Topic 2 - Ideal gases Flashcards
Kinteic theory, Assumptions made, Boyles law, Charles' law, Gay Lussac's law, Combining gas laws, r.m.s speed, Pressure, Maxwell-Boltzmann distribution, Boltzmann constant, A second equation, Particle speeds at different temperatures, Internal energy of an ideal gas
What is the kinetic theory of gases?
It is a model used to describe the behaviour of the particles in an ideal gas
Why are assumptions of gases made?
To keep the kinetic theory model simple
What are the five assumptions made about the particles in an ideal gas?
- Very large number of particles moving in random directions with very high speed
- Occupy a negligible compared with the volume of the gas
- Collisions with each other and the container are perfectly elastic
- Time of collisions is negligible compared to the time between the collisions
- Electrostatic forces are negligible except during collisions
What is Boyles law?
The pressure is indirectly proportional to the volume
What conditions are met in Boyles law?
The mas of the gas is fixed and at a constant temperature
What is Charles law?
Volume is directional proportional to temperature
What conditions are met in Charles law?
The mass of the gas is fixed and the gas is at a constant pressure
What is Gay Lussacs law?
Pressure is directional proportional to temperature
What conditions are met for Gay Lyssacs law?
There is a gas with a fixed mass and constant volume
Why can’t you measure absolute zero (0K)?
As soon as you put the thermometer in there is heat exchange
What three equations can be formed from Boyles law?
P=1/V
PV=Constant
P1V1=P2V2
What three equations can be formed from Charles law?
V=T
V/T=Constant
V1/T1=V2/T2
What three equations can be formed from Gay Lussacs law?
P=T
P/T=Constant
P1/T1=P2/T2
What equation can be formed by combing the gas laws?
PV/T=Constant
P1V1/T1=P2V2/T2
Foe one mole of an indeal gas, the constant is the molar gas constant “R” which is equal to 8.31JK-1mol-1 (in formulae book). For n moles of gas the equation becomes:
PV/T=nR, PV=nRT (in formulae book)
Why is the r.m.s speed used?
If you added up the velocities of a gas they would equal zero
How is the mean square speed calculated?
((V1)^2+(V2)^2+(V3)^2+(V4)^2+…+(VN)^2)/N
How is the root mean square speed calculated?
square root of the mean square speed
What is the equation of pressure (in the formulae book)?
PV=1/3Nm(mean c^2)
What is the range of speeds in a gas at a given temperature known as?
Maxwell-Boltzmann distribution
What happens to the Maxwell-Boltzmann distribution at higher temperatures?
The distribution becomes broader
What happens to the total energy of the gas with time?
It stays constant
What was Boltzmann able to explain with his studies?
He was able to explain how the microscopic properties of particles in substances relate to the macroscopic properties in gas
What is Boltzmann’s constant (in formulae book)?
K=1.38x10-23 Jmol-1K-1
What is the equation for Boltzmann’s constant?
K=R/Na
What does Boltzmann’s constant do?
It relates the mean Ek in a gas to the gas temperature
What is the second equation for an ideal gas?
PV=nRT
(n=N/Na)
PV=(N/Na)RT
PV=NKT
How would you use the equation for an ideal gas and relate it to density?
PV=nRT (n=m/M) PV=(m/M)RT P=(1/M)(m/V)RT P=(1/M)ρRT
What happens to the area underneath the curve of the Maxwell-Boltzmann distribution graph?
It stays the same with heating
How do you rearrange the two PV equations to find out the mean Ek and temperature?
1/3Nm(mean c^2)=NKT 1/3m(mean c^2)=KT m(mean c^2)=3KT 1/2(mean c^2)=3/2KT Ek=1/2m(mean c^2) Ek=3/2KT
How do particles have different speeds at different temperatures?
At a temperature all particles have the same average Ek. However, the particles have different masses so their m.m.s speeds are different
How does temperature effect internal energy in an ideal gas?
All internal energy is Ek. Doubling the temperature, doubles the average EK, therefore doubles the internal energy
