Conditions for real gas ideal behavior: Low Pressure

Gas particles are far apart, making particle volume negligible compared to container volume and minimizing intermolecular interactions such as in a real gas

Conditions for real gas ideal behavior: High Temperature

Gas particles have high kinetic energy and rapid motion

making intermolecular attractive forces insignificant

Conditions for real gas ideal behavior: Small, Non-Polar Molecules

Substances like Helium ($He$) and Hydrogen ($H_2$) possess extremely weak intermolecular forces, behaving closely to an ideal gas.

Solids

Particles experience strong attractive forces, are tightly packed, and only vibrate in fixed positions, giving them a fixed shape, fixed volume, and incompressibility.

Liquids

Particles experience strong attractive forces keeping them close together, but can slide past each other to flow and fill container bottoms while keeping a fixed volume.

Why physical and chemical changes are accompanied by energy changes

Phase and chemical changes require breaking and forming intermolecular forces or chemical bonds, which involve taking in or releasing energy.

Exothermic physical processes

Deposition, condensation, and freezing. (gas—>solid)

Endothermic physical processes

Evaporation, melting, and sublimation. (moving towards gas

Sublimation

Phase transition directly from solid to gas.

Energy change to transition to solid

Remove heat energy.

Energy change to transition to gas

Add heat energy.

Atomic level events during a phase change

Added heat energy is used to disrupt intermolecular forces between molecules rather than increase kinetic energy, keeping temperature constant while potential energy increases.

Distillation

A separation technique based on differences in the boiling points of liquid mixture components.

Combustion

A rapid exothermic reaction between a fuel and oxygen that releases heat and light energy.

Enthalpy ($H$)

The total chemical energy stored in a substance, encompassing chemical potential energy in bonds and particle kinetic energy.

Heat of combustion

The enthalpy change occurring when a specified amount of fuel undergoes complete combustion in oxygen.

Energy

The capacity to do work, measured in Joules ($J$); total energy in an isolated system is conserved.

System (in thermochemistry)

The specific chemical reaction mixture under study.

Surroundings

Everything outside the chemical reaction mixture, including the container, solution, and measuring devices.

Bond breaking and bond forming energy changes

Breaking bonds in reactants requires energy input (endothermic)

forming new bonds in products releases energy (exothermic).

Conservation of energy in reactions

Total energy is conserved; changes in chemical potential energy are offset by opposite changes in heat energy absorbed from or released to the surroundings.

Endothermic reaction definition

A reaction where bond breaking requires more energy than bond forming releases ($\Delta H > 0$), absorbing heat from surroundings and lowering temperature.

Exothermic reaction definition

A reaction where bond breaking requires less energy than bond forming releases ($\Delta H < 0$), releasing heat to surroundings and raising temperature.

Exothermic reaction enthalpy profile

Reactants have higher enthalpy than products resulting in a negative enthalpy change

Endothermic reaction enthalpy profile

Reactants have lower enthalpy than products ($H_{\text{reactants}} < H_{\text{products}}$), resulting in a positive enthalpy change ($\Delta H > 0$).

Formula for enthalpy change ($\Delta H$)

$$\Delta H = H_{\text{products}} - H_{\text{reactants}}$$

Energy profile diagrams

A graphical representation showing enthalpy or potential energy on the y-axis against the reaction progress/coordinate on the x-axis.

Indicators of an exothermic profile

Negative $\Delta H$, energy step goes downward from reactants to products, releasing heat and increasing surrounding temperature.

Indicators of an endothermic profile

Positive $\Delta H$, energy step goes upward from reactants to products, absorbing heat and decreasing surrounding temperature.

Exothermic process example

Cellular respiration.

Endothermic process example

Photosynthesis.

Collision theory requirements

For a reaction to occur, reactant particles must collide with each other, with sufficient energy ($E \ge E_a$), and with correct molecular orientation.

Activation energy ($E_a$)

The minimum energy required for colliding reactant particles to break existing bonds and initiate a chemical reaction.

Transition state / Activated complex

An unstable, high-energy arrangement of atoms occurring at the peak of the activation energy barrier where original bonds are breaking and new bonds are forming.

Activation energy representation on an energy profile

The vertical energy difference from the reactant energy level to the top peak of the transition state.

Enthalpy change representation on an energy profile

The vertical energy difference between the reactant level and product level.

Consequence of a large activation energy

Reactant bonds are strong, requiring significant energy input to break; few particles possess sufficient energy, leading to a slow reaction rate.

Consequence of a small activation energy

Reactant bonds are relatively weak

a large proportion of particles possess sufficient energy to react

fast reaction rate.

Reactants with highest collision efficiency / reaction rates

Aqueous ions, because bonds are already broken and electrostatic attraction aids immediate reaction upon collision.

Orientation of colliding particles

Particles must align in a specific geometry during collision to enable reactive centers to interact and form new bonds.

Effect of concentration on reaction rate

Increasing solute concentration increases the number of particles per unit volume, raising the collision frequency and frequency of successful collisions, thus increasing reaction rate.

Effect of pressure on reaction rate

Increasing gas pressure compresses particles into a smaller volume, increasing particle concentration and collision frequency, which raises reaction rate.

Effect of temperature on reaction rate

Increasing temperature increases average particle kinetic energy,

move faster and more likely to collide with other particles

frequency of collisions increases

More importantly:

higher temp increases the proportion of particles is able to overcome the acitatn energy

freuency of collisions, frequency of successful collisions

Effect of surface area on reaction rate

Breaking a solid into smaller pieces increases exposed surface area, exposing more reactant particles for collision and increasing successful collision frequency.

Catalyst mechanism

Substances that increase reaction rate without being consumed

provides an alternative pathway with a lower activation energy ($E_a$).

Reaction rate behavior over time

Reactions do not proceed at a constant rate; they start fastest and slow down progressively as reactant concentrations deplete.

Why increasing gas volume decreases reaction rate

Increasing volume lowers particle concentration per unit space, decreasing collision frequency and lowering the rate of reaction.

Why small wood pieces burn faster than large logs

Smaller pieces present a larger surface area relative to mass

Exposes more reactant particles for allowing for frequency of collisions with oxygen to increase

Why sulfur burns faster in pure oxygen than air

Pure oxygen provides a higher concentration of reactant molecules than atmospheric air

more particles in the same amount of space

increasing collision frequency and accelerating reaction rate.

Maxwell-Boltzmann distribution curve axes

X-axis represents Kinetic Energy of gas particles; Y-axis represents the proportion/number of particles with that kinetic energy.

Shape of Maxwell-Boltzmann curve

Starts at origin (0,0) because no particles have zero energy, rises steep to a single peak, then decays asymptotically toward zero at high energies.

Area under a Maxwell-Boltzmann curve

Represents the total number of particles present in the gas sample.

Most probable energy on a Maxwell-Boltzmann curve

The kinetic energy value corresponding to the maximum peak of the distribution curve.

Maxwell-Boltzmann curve shape at low temperature

The peak is taller and shifts left towards lower kinetic energy values.

Maxwell-Boltzmann curve shape at high temperature

The peak is lower and shifts right towards higher kinetic energy values.

Effect of molecular mass on particle speed at constant temperature

At equal temperatures, heavier gas molecules possess lower average velocities than lighter gas molecules because kinetic energy ($E_k = \frac{1}{2}mv^2$) is identical.