3B Chapter 13

molecular collisions exert a force on a wall

PV = Nmv²

boltzmann constant Kb

1.38 × 10^-23 J/K

vrms of molecules

rad 3KbT/m

• m = kg/ mol

vrms of atoms

vrms = rad 3RT/M

• M = kg/mol

partial pressure

Pa = Xa (Ptotal)

Xa = mols of gas/ total moles

Pa = kPa

boltzmann factor for populations in discrete energy levels

N2/N1 = e^(-△e/KbT)

thermal energy and specific heat

Eth = 3/2 nRT

molar specific heat of a monatomic gas for constant volume

W = 0 so Q = Eth

Cv = 3/2R = 12.5 J/ mol K

molar specific heat of a monatomic gas for constant pressure

W = P△V = nR△T

Cp = Cv + R = 20.8 J/mol K

degree of freedom

each degree contributes ½ Kb T to the enrgy of a system

potential energy of solids and Cv

Cv = 3R

finding the temperature change if the system is monatomic gas

Cv = 12.5 bc constant volume

plug into Q = nCv△T

finding the temperature change if the system is a diatomic gas

using Cv = 20 J/molK

plug into Q = nCv△T

finding the temperature change if the system si a solid

use Cv = 25 J/mol

plug into Q = nCv△T

mean free path (lambda)

if a molecule has N collisions as it travels a distance L, it is the average distance between collisions

I = L/N

lambda = 1 / (4 rad 2(N/V)r²

N/V = P/KT

diffusion coefficient D

D = 1/3 Vrms (lambda)

diffusion coefficient of a gas at temp and pressure

D = (KbT)³/2 / 4 pi rad6 mpr²

root mean square distance, time, and diffusion coefficient

r(rms) = rad 6Dt

how many hours it takes perfrume to diffuse 3 m in still air

Vrms = rad 6Dt

vrms = 3 m