5. Ideal gases Flashcards
Define the mole:
An amount containing as many particles as there are in 12g of carbon-12
How do you calculate the number of moles in a substance?
n = N / Na
n = number of moles
N = number of molecules
Na = Avogadro’s constant
What is Avogadro’s constant?
Avogadro’s constant tells us that one mole contains 6.02 x 10^23 molecules
Define Avogadro’s constant:
The number of atoms in a 12g of carbon-12
What is the mass of a 12-carbon atom?
12 x 1.66 x 10^-27 = 1.99 x 10^-26 kg
What is molar mass?
The mass of one mole of a substance, expressed in gmol^-1
How else can you calculate the number of moles in a substance?
n = m / Mr
n = number of moles
m = mass of the substance in g
Mr = molar mass of the substance in gmol^-1
How do calculate the mass of one mole of an element using its atomic number?
One mole of any element is equal to the atomic mass of that element in grams
What is an ideal gas?
An ideal gas obeys the relation → pV ∝ T
p = pressure of the gas in Pa
V = volume of the gas in m^3
T = thermodynamic temperature in K
What is Boyle’s law?
P ∝ 1/V at a constant T as a smaller container creates a smaller surface area and so there are more collisions, which creates more pressure
What is Charles’ law?
V ∝ T at a constant p, because the molecules have a higher kinetic energy and so they move about more and move further apart from each other, expanding to create a bigger volume
What is Gay Lussac’s law?
p ∝ T at a constant V, because the molecules have a higher kinetic energy, so they move about more and collide more with the walls of their container, creating more pressure
What is the combined gas law equation?
P1V1/T1 = P2V2/T2
p = pressure of the gas in Pa
V = volume of the gas in m^3
T = thermodynamic temperature in K
What is the ideal gas equation?
pV = nRT
p = pressure in Pa
V = volume in m^3
n = number of moles in mol
R = molar gas constant
T = temperature in K
How can the ideal gas equation be rewritten?
pV = NkT
N = number of moles
k = Boltzmann constant
What is the molar gas constant?
R = 8.31 JK^-1mol^-1
What is Boltzmann constant?
k = R / Na = 8.31 / 6.02 x 10^23 = 1.38 x 10^-23 JK^-1
Name 1-5 assumptions of the kinetic theory of gases:
- Molecules of a gas behave as identical (or all have the same mass)
- Molecules of gas are hard, perfectly elastic spheres
- The molecules are in continuous random motion
- There are no forces of attraction or repulsion between the molecules
- External forces (e.g. gravity) are ignored
Name 6-10 assumptions of the kinetic theory of gases:
- Newton’s laws apply
- The volume of the molecules is negligible compared to the volume of the container
- The molecules collide perfectly elastically with the walls of the container exerting a pressure upon them
- The time of a collision is negligible compared to the time between collisions
- There are a very large number of molecules
What is the equation for the kinetic theory of ideal gases?
pV = 1/3 * N * m * < c^2 >
p = pressure (Pa)
V = volume (m3)
N = number of molecules
m = mass of one molecule (kg)
< c2 > = mean square speed of the molecules (m s–1)
How do you calculate the average speed of the particles in a gas?
√ (< c^2 >) = c r.m.s
Write the kinetic theory of ideal gases equation in terms of density of the gas:
ρ = m / V = Nm / V
→
p = 1/3 * ρ * < c^2 >
Define the translational kinetic energy of a gas:
The kinetic energy of the molecules as determined by their temperature
What is the equation for the translational kinetic energy of one molecule of a gas?
EK = 1/2 * m * < c^2 > = 3/2 * k * T
EK = kinetic energy of a molecule (J)
m = mass of one molecule (kg)
< c2 > = mean square speed of a molecule (m2 s-2)
k = Boltzmann constant
T = temperature of the gas (K)
How do you calculate the average translational kinetic energy for all the molecules in a gas?
EK = 3/2 * N * k * T
