Question

MCAT Tutorial: Kinetic-Molecular Theory & Ideal Gas Laws

Answer 1

\({\bf{Kinetic-Molecular~Theory~of~Gases:}}\) the behavior of gases can be explained by treating gases as a composition of colliding particles

Key Assumptions:
1. gas particles have negligible size
2. particle motion is random in speed and direction
3. minimal attractive/repulsive forces between gases
4. collisions are perfectly elastic (no KE loss)
5. average KE = 1/2(mv)^2 = (3/2)kT

Maxwell Boltzmann Distribution: describes the distribution of the velocity of particles vs. temp; range of speeds is larger at higher temps

Answer 2

\({\bf{Measuring~Pressure:}}\) w/ mannometer, compares the internal pressure of a gas + the height of a column of mercury to measure atmospheric pressure



left: internal pressure of gas = height difference of mercury columns + atmospheric P
right: atmospheric P = internal pressure of gas + height difference of mercury columns

units: 1 atm = 760 mmHg [milometers mercury] = 101. kiloPascals
chemistry often uses atm, physics prefers kPa, be careful between the two

STP = standard temperature and pressure = 1 atm, 0 degrees C (or 273.15K)

\({\bf{Ideal~Gas~Laws:}}\)
- Boyle's: P and V inversely related
- Charles': V and T directly related
- Gay-Lussac: P and T directly related

combing these facts gives us:

P1V1/T = P2V2/T

-Ideal Gas Law: PV = nRT, n = moles, R is the ideal gas constant (differes depending on units, the two most common are 0.08206 L atm/molK and 8.31 kPa/molK

disclaimer: I am not 100% sure what constants are included on the MCAT but it seems like gas constants are included, doesn't hurt to memorize these two anyway since they come up a lot in chem calculations

*Avogadro's Hypothesis [will need to memorize this]: number of moles is proportional to volume at a constant T and P. at STP this is 1 mol = 22.4L * will probably need to memorize this

Misc. Properties of Gases:

-Dalton's Law of Partial pressures: in a mixture of gases, total pressure is sum of the individual pressures of the component gases
- root mean squared velocity = average speed = sqrt(3RT/M)
- Graham's Law: rate of effusion of gas1/effusion of gas 2 = sqrt(MMgas 2 / MM gas1)

Answer 3

the van der waal's equation, accounts for deviations from the ideal gas law

a represents the attraction of molecules (increase in pressure as volume decreases)
b represents the size of molecules (decrease in volume)

Answer 4

Anyway, that's the end of my tutorial, I hope it was a helpful resource. Source material is the 2nd Edition Barron's Prep book for the new MCAT