Kinetic Molecular Theory
Related Examples and Practice Problems
Topic Summary & Highlights
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Core Concept
The Kinetic Molecular Theory explains the behavior of gases based on the motion of their particles. It helps us understand gas laws, pressure, temperature, and volume in terms of particle movement and collisions.
Practice Tips
Kinetic Molecular Theory explains gas behavior in terms of particle motion, collisions, and energy.
Postulates include constant motion, elastic collisions, lack of intermolecular forces, and a direct relationship between temperature and kinetic energy.
Explains Gas Laws: KMT provides a molecular-level explanation for Boyle’s, Charles’s, Gay-Lussac’s, and Avogadro’s laws.
Limitations: KMT assumes ideal behavior, which real gases approximate but do not always follow, especially at high pressures and low temperatures.
Key Postulates of Kinetic Molecular Theory
Gases are Composed of Tiny Particles:
Gas particles (usually molecules or atoms) are very small compared to the distances between them.
Most of the volume of a gas is empty space, making gases compressible.
Particles Move in Constant, Random Motion:
Gas particles are in constant, straight-line motion, moving randomly in all directions.
The random motion of particles is responsible for the gas’s tendency to fill any container.
Collisions Between Particles are Elastic:
When gas particles collide with each other or the walls of the container, there is no loss of kinetic energy.
In an elastic collision, kinetic energy is transferred but the total energy remains the same.
No Intermolecular Forces Act Between Particles:
Gas particles do not attract or repel each other.
They are assumed to move independently of one another, with no interactions except during collisions.
The Average Kinetic Energy of Gas Particles is Proportional to Temperature:
The temperature of a gas is directly proportional to the average kinetic energy of its particles.
Higher temperatures mean particles have higher kinetic energy and move faster.
Important Equations and Concepts
Average Kinetic Energy and Temperature:
The average kinetic energy of gas particles is given by: $\text{KE}_{\text{avg}} = \frac{3}{2} kT$
Where:
$\text{KE}_{\text{avg}}$ = Average kinetic energy of particles
k = Boltzmann constant ($1.38 \times 10^{-23} \, \text{J/K})
T = Temperature in Kelvin (K)
This equation shows that as temperature increases, the average kinetic energy of gas particles also increases.
Root Mean Square Speed:
The root mean square speed (urmsu_{\text{rms}}urms) is the square root of the average of the squares of the particle speeds and provides a measure of the typical speed of gas particles: $u_{\text{rms}} = \sqrt{\frac{3RT}{M}}$
Where:
R = Ideal gas constant ($8.31 \, \text{J} \cdot \text{mol}^{-1}$)
T = Temperature in Kelvin (K)
M = Molar mass of the gas in kilograms per mole (kg/mol)
This formula indicates that lighter gases (lower M) move faster at a given temperature than heavier gases.
Pressure and Collisions:
The pressure exerted by a gas is due to collisions of particles with the walls of the container.
The frequency and force of these collisions depend on the number, speed, and mass of the gas particles, which are influenced by temperature and volume
Example Problem: Using KMT to Explain Gas Behavior
Problem: Explain why a balloon expands when it is heated.
Solution:
According to KMT, heating a gas increases the average kinetic energy of its particles, causing them to move faster.
Faster-moving particles collide more forcefully with the walls of the balloon, increasing the internal pressure and pushing the balloon outward.
If the balloon is flexible, it will expand until the pressure inside matches the outside pressure.
The KMT Hand Mnemonic
Here are TWO options to use your hand to memorize the KMT
Thumb: Tiny Particles
Think of your thumb as a small, isolated particle. This represents the first postulate: gases are composed of a large number of tiny particles that are far apart relative to their size. Therefore, the volume of the particles themselves is negligible compared to the volume of the container.
Index Finger: Constant, Random Motion
Wiggle your index finger back and forth and in different directions. This motion represents the second postulate: the gas particles are in constant, random, straight-line motion.
Middle Finger: No Intermolecular Forces
Hold your middle finger up, as if to say "no" or to show a lack of attraction. This symbolizes the third postulate: there are no attractive or repulsive forces between the gas particles.
Ring Finger: Elastic Collisions
"Ring" and "Spring" rhyme, and a spring-like bounce is what an elastic collision is. Gently tap your ring finger against another finger or your palm. This represents the fourth postulate: collisions between particles and with the container walls are perfectly elastic. This means no kinetic energy is lost during the collision, though it may be transferred from one particle to another.
Pinky Finger: Kinetic Energy and Temperature
Your pinky is often used to make a "pinky promise." Think of this as a promise or a direct relationship. This represents the fifth and final postulate: the average kinetic energy of the gas particles is directly proportional to the absolute temperature (in Kelvin). This means that as temperature increases, the particles move faster, and as it decreases, they slow down.
