15 - Ideal Gasses Flashcards
What is the SI unit for the amount of a substance?
Mole (mol)
Define the mole.
The amount of a substance that contains as many elementary entities as there are atoms in 12g (0.012kg) of carbon-12.
The Avogadro constant.
What is the sign for the Avogadro constant?
Also what is it?
Nₐ
6.02x10²³
What does one mole of any substance contain?
The Avogadro constant of individual molecules.
How do you calculate the number of molecules in a substance?
N = n x Nₐ
What is the molar mass of a substance?
The mass of a single mole of the substance.
M
How do we calculate the mass of a substance from the molar mass?
m = n x M
What is the kinetic theory of gases?
A model used to describe the behaviour of the atoms / molecules in an ideal gas.
Why do we use the kinetic theory of gases?
Because real gases have complex behaviour which we must simplify.
What are the assumptions made in the kinetic theory of gases?
- Very large number of molecules moving in random directions with random speeds
- Molecules occupy a negligible volume compared to the volume of the gas
- Collision of molecules and sides of container are perfectly elastic
- Time of colisions is negligible compared to time between collisions
- Electrostatic forces between molecules are negligible except during collisions
What is the relationship between the volume of a container and the pressure inside it?
(What are the other conditions for this to be true?)
P ∝ 1/v
If temperature and mass of gas remains constant
What is Boyle’s law?
P ∝ 1/v
If temperature and mass of gas remains constant
What is the relationship between the pressure of an ideal gas and the temperature?
(What are the other conditions for this to be true?)
P ∝ T
If volume and mass of gas remain constant
How does the relationship between the pressure of an ideal gas and the temperature help us find the value of absolute zero.
Plot graph of pressure against temperature.
Extrapolate backwards to where pressure = 0.
How do we combine the relationships between pressure and volume and pressure and temperature?
PV / T = Constant
What is the molar gas constant?
What is its symbol?
The constant from the equation PV / T for one mole of gas.
R
What is the equation of state of an ideal gas?
PV = nRT
P = Pressure V = Volume n = number of moles R = molar gas constant T = Temperature
What is the SI unit of temperatute?
Kelvin
K
What is the SI unit for pressure?
Pascal
Pa
What is the SI unit for volume?
m³
On a graph of PV against T, what does the gradient represent?
nR
y = mx + c
Pv = (nR)T + 0
How do we calculate root mean square speed?
Square all velocity values
Find mean of squared values
Square root mean
Why do we use root mean square speed?
Because velocities are vectors and just the mean would cancel out to equal 0.
Squaring the velocities removes the negative.
What is the Maxwell-Boltzmann distribution?
The range of speeds of particles in a gas at a constant temperature.
Where is the most probable speed on the Maxwell-Boltzmann distribution curve?
At the peak
Where is the mean speed on the Maxwell-Boltzmann distribution curve?
Slightly to the right of the peak,
Between the peak and the RMS.
Where is the root mean square speed on the Maxwell-Boltzmann distribution curve?
Further right of the peak.
Right of the mean speed.
How does changing the temperature affect the Maxwell-Boltzmann distribution?
It becomes more spread out.
All three speed values become larger.
Define the Boltzmann constant.
Molar gas constant divided by the Avogadro constant.
k = R / Nₐ
What is the symbol of the Boltzmann constant?
k
LOWERCASE
How can the Boltzmann constant be incorporated into the equation of state of an ideal gas?
PV = nRT (equation of state of an ideal gas)
R = kNₐ (Rearrange formula for Boltzmann constant)
PV = knNₐT (Sub in formula above)
n x Nₐ = N (number of moles x Avogadro = number of molecules)
PV = NkT
What does the symbol “k” represent?
Boltzmann constant
What does the symbol “R” represent?
Molar gas constant
What does the symbol “Nₐ” represent?
Avogadro constant
What is the derivation of the equation:
(1/2)mc̅ ²kT = (3/2)kt?
Probably use paper
1/3 Nmc̅ ² = NkT
1/3mc̅ ² = kT (Cancel N)
REWRITE LHS
(2/3)(1/2mc̅ ²) = kt
1/2mc̅ ² = 3/2kt
What does the equation 1/2mc̅ ² equal?
The mean average kinetic energy of the particles in the gas.
1/2 mv²
What is the relationship between the mean kinetic energy of particles in the gas and the temperature of the gas?
Eₖ ∝ T
What is the internal energy of an ideal gas and why?
A sum of the kinetic and potential energies of the particles in the gas.
Ee assume that the electrostatic forces between particles are negligible.
Internal energy of ideal gas = kinetic energy of all of the particles.
What would happen to the internal energy of an ideal gas if you doubled the temperature?
It would also double.
Eₖ ∝ T
THEREFORE
Internal E ∝ T
