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Module 5 - Chapter 15 - Ideal gases - Coggle Diagram
Module 5 - Chapter 15 - Ideal gases
Mole
Amount of substance - number of elementary entities within a given sample of substance
One mole - amount of substance that contains as many elementary entities as there are atoms in 12g of Crbon-12 (Avogadro consant)
Molar mass - mass of one mole of substance
Kinetic theory
Ideal gas assumption
Particles have a negligible volumes compared to the volume of the gas
Gas particles move in random directions with random speeds
Electrostatic forces between particles are negligible except during collisions
Time of collisions between particles is negligible comparedto time between collisions
Perfect elastic collisions between molecules and eachother/ container
Pressure
When particle collide with walls of a container, container exerts a force on them changing their momentum
Total momentum change is -2mu
Atoms also exerts an equal and opposite force on the wall
Total force exerted is F, and pressure exerted on the wall is F/A
Distribution
Maxwell-Boltzmann distribution discribes the range of speeds of particles in a gas at a given temperature
Number of particles with speed v on y axis, speed on x
Hotter the gas, the greater the range of speeds
Areas under the curve stays constant (number of particles)
Gas laws
Boyle's law
When temperature and number of particles remain constant, pressure is inversely proportional to volume
If fixed mass of gas is in a sealed box, halving the volume (slowly, so pressure remains constant) will compress the gas and pressure exerted on box doubles
pressure law
When volume and number of particles remain constant, pressure is directly proportion to its absolute temperature
For a fixed number of particles in a sealed box, doubling temperature doubles pressure the gas exerts on the container wall
Absolute 0
Increase temperature of water bath, pressure increase of gas can be recorded
Plot a graph of pressure (y) against temperature (x, celcius).
Extrapolate the graph to the x intercept where the pressure is 0
Charle's law
When volume and number of particles are consant, pressure is directly proportional to temperature
Avogadro's law
For a constant pressure and temperature, number of particles/ moles is directly proportional to the volume
Combining
For one mole of an ideal gas, the constant is called the molar gas constan (8.31JK^-1mol^-1)
Pressure at microscopic levels
Root mean square speed
Velocity of each atom is squared. The average is then found and the square root is taken
Velocity is a vector, if we calculated the average velocity of particles in a gas, the average would be 0
A single gas particle makes repeated collisions with the container walls of side length L. Particle has mass m and velocity c
Elastic collisions results in a change in momentum of 2mc
Time between collisions is
Force exerted by particle on wall =
If there are N particle in the container, we use root mean squared speed.
About 1/3 of particle are moving between two opposite faces of the container
force =
Pressure exerted by gas must equal the force exerted by all the particles divided by cross sectional area
Boltzmann constant
Boltzmann constant (k) = molar gas constant divided by the Avogadro constant
You can sub the definition of k into ideal gas equation pV = nRT to get pV = Nkt
Mean kinetic energy and temperature
We can combine ideal gas equation and pressure at microscopic levels
N can be cancelled out
Rewrite the equations
LHS is the mean average kientic energy of gas particles
Since all other values are constant
Doubling absolute temperature doubles average kineic energy of particles
Particle speeds
At a given temperature, atoms in different gases have the same average kinetic energy
As particles have different masses, their r.m.s are different, lighter atoms move faster
Internal energy of ideal gases
No potential energy in an ideal gas
All the interal energy is in the form of kinetic
Doubling temperatue of ideal has doubles its average kinetic energy and also its internal energy
