C15 Ideal Gases Flashcards
SI unit of measurement for the amount of a substance
The Mol (Mole)
Define ‘one mole’
The amount of substance that contains as many elementary entities as there are atoms in 12g of carbon-12.
State Avogrado’s Constant
6.022 x 10^23
Formula to calculate number of particles in a substance, N
N = n x N(a)
n = number of moles
N(a) = Avogadro’s Constant
Formula to calculate the molar mass of a substance, M
M = m / n
State assumptions made in the kinetic model for an ideal gas
- The gas contains a very large number of particles moving in random directions with random speeds.
- The particles of the gas occupy a negligible volume compared with the volume of the gas.
- The collisions of the particles with each other and the container walls are perfectly elastic (no KE lost).
- The time of the collisions between the particles is negligible compared to the to the time between the collisions.
- Electrostatic forces between particles are negligible except during collisions.
How does the speed/velocity/momentum of an atom change when it bounces off a boundary at?
- Speed remain the same, as it is a scalar.
- Velocity is the negative speed, as the direction is opposite.
- Change in momentum = -2mu
State Boyle’s Law and conditions
P ∝ 1/V or pV = constant
Assuming constant temperature and mass of the gas.
State the relationship between pressure and temperature, and its conditions
p ∝ T or p/T = constant
Assuming the volume and the mass of the gas remain constant.
T is always measured in kelvin
Combining the gas laws formula and how it can be applied (for an ideal gas)
- pV / T = constant
- Can be used when conditions are changing from an initial state to a final state
- P1V1 / T1 = P2V2 / T2
State the equation of state for an ideal gas
- For one mole of an ideal gas, the constant in the combined temperature is the molar gas constant, R
- pV / T = nR or pV = nRT
State the value/unit for R (molar gas constant)
8.31 J K-1 mol-1
Describe the graph of pV against T
- This produces a straight line through the origin, as pV ∝ T
- By comparing y = mx + c and pV = nRT
- Gradient: nR
- The greater the number of moles, the steeper the line.
Average velocity of particles in a gas
It would be 0 m/s, as the particles all move in random directions at different speeds, cancelling out.
Average velocity of particles in a gas
It would be 0 m/s, as the particles all move in random directions at different speeds, cancelling out.
How do we determine r.m.s speed
- The velocity of each particle is squared, and the average of these squares is calculated.
- The square root of the average is taken.
Formula for pressure at the microscopic level
pV = 1/3 Nmc(squared bar)
where:
N = number of particles in the gas
m = mass of each particle
c (squared bar) = mean square speed of the particles
Deriving pV = 1/3 Nmc(squared bar)
- Consider a single gas particle, mass m, velocity c, in a cube container of sides L.
- The time t between collisions is 2L / c
- Force = change in momentum / time
- Force = 2mc x c / 2L = mc(squared) / L
- If there are N particles, average force = mc(squared bar) / L, where c(squared bar) = mean square speed
- On average, about 1/3 of the particles are moving between opposite faces.
- CSA = L^2
- Force = mc(squared bar) x N x 1/3
- p = Nmc(squared bar) / 3L x 1 / L(squared)
- L(cubed) = volume
- pV = 1/3Nmc(squared bar)
What is the Maxwell-Boltzmann distribution?
- In a container, gas particles will all be moving at different speeds, from very fast to very slow.
- The range of speeds the particles can take at a given temperature is the Maxwell-Boltzmann distribution.
How does changing the temperature of a gas affect the Maxwell-Boltzmann distribution?
- The hotter that gas becomes, the greater the range of speeds.
- The modal speed and r.m.s increases.
- The distribution becomes more spread out.
State the Boltzmann constant
k = R / N(a)
1.38 x 10^-23 J/K
The second equation of the state of an ideal gas, by substituting the Boltzmann constant
pV = nRT —> pV = nKN(a)T
Number of particles in the gas, N = n x N(a)
pV = NkT
Equation that relates the mean KE of a particle to the absolute temperature of the gas
1/3Nmc(squared bar) = NkT
Cancel out N, sub out 2/3
1/2mc(squared bar) = 3/2 kT
Relationship between temperature and kinetic energy and conditions
E(k) ∝ T
Assuming the temperature is measured in kelvin.
Internal energy of an ideal gas
- In an ideal gas, there are negiblible electrostatic forces between particles unless during a collision.
- This means the internal energy of a particle in an ideal gas is entirely its kinetic energy.
- Doubling temperature doubles K(e), so internal energy.
