Ideal gases Flashcards
1
Q
What is the lowest possible temperature and absolute zero?
A
- The lowest possible temperature is 0K (-273.5C). It is not possible to have a lower temperature than this
- Absolute zero is defined as the temperature at which the molecules in a substance have zero kinetic energy
- This means for a system at 0K, it is not possible to remove any more energy from it
2
Q
What is 1 kelvin in degrees celcius?
A
- 1 Kelvin 1 degree celcius
- 1K = 1C
3
Q
What is Boyle’s law?
A
- If the temperature of an ideal gas is constant, the pressure is inversely proportional to the volume of the gas
- P ∝ 1 / V
- P1V1 = P2V2
- Graph: Pressure vs volume - decreasing line of decreasing gradient
4
Q
What is Charles’s law?
A
- If the pressure of an ideal gas is constant, then volume is directly proportional to the temperature of the gas
- V ∝ T
- V1 / T1 = V2 / T2
- Graph: temperature vs volume - straight line through the origin
5
Q
What is the Pressure law?
A
- If the volume of an ideal gas is constant, the pressure is proportional to the temperaure
- P ∝ T
- P1 / T1 = P2 / T2
- Graph: temperature vs pressure - straight line through the origin
6
Q
What is an ideal gas?
A
- A gas that obeys the formula pV ∝ T
7
Q
What is pressure in an ideal gas?
A
- The frequency of collisions of the gas molecules per unit of area of a container
8
Q
What are the assumptions of an ideal gas?
A
- Has molecules of negligible volume
- Collisions are elastic
- Cannot be liquified
- Has no interactions between the molecules except during collisions
- Obeys the ideal gas laws
9
Q
What is the equation of an ideal gas?
A
- pV = nRT
- pressure x volume = number of moles x molar gas constant x temperature
- pV = NkT
- pressure x volume = number of molecules x boltzmann constant x temperature
10
Q
Why does a gas do work on the surroundings?
A
- When a gas expands, it does work on its surroundings by exerting pressure on the walls of its container
- The work done can be calculated with:
- W = p x change in v
11
Q
What is Boltzmanns constant?
A
- k = R / Na
- R = molar gas constant
- Na = avogadros constant
12
Q
What are the assumptions of the kinetic theory?
A
- Molecules of gas all have the same mass
- Molecules of gas are hard, perfectly elastic and sphere
- The volume of the molecules is negligible compared to the volume of the container
- The time of a collision is negligible compared to the time between collisions
- There are no intermolecular forces between the molecules
13
Q
Equation for the kinetic theory of gases
A
- pV = 1/3Nm(crms)^2
- p = pressure
- V = volume
- N = number of molecules
- M = mass of one molecule
- Crms = root mean squared speed of the molecules
- p = 1/3ρ(crms)^2
14
Q
How does temperature effect crms?
A
- As temperature increases, the kinetic energy of the molecules in the gas increases, leading to an increase in average velocity
- Crms = root (3kT / m)
- Hence, crms is proportional to the square root of the temperature
15
Q
How to prove base units of p = 1/3ρ(crms)2
A
- p = 1/3 x m/v x (crms)2
- p = 1/3 x Nm/v x (crms)2
- pV = 1/3 x Nm x (crms)2
- p = F/A = (mass x acceleration) / area
- [p] = (kg x ms-2) / m2
- [v] = m3
- [pV] = kgm2s-2
- [m] = kg
- [crms2] = m2s-2
- [1/3Nmcrms2] = kgm2s-2
16
Q
How to prove Boyle’s law?
A
- Attach a syringe to a clamp with the nozzle plugged and a string attached to the bottom and record the volume of gas inside the syringe
- Place weights onto the string of the syringe. Wait a few mins for the temperature to reach thermal equilibrium (constant temperature) and record the new volume
- Repeat by increasing mass and recording new volume
- Calculate cross sectional area of the syringe. Use p = F/A to calculate pressure exerted at each weight added (F = mxg)
- Calculate pressure of the gas by subtracting pressure of weights from atmospheric pressure
- Plot pressure of gas against 1/volume. You should have a straight line
