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Physics Year 13 > Chapter 15 - Ideal Gases > Flashcards

Chapter 15 - Ideal Gases Flashcards

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1
Q

what is the SI unit for amount of substance and what is the constant associated with it and the definition

A

the mole = 6.02x10^23
“one mole is the amount of substance that contains as many elementary entities as there are atoms contained within 12g of carbon-12”

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2
Q

what is the formula for number of particles and the mole

A

N = n x NA

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3
Q

what is the formula for molar mass

A 
Mass = moles x Mr
M = n x Mr
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4
Q

what is the kinetic theory of gases

A

the kinetic theory of gases is a modal used to describe the behaviour of an ideal gas

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5
Q

what are the modelling assumptions we make with an ideal gas

A
  • the gas contains a very large number of particles, all with random motion
  • particles occupy a negligible space/volume in the container they fill
  • collisions of all particles with each other and container walls are perfectly elastic
  • time of collisions is negligible
  • electrostatic forces are negligible
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6
Q

how to calculate pressure/force from a single particle

A

F(atom) = -2mu/deltaT

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7
Q

state Boyle’s Law and the associated equation and proportionality

A

” If the temperature and mass of a gas remain constant then the pressure of a gas is inversely proportional to it’s volume”

pv = constant
P = k/v
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8
Q

describe the equipment and method for investigating Boyle’s Law

A

Have either:

  • gas and oil in a container with volume markers, connected via a tube with a pressure sensor to a pump
  • OR a sealed gas syringe with a space to add masses to the top

method:

  • measure initial temp and press of gas, and volume
  • slowly increase pressure so that temperature doesn’t increase
  • record volume at different pressures
  • plot P against 1/v
  • this should give a straight line graph of gradient k with a differing gradient depending on temperature
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9
Q

State Charles’ law and the relevant equations and proportionalities

A

“where pressure and amount of gas are constant volume of gas is directly proportional to temperature”

V/T = constant
V = kT
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10
Q

state the pressure law and relevant equations and proportionalities

A

“if the volume and mass of a gas remain constant then the pressure is directly proportional to the temperature”

P/T = k
P= kT
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11
Q

explain a suitable practical to investigate the pressure law

A
  • have a water bath with a thermometer, and a tube with dry air connected to a pressure gauge
  • take the initial temp and pressure
  • increase temperature and measure pressure and temp (Celsius) at set intervals
  • plot pressure against temp, extrapolate line to pressure = 0, this is where T = absolute 0
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12
Q

how can we combine the gas laws

A

we can combine them to give
PV/T = k

where p, v, and t change we can have

P1V1/T1 = P2V2/T2

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13
Q

what is the ideal gas equation and the value of the molar gas constant

A 
pV = nRT
R = 8.31
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14
Q

what is the issue with taking the vector sum of the velocities of particles in a gas

A

they would all cancel out to give average velocity = 0

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15
Q

how do we get around this and what is RMS speed

A
  • We use RMS (root-mean-square) speed
  • we find C^2 for each molecule
  • we sum them and then divide by the number of molecules to give
    C^2 (bar)
  • we then root it to get RMS speed
    so
    RMS = sqrt( C^2 (bar))
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16
Q

how do we derive the pv = 1/3… equation

A
  • we have a box of length L, a particle (velocity u) collides with a wall
  • the change in momentum of the particle is 2mu
  • the time between collisions is 2L/u
  • thus the average force is 2mu/(2L/u) = mu^2/L
  • the average pressure on a wall then is (mu^2/L)/A = mu^2/vol
  • so total pressure (from all particles) = Nmu^2/vol
  • but only 1/3 of all particles will hit one wall so 1/3Nmu^2/vol = pressure
  • so pV = 1/3Nmu^2
17
Q

what is the equation linking pV and N (number of particles)

A

pV = 1/3Nmc^2
where c^2 is a mean square speed

N is the number of particles

18
Q

what does the Maxwell-Boltzmann distribution show and where do most probable speed, avr speed, and rms speed lie

A

the range of molecular speeds in a gas at a given temperature
going left to right, MPS, AvrS, RMS

19
Q

what is the Boltzmann Constant

A
  • The Boltzmann constant, k, is a constant equivalent to R/NA
  • 1.38x10^-23 JK^-1
20
Q

what is directly proportional to temperature which proves what temperature is

A

Ek direct prop. to T

21
Q

do the derivation for Ek direct prop. to T and what to remember

A 
pV = nRT
R = kNA
so pV = nNAkRT
so pV = NkT
also pV = 1/3 Nmc^2
so 1/3Nmc^2 = NkT
so 1/3mc^2 = kT
so 2/3 * 1/2mc^2 = kT
so given 2/3 and k are constants
and Ek = 1/2mc^2
Ek is direct prop. to T
this only works in kelvin
22
Q

what are the three equations for

pV = …

A 
pV = nRT
pV = NkT
pV = 1/3Nm (c^2(bar))
23
Q

what to remember about Ek vs speed

A
  • at a given temperature, all molecules have the same average Ek
  • this doesn’t necessarily mean they have the same velocity as they have different masses
24
Q

how does the internal energy of an ideal gas change with temperature

A
  • internal energy is formed of the sum of all kinetic and potential energies
  • an ideal gas has no potential energies
  • thus it only has kinetic energy
  • as kinetic energy is directly proportional to temperature
  • for an ideal gas
    I.E. is directly proportional to temp
25
Q

why is the internal energy of a real gas not directly proportional to temperature

A
  • In a real gas, there are some potential energies, thus although doubling the temperature doubles kinetic energy, it does not necessarily double the internal energy
26
Q

equation for PV including K

A

Pv = NKT

27
Q

equation linking K and Ek

A

3/2 KT = 1/2 mc^2(bar)

28
Q

what are the two main conclusions we can draw from Brownian motion experiments

A
  • gas molecules have random motion
  • mass of smoke/pollen particles is greater than mass of water molecules

Avoid elastic collisions

Physics Year 13 (15 decks)

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