chapter 15 - ideal gases Flashcards
avagadros number
in 1 mole there are 6.02*10^23 particles
no. particles = no. moles * Avagadros no.
ideal gas - kinetic model assumptions
- gas contains a very large no. atoms moving in random directions at diff speeds
- atoms have negligible volume compared to volume of the gas
- collisions with each other and the walls of containers are perfectly elastic
- time of collisions is negligible to time between collisions
- electrostatic forces are negligible except during collisions
how does a gas cause pressure
- atoms are always moving in a gas
- when they collide with a wall the container exerts a force on them causing them to change direction
- therefore they change momentum
- F = 2mu/t
- due to N3 atoms exert force on the wall
- because a large no particles collide with the wall P = F/A
ideal gas equation
PV/T = constant
P vs V at constant temp - Boyles law
- set up a syringe with a fixed about of gas
- change force applied to top by changing mass applied on top - use balance to measure masses - repeat 3 times and average
- F = mass added *g
- pressure = F/area
- use callipers to measure d in 3 places and average A = pi(d/2)^2
- volume measured off syringe in cm^3
- take measurements of room temp throughout - keep constant
- plot P against 1/V (straight line through origin)
V vs T at constant pressure - Charles Law
- set up with water baths at different temps from 10-70ºC
- put syringe in lowest temp water
- measure volume off scale
- change water bath repeat for 6 temps
- repeat 3 times and average
- plot V against T (straight line through origin)
assume: - thermal equilibrium reached before measurements
- perfect seal on syringe
- constant pressure with surroundings
if no scale on syringe
1cm^3 = 1ml
or Vol = 𝞹r²h
P vs T at constant V
- same method as V vs T at constant P
- but measure P using a jolly bulb and barometer
(use jolly bulb - as will keep shape at range of temps - fixed vol + amount of gas) - if using a heat plate not water bath assume heating whole bulb
- plot P against T (straight line through origin)
ideal gas equation moles
PV = nRT
ideal gas equation particles
PV = NkT
why use rms speed
bc all atoms in a gas are moving randomly in different directions at different velocities (even at same temp)
- if we calculated average velocity it would be zero so measure rms speed instead
prop to temp in kelvin
how to calc rms speed
- square velocities
- take the mean
- root it
if a box is 3d how many particles collide with one plane
1/3
maxwell Boltzmann distribution
graph of no particles with speed v against speed
at low temp more particles are at the rms speed but rms speed is lower
at low temp the distribution is less spread out
rms speed is at peak of curve
why less He
- high temp after Earths formation
- means individual He atoms reach high enough speeds to escape Earths grav pull
- N2 and O2 arent as fast so dont
boltzmann constant
k = R/avagadros no.
internal energy of an ideal gas
- due to negligible PE theres only KE
is IE is prop to KE which is prop to temp
proving KE is prop to T (kelvin)
PV = 1/3Nm c²
PV = NkT
NkT = 1/3Nm c²
1/2 *2/3 mc² = kT
1/2mc² = 3/2 kT
KE is prop to T
ideal gas equation with rms speed
PV = 1/3Nm c²
P = 1/3ρc²
boyles law
pressure is inversely proportional to volume at constant temp
PV = constant
