15. Ideal gases Flashcards
(13 cards)
Define One Mole
The amount of substance that contains as many elementary entities as there are atoms in 0.012kg (12g) of carbon-12
Explain, in terms of the behaviour of its molecules, how a gas exerts a pressure on the walls of its container [4 marks]
A change in momentum occurs when molecules collide with the walls of container
Hence, walls exert a force on the molecule (by Newtons 2nd law)
The total force exerted by the molecules on the wall is equal to the total force exerted by the wall on the molecules (by Newtons 3rd law)
pressure = total force on wall / area of wall
What are the assumptions for the kinetic model of ideal gases?
R - Random - Large number of molecules in random, rapid motion
A - Attraction - Negligible forces of attraction between particles except during collisions
V - Volume - Particles occupy negligible volume compared to the volume of gas
E - Elastic - All collisions are perfectly elastic
D - Duration - The time of the collisions is negligible compared to the time between collisions
List the gas laws and explain
Boyles law - For a gas at a fixed temperature and mass, its pressure is inversely proportional to its volume.
pV = constant
For a gas at a fixed volume and mass, its pressure is directly proportional to its temperature.
p/T = constant
For a gas at a fixed pressure and mass, its volume is directly proportional to its temperature.
V/T = constant
pV/T = constant
Derive pV = nRT
pV/T = constant
For 1 mole of an ideal gas, constant = ideal gas constant = 8.31JK^-1mol^-1 = R
For n moles of a gas : pV/T = nR, pV = nRT
What are the steps to determining the root mean square speed?
- square the velocity of each particle
- find the mean of the squares
- square root it
What is the equation that has the mean square speed in it?
pV = 1/3Nmc2
Draw the Maxwell-Boltzmann distribution for speeds of particles
y-axis = number of particles with speed v
x-axis = speed of particle
T1 curve higher
T2 curve lower and flatter
T2>T1
What is the equation for the Boltzmann constant?
k = R/NA
What equation can be derived from k = R/NA and pV = nRT ? (do the derivation)
k = R/NA —> R = kNA
pv = N(kNA)T
N = nNA
pV = NkT
Derive 1/2mc2 = 3/2kT
pV = 1/3Nmc2 , pV = NkT
1/3Nmc2 = NkT
1/3mc2 = kT
mc2 = 3kT
1/2mc2 = 3/2kT
What is the relationship between kinetic energy and temperature and how did we derive this relationship?
1/2mc2 = 3/2kT
Ek = 3/2kT
Ek is directly proportional to T
What is the internal energy of an ideal gas?
Internal energy of a gas is the sum of the kinetic and potential energies
One assumption of an ideal gas is that electrostatic forces between particles are negligible except during collisions
Therefore there is no electrical potential energy in an ideal gas so all the internal energy of an ideal gas is kinetic energy
So kinetic energy is directly proportional to the internal energy of an ideal gas
