Ideal Gas Law & Maxwell-Boltzmann Distribution (Lecture Notes)

A set of practice flashcards covering key concepts from the lecture notes on ideal gases and the Maxwell-Boltzmann distribution.

What is the ideal gas law that relates P, V, n, and T for a perfect gas?

PV = nRT (the ideal gas law).

What does the constant R represent in the ideal gas law, and does it depend on units?

R is the ideal gas constant; its numerical value and units depend on the units used for pressure and volume.

What does SATP stand for, and how does it relate to STP?

SATP = Standard Ambient Temperature and Pressure (room-like conditions); STP = Standard Temperature and Pressure (0°C, 1 atm); SATP is more commonly used nowadays.

What is molar volume?

Molar volume V_m = V/n, the volume per mole of gas.

What is the partial pressure of a component j in a gas mixture (for an ideal gas)?

Pj = nj RT / V.

What does Dalton's law state about total pressure in a gas mixture?

Ptotal = Σj P_j (the total pressure is the sum of the partial pressures).

What must the mole fractions in a gas mixture sum to?

One (Σ x_i = 1).

What must the sum of all moles equal in a gas mixture?

Total moles n = Σi ni.

What is a 'perfect gas' as described in the notes?

A gas with only kinetic energy, no intermolecular forces; molecules collide elastically; idealized gas.

What is Boltzmann's constant k_B, and what is its value?

k_B = 1.38 × 10^−23 J/K; relates molecular energy to temperature.

How are R and k_B related via Avogadro's number?

R = NA kB (macroscopic gas constant is related to microscopic Boltzmann constant).

What distribution describes the speeds of gas molecules at a given temperature?

Maxwell-Boltzmann distribution of speeds.

What is the form of the Maxwell-Boltzmann speed distribution for speed v?

f(v) = 4π (m/(2πkT))^(3/2) v^2 exp(- m v^2 / (2 k_B T)) (the speed distribution, with the appropriate normalization).

What is the Boltzmann distribution for energy E?

P(E) ∝ exp(-E/(k_B T)).

How is pressure connected to molecular momentum in kinetic theory?

Pressure arises from momentum transfer to container walls during molecular collisions; connects microscopic speeds to macroscopic P.

How can PV = nRT be used to analyze changes when T or V changes while n is fixed?

If n and T are constant, P ∝ 1/V (Boyle's law); increasing V decreases P and vice versa.