Kinetic molecular theory (KMT) is a particulate model that links what individual gas particles do (continuous, random motion, elastic collisions) to macroscopic gas properties like pressure, temperature, diffusion and effusion. Key points from the CED: KE = 1/2 mv², Kelvin temperature ∝ average kinetic energy, and the Maxwell–Boltzmann distribution shows how particle speeds/energies spread at a given T. Using KMT you can explain why increasing T raises average speed, why lighter molecules move faster (same KE → larger v for smaller m), and why pressure changes when particles hit container walls more often or harder. This topic is tested in AP Chem under 3.5.A (use graphs of Maxwell–Boltzmann and do KE/speed calculations on the exam). For a focused review, see the Topic 3.5 study guide (https://library.fiveable.me/ap-chemistry/unit-3/kinetic-molecular-theory-gases/study-guide/nBJY7t92TEJmGXm9HHTU) and practice problems at (https://library.fiveable.me/practice/ap-chemistry).

KMT explains gas behavior by linking particle motion to macroscopic properties. Key assumptions: gas particles are far apart, in continuous random motion, have negligible volume, and undergo elastic collisions. From this you get: - Pressure: collisions of particles with container walls produce pressure; more frequent or more energetic collisions (higher n, T, or speed) → higher P. - Temperature & KE: Kelvin T is proportional to average kinetic energy (KE = 1/2 mv²). Raising T increases average speed and shifts the Maxwell–Boltzmann distribution to higher energies. - Volume and compressibility: large distances between particles make gases highly compressible. - Diffusion/effusion: random motion + mean free path determine mixing rates; lighter molecules have higher rms speed (v rms ∝ 1/√molar mass) so they diffuse/effuse faster (Graham’s law). - Nonideal behavior arises when particle volume and intermolecular forces matter (deviations from ideal gas law). For AP exam framing, be ready to use KE = 1/2 mv², interpret Maxwell–Boltzmann curves, and connect particle-level ideas to P, V, T, diffusion, and effusion (CED 3.5.A). Review the Topic 3.5 study guide (Fiveable) here: (https://library.fiveable.me/ap-chemistry/unit-3/kinetic-molecular-theory-gases/study-guide/nBJY7t92TEJmGXm9HHTU) and practice problems at (https://library.fiveable.me/practice/ap-chemistry).

The Maxwell–Boltzmann distribution is a graph that shows how the speeds (or kinetic energies) of particles in a gas are spread out at a given temperature. Key points: the area under the curve equals the total number of particles, the peak is the most probable speed, the mean speed and the root-mean-square (rms) speed are a bit higher than the peak, and KE = 1/2 mv^2 links speed to kinetic energy. When T increases the curve flattens and shifts to higher speeds (average KE ∝ T in Kelvin). At the same T, lighter molecules have a curve shifted to higher speeds than heavier ones—that’s why diffusion/effusion rates differ (Graham’s law). On the AP exam you may be asked to interpret or compare these curves (CED 3.5.A; see the KMT study guide on Fiveable for practice and visuals: https://library.fiveable.me/ap-chemistry/unit-3/kinetic-molecular-theory-gases/study-guide/nBJY7t92TEJmGXm9HHTU). For more practice questions, try Fiveable’s AP Chem problem set (https://library.fiveable.me/practice/ap-chemistry).

Temperature is a measure of the average kinetic energy (KE) of gas particles. Quantitatively, KEavg ∝ T (in Kelvin), and for a single particle KE = 1/2 mv²—so as T increases the average speed (and root-mean-square speed) of particles increases. On a Maxwell–Boltzmann plot, raising T shifts the distribution to higher speeds and flattens/broadens it (more particles at very high energies). At the same T, lighter molecules move faster than heavier ones because v ∝ √(1/m). This idea is central to KMT (CED 3.5.A: KE relation, Maxwell–Boltzmann) and shows up on AP questions asking you to compare speeds, energies, or shapes of the distribution. Review the Topic 3.5 study guide for practice and graphs (Fiveable: https://library.fiveable.me/ap-chemistry/unit-3/kinetic-molecular-theory-gases/study-guide/nBJY7t92TEJmGXm9HHTU) and try extra practice problems (https://library.fiveable.me/practice/ap-chemistry) to prep for unit 3 items on the exam.

Because temperature (in Kelvin) measures the average kinetic energy of particles, heating a gas raises that average KE. Kinetic molecular theory and the equation KE = 1/2 mv^2 show why: if average KE goes up, the average speed v must increase (for a given mass m). On the molecular level the Maxwell–Boltzmann distribution shifts: the peak moves to higher speeds and the curve broadens as T increases, so more particles have higher velocities. Mathematically, root-mean-square speed v_rms = sqrt(3RT/M), so v_rms grows roughly with the square root of T (double T → v_rms increases by √2). Collisions remain elastic, but with higher speeds collisions happen more often and transfer more momentum, which explains macroscopic effects like higher pressure if volume is fixed. For a clear CED-aligned review, see the Topic 3.5 study guide (https://library.fiveable.me/ap-chemistry/unit-3/kinetic-molecular-theory-gases/study-guide/nBJY7t92TEJmGXm9HHTU). For extra practice, try problems at (https://library.fiveable.me/practice/ap-chemistry).

KE = 1/2 mv^2 just says how much kinetic energy (energy of motion) a single particle has. Break it down: - m is the particle’s mass (use kg), v is its speed (m/s). - Square the speed (v^2) so faster particles get a lot more energy, then multiply by mass and 1/2. Units give joules (J). In Kinetic Molecular Theory (CED 3.5.A.2) this equation links microscopic motion to macroscopic properties: the average KE of gas particles ∝ temperature (Kelvin). So at the same T, all gases have the same average KE, but lighter particles (small m) must move much faster than heavier ones to match that KE—that’s why H2 effuses and diffuses faster than O2. The Maxwell–Boltzmann curve shows the distribution of those speeds (3.5.A.1, 3.5.A.4). On the AP, you might use KE = 1/2 mv^2 to compare speeds or relate average KE to temperature. For a deeper refresher, check the Topic 3.5 study guide (https://library.fiveable.me/ap-chemistry/unit-3/kinetic-molecular-theory-gases/study-guide/nBJY7t92TEJmGXm9HHTU) and hit practice problems (https://library.fiveable.me/practice/ap-chemistry).

Average kinetic energy is a property of the whole sample—it’s the mean of all particles’ kinetic energies and is directly proportional to the Kelvin temperature (〈KE〉 ∝ T). Individual particle energy is what one gas molecule actually has at a moment, given by KE = 1/2 mv². Because particles move randomly, individual KE values vary widely; the Maxwell–Boltzmann distribution shows that spread (most probable, average, and rms speeds differ). So: at a fixed temperature the average KE is fixed, but some particles have less energy and some have more—only the mean is tied to T. On the AP exam you’ll see this on Maxwell–Boltzmann graphs and in questions about temperature, rms speed, and distribution shape (CED 3.5.A.1–3). For a quick refresher, check the Topic 3.5 study guide (https://library.fiveable.me/ap-chemistry/unit-3/kinetic-molecular-theory-gases/study-guide/nBJY7t92TEJmGXm9HHTU) and try practice problems (https://library.fiveable.me/practice/ap-chemistry).

Read the axes first: x = speed (or kinetic energy), y = number (or fraction) of particles. Key features to label and use on the AP exam: - Peak = most probable speed (the single highest point). - Mean (average) speed lies a bit to the right of the peak; RMS speed is slightly further right than the mean. - Area under the curve = total number of particles (so shaded areas compare fractions/probabilities). Use KE = 1/2 mv² and the CED fact that average KE ∝ T (Kelvin) to reason about shifts: increasing T shifts the curve right and flattens it (more high-speed particles); decreasing molar mass shifts the curve right and widens it (lighter molecules move faster at same T). For exam answers, point out relative positions (which curve is higher at low speeds, which peaks right) and use phrases from the CED: most probable speed, average kinetic energy, root-mean-square speed, temperature dependence. Practice reading/labeling graphs on Fiveable’s topic guide (https://library.fiveable.me/ap-chemistry/unit-3/kinetic-molecular-theory-gases/study-guide/nBJY7t92TEJmGXm9HHTU) and try more problems (https://library.fiveable.me/practice/ap-chemistry).

As temperature increases the Maxwell–Boltzmann curve shifts and changes shape because particle kinetic energies broaden and the average kinetic energy rises. KE = 1/2 mv² and the average KE ∝ T (Kelvin), so higher T means higher typical speeds (vmp and vrms scale with √T/m). On a plot this does three things: the peak (most probable speed) moves to higher speeds, the curve flattens (becomes broader) because speeds are more spread out, and the height of the peak decreases so the area (total number of particles) stays constant. At lower T the curve is narrow and tall—most particles cluster near a single speed. This is exactly what the CED expects you to explain graphically for Topic 3.5 (KMT/Maxwell–Boltzmann). Want to practice sketching and calculations for vmp and vrms? See the Topic 3.5 study guide (https://library.fiveable.me/ap-chemistry/unit-3/kinetic-molecular-theory-gases/study-guide/nBJY7t92TEJmGXm9HHTU) and more practice problems (https://library.fiveable.me/practice/ap-chemistry).

Think of a gas as trillions of tiny particles moving randomly—that microscopic motion is what creates the macroscopic stuff you measure. Kinetic molecular theory (KMT) says pressure comes from particles hitting container walls (more collisions or harder hits → higher P). Temperature (in K) is directly proportional to the average kinetic energy, KE = 1/2 mv², so if T rises the average v and KE rise. The Maxwell–Boltzmann distribution graph shows that raising T moves the peak right and flattens the curve (more fast particles, broader spread). Particle mass matters too: lighter molecules have higher speeds at the same T (root-mean-square speed ∝ 1/√m). Mean free path, diffusion, and effusion follow from collision frequency and speed—more collisions slow diffusion; smaller mass or higher T speeds up effusion (Graham’s law). On the AP exam, you may be asked to explain these links or interpret a Maxwell–Boltzmann curve (Topic 3.5 in Unit 3). For a clear refresher, check the KMT study guide (https://library.fiveable.me/ap-chemistry/unit-3/kinetic-molecular-theory-gases/study-guide/nBJY7t92TEJmGXm9HHTU) and try practice problems at (https://library.fiveable.me/practice/ap-chemistry).

“Continuous random motion” means gas particles are always moving (continuous) and their directions and speeds change unpredictably (random) because they travel in straight lines between collisions and then bounce off other particles or container walls. Between collisions each particle has a definite velocity, and collisions are treated as elastic so kinetic energy is conserved on average. At a given temperature the distribution of those speeds follows the Maxwell–Boltzmann curve, so not every particle has the same speed—there’s an average (related to KE = 1/2 mv²), a most probable speed, and a spread that widens with temperature. Microscopically this motion explains macroscopic gas behavior: frequent wall collisions give pressure, higher T raises average kinetic energy (and pressure or speed), and diffusion/effusion arise from the random straight-line flights and collisions. For more AP-aligned review see the Topic 3.5 study guide (https://library.fiveable.me/ap-chemistry/unit-3/kinetic-molecular-theory-gases/study-guide/nBJY7t92TEJmGXm9HHTU) and practice problems (https://library.fiveable.me/practice/ap-chemistry).

Kinetic molecular theory (KMT) explains why the ideal gas law works. KMT says gas particles move randomly and collide elastically with container walls; those collisions create pressure. Using KE = 1/2 mv² and the average of v², kinetic theory gives a microscopic relation: P V = (1/3) N m⟨v²⟩. Because average kinetic energy per particle ⟨KE⟩ = 1/2 m⟨v²⟩ and Kelvin temperature is proportional to ⟨KE⟩, you get P V = N kT (k = Boltzmann constant). Replacing N with n·NA and k·NA = R yields the macroscopic ideal gas law: P V = n R T. On the AP (CED 3.5.A.1–3) you should be able to link particle motion, KE, and the Maxwell–Boltzmann distribution to this derivation. For a clear walkthrough and practice, see the Topic 3.5 study guide (https://library.fiveable.me/ap-chemistry/unit-3/kinetic-molecular-theory-gases/study-guide/nBJY7t92TEJmGXm9HHTU) and more practice problems (https://library.fiveable.me/practice/ap-chemistry).

Temperature in K is used because Kelvin is an absolute temperature scale—0 K (absolute zero) means zero thermal energy. In K the temperature is directly proportional to the average kinetic energy of particles (CED 3.5.A.3). That’s why kinetic-energy relations like KEavg ∝ T (and formulas derived from the Maxwell–Boltzmann distribution) use T in kelvins: if you doubled T (K), the average kinetic energy of the gas particles doubles. Celsius or Fahrenheit are shifted scales (their zero points aren’t zero kinetic energy), so they don’t keep that direct proportionality. On the AP exam you’ll see this in KMT questions (3.5.A) and when using KE = 1/2 mv² or rms speed formulas—always plug T in K. For more practice and a clear rundown on KMT and Maxwell–Boltzmann graphs, check the Topic 3.5 study guide (https://library.fiveable.me/ap-chemistry/unit-3/kinetic-molecular-theory-gases/study-guide/nBJY7t92TEJmGXm9HHTU). Fiveable’s unit study guides and practice problems are handy if you want extra problems to master this.

As temperature increases the Maxwell–Boltzmann speed (or kinetic energy) distribution shifts and spreads: the peak (most probable speed) moves to higher speeds, the curve becomes broader and lower (flatter), and the high-speed tail gets longer. That happens because Kelvin temperature is proportional to average kinetic energy (KE = 1/2 mv²), so raising T increases the average and root-mean-square speeds (v_rms ∝ √T). The total area under the curve (total number of particles) stays the same. On AP tasks you should be able to sketch/interpret this graph and relate shifts to higher average KE and faster molecular motion (CED 3.5.A.1–3.5.A.4). For a quick refresher, see the Topic 3.5 study guide (https://library.fiveable.me/ap-chemistry/unit-3/kinetic-molecular-theory-gases/study-guide/nBJY7t92TEJmGXm9HHTU) and try practice problems (https://library.fiveable.me/practice/ap-chemistry).

On FRQs use a simple particulate sketch plus short, specific statements tying particle behavior to macroscopic gas properties. Steps you can follow: - Draw particles (dots) with arrows showing speeds; label faster/average using KE = 1/2 mv² and note temperature ∝ average KE (CED 3.5.A.2–3). - For changes (T, V, n, or molar mass) show how the Maxwell–Boltzmann curve shifts/changes shape (most probable, average, rms speeds) and state the effect on pressure, diffusion, effusion, or mean free path (use terms: elastic collisions, mean free path, molar mass). - Use comparisons: “At higher T arrows longer → greater avg KE → more frequent/energetic collisions → higher P (if V constant).” - If asked to justify, cite conservation of energy in elastic collisions or kinetic theory relations (root-mean-square speed ∝ 1/√m). - Always label diagrams and connect each particulate claim to a macroscopic observation (describe → explain → justify, per AP FRQ verbs). Practice these on the Topic 3.5 study guide (https://library.fiveable.me/ap-chemistry/unit-3/kinetic-molecular-theory-gases/study-guide/nBJY7t92TEJmGXm9HHTU) and hit practice problems (https://library.fiveable.me/practice/ap-chemistry).