15 - Ideal Gases Flashcards
number of atoms =
N=nxNa
number of atoms/molecules = number of moles x Avagadros constant
1 mol
is the amount of substance that contains 6.02x10^23 atoms
mass and molar mass
m=nM
mass = number of moles x molar mass
kinetic model for ideal gas
large number of molecules in random, rapid moton
partcles occupy negligible volume compared to volume of gas
all collisions are perfectly elastic
time of collisions is negligible compared to time between collisions
negligible electrostatic forces between particles except during collision
how does gas in a container produce pressure?
collisions with wall are elastic so speed does not change, only velocity and therefore momentum (change is equal to 2mv. N2L states that force acting on the atom is equal to rate of change of momentum and with N3L, the atom exerts an equal and opposite force on the wall. pressure given by total force exerted on wall divided by the cross sectional area of the wall
Boyles law
for a fixed mass of gas at a constant temperature:
pV=constant
p1v1=p2v2
reducing volume slowly ensures
temperature stays constant
define ideal gas
a gas that obeys boyle’s law at all temperatures
why dont real gases obey boyles law when cooled near condensation point?
gas turns into liquid
room temp
20°C (293K)
atmospheric pressure
101kPa
in all directions
Pressure law
for a fixed mass of gas at a constant volume:
p/T = constant
p1/T1=p2/T2
proportional if T in kelvins
Charles’ law
for a fixed mass of gas at a constant pressure:
V/T = constant
V1/T1=V2/T2
proportional if T in kelvins
estimating absolute 0
heater heats up water bath heating dry air in sealed vessel. temp of water bath increases (measure temp using thermometer), resulting increase in pressure as p/T = constant (recorded from pressure gauge) - regular 5℃ intervals
volume constant as changing it would also affect temp and/or pressure
draw graph of pressure / temp (p/℃ ) and LOBF, extrapolate back to where pressure is 0 (x intercept)
here is where the particles are not moving - minimum internal energy therefore zero pressure - absolute 0
Ideal gas law equation
for gas of constant mass:
pV/T = constant
p1V1/T1 = p2V2/T2
constant = nR
where n is number of moles of gas, R is molar gas constant
so pV=nRT
gradient of pV/T graph
=nR
so the more moles of gas, the steeper
why do we use Crms
velocity is a vector so velocities of the particles would cancel out and average velocity would equal 0
pressure kinetic theory equation
pV= 1/3 N m ⁻c^2
pressre
volume
number of molecules
mass of one molecule
> Nm = total mass
⁻c^2 mean square speed
mass of one molecule
Mmolecule=M/Na
M - molar mass
Na- Avagadros constant
Maxwell-Boltzmann distribution
the range of speeds of the particles in a gas due to random velocities and directions of particles (some very fast and some very slow)
the speed of an individual molecule changing as it collides will not impact overall distribution of speeds (if temp is constant)
effect of changing temperature on Maxwell-Boltzmann distribution
the greater the range of speeds -distribution becomes more spread out, most common speed and rms speed increase
peak decreases, graph spreads out
Boltzmann constant
R/Na
molar gas constant / avagadros constant
new ideal gas equation
n=N/Na
> pV=nRT
> pV=(N/Na)RT
as k = R/Na
> pV = NkT
where N is the number of molecules, k is boltzmann constant
average molecular kinetic energy and temperature equation
pV= 1/3 N m ⁻c^2 pV=NkT
1/2 m ⁻c^2 = 3/2 kT
Ek = 3/2 kT
Ek∝T
kinetic energy of a molecule is directly proportional to its absolute temperature in kelvin
