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Level 79

Ideal Gases & Kinetic Theory


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What is an ideal gas?
A gas that obey's Boyle's law. Boyle's law states that, provided a gas is isothermal, the pressure of a gas times the volume of a gas is equal to a fixed constant. This implies …
State Boyle's Law
At a constant temperature/for an isothermal change, the pressure of a gas is inversely proportional to the volume of the gas
State Charles' Law
At a constant pressure/for an isobaric change, the volume of a gas is directly proportional to the absolute temperature of the gas
State the Pressure Law
At a constant volume/for an isochoric/isovolumetric change, the pressure of a gas is directly proportional to the absolute temperature of the gas
PV = nRT
Equation for gas law
How can you derive the ideal gas equation?
Using Boyle's, Charles' and the Pressure laws, one can show that for a fixed mass of gas
pV = NkT
State the equation of state of an ideal gas/the ideal gas law in terms of Boltzmann's constant and the number of molecules in the gas
The number of molecules
What does big N stand for?
What does little n stand for?
The number of mols of molecules
N = nN(A) where N(A) is avagadro's constant
How can you derive the equation of state of an ideal gas?
What is R?
The molar gas constant
Boltzmann's constant
What is k?
What is molarity?
The number of moles in a certain quantity of a substance
What is molar mass?
The mass of one mole of the substance
What is the definition of Avagadro's constant, N(A)?
The number of atoms in exactly 12g of Carbon 12
Describe Brownian motion
The random motion of small particles suspended in a fluid (a liquid or a gas) resulting from their collision with the quick atoms or molecules in the gas or liquid
What is Brownian motion evidence for?
The existence of atoms/the molecular model of gases
Describe and explain the motion of small particles of soot suspended in a sample of gas
The smoke particles move randomly in all directions, frequently changing directions. This is called Brownian motion;
Why do gas particles exert a pressure on their container?
Particles collide with the walls of the container and undergo a change in momentum (Δρ );
Boyle's Law: P ∝ 1/V;
Using kinetic theory, explain Boyle's Law regarding a fixed mass of gas in a container at a constant temperature
Using kinetic theory, explain Charles' Law regarding a fixed mass of gas in a container at a constant pressure
As the temperature of the gas increases, the average kinetic energy of the particles increases and thus so does the mean speed;
What is a Maxwell-Boltzmann distribution
A graph showing the distribution of molecular energies/kinetic energies/speeds of molecules in a gas
Flatter with the peak shifted to the right
What does the Maxwell-Boltzmann distribution of a sample of a gas occurring under a higher temperature look like in comparison to the same reaction at a lower temperature? Why?
The total number of molecules
What does the area under a Maxwell-Boltzmann distribution represent?
All molecules are identical
What assumptions are made in deriving the kinetic theory equation
pV = 1/3 Nm(c-rms)(sqd)
What is the kinetic theory equation?
Derive the kinetic theory equation
Consider one molecule in a cube with side l
Nm/V = density
How can we express the kinetic equation in terms of the density of the gas?
What is significant about the internal energy of a gas?
It is only composed of the kinetic energy of the molecules of the gas
What is thermal equilibrium?
If no energy is transferred as heat between an object and its surroundings
pV = NkT = 1/3 Nm*c(xrms)(sqd)
How can you derive the equation for the mean kinetic energy of a single gas molecule in an ideal gas?
Ek = 3RT/2N(A)
Derive the equation for the total kinetic energy (therefore internal energy) of n mols of a gas from the equation for one molecule
Ek = 3/2 nRT
What is the equation for the total kinetic energy of n mols of gas?
What is meant by the term "random motion"?
No observable pattern to the motion as molecules have no "preferred" direction
Each gas has the same number of molecules
If two cylinders of equal volume contain different pure gases at the same temperature and pressure why is the energy required to raise the temperature of both gases identical even though one gas has molecules of higher mass?