Gases Flashcards
Topic 1, Lectures 2-4 - Colan Hughes (35 cards)
Ideal gas
- No interparticle forces
- 0 volume
Though these are false assumptions, if a gas has a low enough density, the forces and volumes become negligible due to high particle separation.
Ideal gas equation
pV = nRT
Pa, m^3, K
What is R equivalent to?
KbNa where Kb is the Boltzmann constant and Na is Avogadro’s constant
Ideal gas equation of state
The equation can also be used to calculate the effect of changing conditions on other properties. E.g., if a gas is cooled at a fixed volume, pressure will change. P changes proportionally to T.
Mixtures of ideal gases
It is assumed that all ideal gases behave in the same way; as a result, properties are determined by the number of moles rather than the identity of the particles.
Dalton’s Law
The pressure of a mixture of gases is equal to the sum of the partial pressures of each gas.
Mixture of ideal gases equation
P(tot) = n(a)RT/V + n(b)RT/V
Elastic collisions
Collisions that conserve total kinetic energy. Conserve momentum.
Inelastic collisions
Collisions that involve a change in kinetic energy. Conserve momentum.
Collisions in atomic gases
All collisions are elastic; atoms bounce off of each other, not converting any energy.
Collisions in molecular gases
Most collisions are inelastic, as kinetic energy can be translated into rotational or vibrational energy and vice versa. Because both options are possible, the collisions are seen as elastic on average.
Real gases
Refers to gases that deviate from ideal behaviour, especially under high pressure and low temp conditions. They have intermolecular forces and finite volumes.
Compression factor
When the ideal gas equation is rearranged to: pV/nRT = 1, it can be used for real gases as well; however, because they deviate from ideal behaviour, the 1 is replaced by Z, the compression factor.
Z values
If Z > 1, the real gas is harder to compress than an ideal gas.
If Z < 1, the real gas is easier to compress than an ideal gas.
Van der Waal’s equation
(p + a/v^2)(V - b) = nRT
1: Corrects for the attractive forces between gas molecules. It becomes most significant when the gas molecules are close together, where intermolecular attractions (a) cause the gas to exert a lower pressure than expected.
2: Accounts for the finite volume of real gas molecules. The volume available for the molecules to move around in is reduced by the volume taken up by the molecule (b).
Berthelot equation
Derived in the same way as the VdW equation but with temperature dependence for internal pressure.
Virial equation of state
pV(m) = RT(1 + B/V(m) + C/V(m^2) + …)
The terms in the bracket are equal to Z. By measuring Z at different conditions, the values of the coefficients can be determined.
Liquefaction
Liquefaction isn’t possible for ideal gases, as there are no interparticle interactions. Real gases can be liquefied.
Supercritical fluid formation
Forms through sealing a liquid inside a vessel, causing a vapour to form above. As temperature increases, the vapour pressure increases until the liquid and gas have the same density, until finally a single phase exists at a critical temperature.
Supercritical fluid
On the phase diagram, there is a line representing the end of the coexistence of liquid and gas. After this point, only supercritical fluid exists. As it cannot be compressed, it is considered a gas; however, it can have a much higher density than subcritical gases given the pressure is high enough.
Uses of supercritical fluids
Supercritical CO2 can be used to extract caffeine from coffee. They can be used to aid chemical reactions without relying on the use of traditional, environmentally harmful solvents.
Measuring speed of gas particles
Experimental: Uses spinning discs with slits that are offset from the adjacent discs’. The different rates of spin allow for different particle speeds to be selected. Measuring the number of particles passing through gives a normal distribution of speeds (Maxwell distribution).
Maxwell averages
The peak indicates the most probable speed: V(mp)
Calculated: (2KbT/m)^1/2
Mean: V(m) = (8KbT/πm)^1/2
Root-mean-square: V(rms) = (3KbT/m)^1/2
Equal to the root of the integral v^2f(v) dv
When expressing the averages with molar mass, Kb is replaced by the gas constant R (kgmol^-1)
How factors affect maxwell
Temperature and particle mass changes impact the height and width of the graph, but not the shape. Higher temps and lower masses lead to wider distributions.
