Chapter 15 - Ideal Gases Flashcards
what is the SI unit for amount of substance and what is the constant associated with it and the definition
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”
what is the formula for number of particles and the mole
N = n x NA
what is the formula for molar mass
Mass = moles x Mr M = n x Mr
what is the kinetic theory of gases
the kinetic theory of gases is a modal used to describe the behaviour of an ideal gas
what are the modelling assumptions we make with an ideal gas
- 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
how to calculate pressure/force from a single particle
F(atom) = -2mu/deltaT
state Boyle’s Law and the associated equation and proportionality
” 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
describe the equipment and method for investigating Boyle’s Law
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
State Charles’ law and the relevant equations and proportionalities
“where pressure and amount of gas are constant volume of gas is directly proportional to temperature”
V/T = constant V = kT
state the pressure law and relevant equations and proportionalities
“if the volume and mass of a gas remain constant then the pressure is directly proportional to the temperature”
P/T = k P= kT
explain a suitable practical to investigate the pressure law
- 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
how can we combine the gas laws
we can combine them to give
PV/T = k
where p, v, and t change we can have
P1V1/T1 = P2V2/T2
what is the ideal gas equation and the value of the molar gas constant
pV = nRT R = 8.31
what is the issue with taking the vector sum of the velocities of particles in a gas
they would all cancel out to give average velocity = 0
how do we get around this and what is RMS speed
- 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))
how do we derive the pv = 1/3… equation
- 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
what is the equation linking pV and N (number of particles)
pV = 1/3Nmc^2
where c^2 is a mean square speed
N is the number of particles
what does the Maxwell-Boltzmann distribution show and where do most probable speed, avr speed, and rms speed lie
the range of molecular speeds in a gas at a given temperature
going left to right, MPS, AvrS, RMS
what is the Boltzmann Constant
- The Boltzmann constant, k, is a constant equivalent to R/NA
- 1.38x10^-23 JK^-1
what is directly proportional to temperature which proves what temperature is
Ek direct prop. to T
do the derivation for Ek direct prop. to T and what to remember
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
what are the three equations for
pV = …
pV = nRT pV = NkT pV = 1/3Nm (c^2(bar))
what to remember about Ek vs speed
- 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
how does the internal energy of an ideal gas change with temperature
- 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
