Ideal Gases Flashcards
define a mole (unit of substance, not mass)
the amount containing as many as particles as there are atoms in 12g oc carbon-12. this is equal to the Avogadro constant
describe how pressure is exerted by an ideal gas on its container, w respect to temp, pressure, and vol
- molecules of gas are free to move around in box and they move randomly at high speeds
- temp is related to average speed of molecules; hotter gas, faster molecules. therefore more frequent collisions
- since force is rate of change of momentum, each collision applies a force across wall’s surface area. the faster they hit, the greager force on them
- since pressure is force per unit area
- higher temp leads to higher pressure
-if volume of box decreases but temp is constant, smaller wall surface area hence more collisions
define Avogadro’s constant
number of atoms of carbon-12 in 12g of carbon-12; eqal to 6.0210^23 per mol
ie 1C atom = 1.9910^-26 kg (12u)
so xC atoms = 0.012 kg
x= 6.02*10^23 atoms
one mole of an element is that element’s _
relative atomic mass in g
define pressure in ideal gases
frequency of collisions of gas molecules per unit area of container
state boyles law, and hence state the relationship between pressure and volume for a fixed mass of gas at constant temp
P is proportional 1/V
P1V1=P2V2
state charles law, and hence state the relationship between thermodynamic temp and volume for a fixed mass of gas at constant pressure
V is proportional to T
V1/T1 = V2/T2
state charles law, and hence state the relationship between thermodynamic temp and volume for a fixed mass of gas at constant pressure
V is proportional to T
V1/T1 = V2/T2
state pressure law, and hence state the relationship between pressure and thermodynamic temp for a fixed mass of gas at constant volume
P is proportional to T
P1/T1 = P2/T2
what is the eqn of state/ ideal gas eqn. Then, state it in its other form
pV = nRT
pV = NkT
note: T is thermodynamic temp so should be in K
define the boltzmann constant equation
k=R/NA, where R=molar gas constant, and NA= Avogadro constant
define an ideal gas
a gas which obeys the equation of state PV=nRT at all pressures, volumes, and temps
define the boltzmann constant equation
k=R/NA, where R=molar gas constant, and NA= Avogadro constant
- what is the function of the boltzmann constant.
- and why is its value so small?
- relates properties of microscopic proerties ie KE of gas molecules to macroscopic properties ie temp
- small because increase in ke of a molecule is very small for an increase in temp
what does the kinetic theory of gases model
the thermodynamic behaviour of gases by linking the micrscopic properties eg mass and speed to macroscopic ones eg pressure, volume, temp
state the assumptions of the kinetic theory
- molecules behave as identical, hard, perfectly elastic spheres
- volume of molecules is negligible compared to volume of container
- time duration of a collision is negligible compared to time in between collisions
- no forces of attraction or repulsion between molecules
- molecules in continuous random motion
- no. of gas molecules in a container is v large so the agerage behavior is considered (large sample size)
why are the velocities of gas molecules squared?
- particles travel in all direction in 3D space and velocity is a vector, so some velocities will have a negative direction and others positive
- the large no of molecules’ velocities in opp directions will cancel out, giving a net zero
- to find the pressure of a gas, we have to eliminate this issue hence we square
how to calculate everage speed of gas particles
square root of mean square speed
describe the theroy part behind the derivation of the kinetic thoery of gases equaton
basic notion:
- when molecules rebound from the container wall the change in momentum produces a force (exerted by particle on wall)
- overall pressure is created as many molecules in random motion exert forces (per unit area)
deeper idea:
- molecule, mass m and speed c, moves paralell to a side and collides at regular intervals with ends and exerts force which contributes to pressure
- total pressure exerted by all molecules can be found
state the 5-step derivation
1) change in momentum as a singlr molecule hits wall perpendicularly. final velocity in opp direction is -c so -mc - +mc=-2mc
2) no. of collisions per second by the molecule on a wall . time between collision ie hit a wall and back, t=2l/c. (this is also the time for change in momentum)
3) find rate of change of p ie F=P/t which is = 2mc/(2l/c) (not -2mc/(2l/c) cos that would be force on molecule ie in direction of ITS change in p, we want force on wall BY molecule ie the opp) = mc^2/l
4) pressure from one molecule= f/a= (mc^2/l)/l^2. So P from many =N(mc^2/l)/l3 but its cos each molecule has a diff velocities- more deets about this in notes
5) irl, molecules are moving in 3Ds equally not just opp walls at 90. hence c^2=cx^2+cy^2=cz^2, but they all equal/same mean due to random motion so c^2=3cx^2 and cx^2 (mean square speed in any direction) =1/3cx^2.
6) Finally, sub back into P=Nm/l3 giving PV=1/3Nm or P=1/3p (as No of molecules *m of one molecule= total gas mass and this /l3 ie V is together = density p)
average KE aka
mean KE
mean translational KE
PV=NkT and PV= 1/3Nm soo…? (derivation of average KE eqn for one molecule)
- equating gives 1/3Nm=NkT
- further, m=3kT
- since we know that KE=1/2mv^2, where v^2 is for velocity of any one molecule we use ie the average speed of all molecules
- divide both sides by 2 to get the Average Translational Kinetic Energy of AN ideal gas molecule : 1/2m=3/2kT
what does 1/2m=3/2kT tell us about the mean KE of an ideal gas molecule
is proportional to the thermodynamic temp
define translational kinetic energy
the energy a molecule has as it moves from one point to another
