15 - Ideal Gases

Question 1

number of atoms =

Answer 1

N=nxNa
number of atoms/molecules = number of moles x Avagadros constant

Question 2

1 mol

Answer 2

is the amount of substance that contains 6.02x10^23 atoms

Question 3

mass and molar mass

Answer 3

m=nM
mass = number of moles x molar mass

Question 4

kinetic model for ideal gas

Answer 4

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

Question 5

how does gas in a container produce pressure?

Answer 5

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

Question 6

Boyles law

Answer 6

for a fixed mass of gas at a constant temperature:
pV=constant
p1v1=p2v2

Question 7

reducing volume slowly ensures

Answer 7

temperature stays constant

Question 8

define ideal gas

Answer 8

a gas that obeys boyle’s law at all temperatures

Question 9

why dont real gases obey boyles law when cooled near condensation point?

Answer 9

gas turns into liquid

Question 10

room temp

Answer 10

20°C (293K)

Question 11

atmospheric pressure

Answer 11

101kPa
in all directions

Question 12

Pressure law

Answer 12

for a fixed mass of gas at a constant volume:
p/T = constant
p1/T1=p2/T2
proportional if T in kelvins

Question 13

Charles’ law

Answer 13

for a fixed mass of gas at a constant pressure:
V/T = constant
V1/T1=V2/T2
proportional if T in kelvins

Question 14

estimating absolute 0

Answer 14

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

Question 15

Ideal gas law equation

Answer 15

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

Question 16

gradient of pV/T graph

Answer 16

=nR
so the more moles of gas, the steeper

Question 17

why do we use Crms

Answer 17

velocity is a vector so velocities of the particles would cancel out and average velocity would equal 0

Question 18

pressure kinetic theory equation

Answer 18

pV= 1/3 N m ⁻c^2
pressre
volume
number of molecules
mass of one molecule
> Nm = total mass
⁻c^2 mean square speed

Question 19

mass of one molecule

Answer 19

Mmolecule=M/Na
M - molar mass
Na- Avagadros constant

Question 20

Maxwell-Boltzmann distribution

Answer 20

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)

Question 21

effect of changing temperature on Maxwell-Boltzmann distribution

Answer 21

the greater the range of speeds -distribution becomes more spread out, most common speed and rms speed increase

peak decreases, graph spreads out

Question 22

Boltzmann constant

Answer 22

R/Na
molar gas constant / avagadros constant

Question 23

new ideal gas equation

Answer 23

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

Question 24

average molecular kinetic energy and temperature equation

Answer 24

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

Question 25

kinetic energy of different atoms

Answer 25

every gas molecule has the same mean kinetic energy, so more massive molecules have lower r.m.s. speeds

Question 26

explain why there is such little helium in atmosphere

Answer 26

heliums have a very small mass so have higher rms speed. according to maxwell-boltzmann distribution, some helium atoms have higher speeds than the rms speed. over time, these atoms have escaped the earth’s atmosphere

Question 27

internal energy of an ideal gas

Answer 27

internal energy is sum of kinetic and potential. no electrostatic forces between molecules in gas so no potential energy. so for ideal gases the kinetic energy is equal to total internal energy
internal energy ∝ temperature