Thermodynamics Properties Flashcards
What’s the principle of corresponding states?
All fluids, when compared at the same T and P have
approximately the same Z and all deviate from ideal gas behaviour to about the same degree.
How does the compressibility factor, Z, vary between gases?
Pv = ZRT
Z = 1 for ideal gas
Z < 1 for real gas
Z depends on T and P and chemical nature of the gas
What’s acentric factor?
A measure of how non-spherical a molecule is. (Symbol = omega)
Zero would be given to spherical molecules e.g. argon
What’s Amagat’s law of partial pressures?
The total volume of a non-reacting mixture of gases at constant temperature and pressure should be equal to the sum of the individual partial volumes of the constituent gases.
Dalton’s Law assumes that the gases in the mixture do not have any interaction
Each gas independently applies its own pressure, the sum of which is the total pressure.
Amagat’s Law assumes that the volumes of each component gas (at the same temperature and pressure) are additive.
The compressibility is averaged over all of the components at the conditions of the mixed system.
What do ideal and real gases depend on?
Ideal - temperature
Real - temperature and pressure
What’s a partial molar property?
A thermodynamic quantity which indicates how an extensive property of a solution or mixture varies with changes in the molar composition of the mixture at constant temperature and pressure.
What’s the Clausius-Claperyron equation?
(dP/dT)sat = Δhᵥₐₚ/TΔvᵥₐₚ
The Clapeyron equation allows determination of the change in enthalpy associated with a phase change from a knowledge of P, v, and T data alone.
It pertains to the relationship between the pressure and temperature for conditions of equilibrium between two phases.
What’s enthalpy departure?
When enthalpy becomes dependent on pressure as well as temperature and behaves different to that of a real gas.
How is enthalpy departure calculated?
dh is to be found between two state points.
- Compute the enthalpy of departure between the real v1 and infinite volume at T1
- Add the DhIdeal due to the DT from T1 to T2
- Subtract the enthalpy of departure between the real v2 and infinite volume at T2
h2 – h1 = (h2 – h1)ideal – RTc (Zh2 – Zh1)
What’s fugacity?
A thermodynamic property of a real gas which if substituted for the pressure or partial pressure in the equations for an ideal gas gives equations applicable to the real gas.
Considered as effective pressure
How is the K value for VLE determined?
Ki = Yi /Xi (vapour/liquid mole fraction)
The greater the K value, the more volatile the substance.
Ki = v*gamma/Ø
What is the equilibrium vaporisation ratio?
Ki = yi / xi = P*I/P = f(P,T)
It is the ratio of vapour to liquid mole fractions of a certain component.
What is fugacity?
In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant.
It is equal to the pressure of an ideal gas which has the same temperature and molar Gibbs free energy as the real gas.
The concept of fugacity solves a mathematical problem with the chemical potential when pressure tents to zero.
How is fugacity found for non-ideal gases, considering G, R and T?
dG = RT*ln f
How is residual volume of a real gas determined (when considering fugacity)?
Residual volume = RT/P - V
Real gas at P = 0: RT/P-V is finite
Ideal gas at P = 0: RT/P-V = 0
How can fugacity be related to entropy and enthalpy?
ln (f/p) = (H-H)/RT - [(S-S0)/R + ln (P/P0)]
Where f/p is the fugacitiy coefficient.
What are the vapour and liquid phase fugacity coefficients?
Vapour phase:
ϕ = f’/P = f’/yP
Liquid phase:
v = f*/P
Where f* is standard state fugacity and f’ is fugacity of the pure liquid.
They can be determined using a table
How is liquid phase activity coefficient determined? (gamma)
γ = f’/x f* = a/x
Where: γ - activity coefficient f' - fugacity of pure liquid at system temperature and total system pressure f* - standard state fugacity x - mole fraction a - activity of compound
What are the 3 coefficients (considering fugacity and thermodynamics) which describe non-deal behaviour?
ϕ - Vapour phase fugacity coefficient
v - liquid phase fugacity coefficient
γ - activity coefficient
How can K be determined using fugacity?
K = v*γ/ϕ
= liquid phase fugacity coefficient * activity coefficient / vapour phase fugacity coefficient
Under what conditions may you not assume the activity coefficient of a liquid mixture is 1
Can assume ideal liquid if the molecules are almost identical.
The more dissimilar the liquid components the more the activity coefficient is expected to deviate from 1.
What is flash evaporation?
Flash evaporation is when a saturated liquid stream undergoes a reduction in pressure by passing through a throttling device.
If the saturated liquid is a single-component liquid, a proportion of the liquid “flashes” into vapor.
The flashed vapor and the liquid cool to the saturation temperature at the reduced pressure.
How is flash evaporation used for separations?
Flash evaporation is also used to separate out components of multi-component liquids
The flashed vapor has a higher proportion of the more volatile component
The less volatile component is concentrated in the remaining liquid
How are bubble and dew point calculated?
To calculate bubble point temperatures, you know the amount of your desired component i in the liquid (xi) and need to calculate the unknown composition of the vapour You know that the overall vapour satisfies the condition.
And you need to solve for the unknown yi (mole fraction of your desired component i that goes into the vapour)
To calculate dew point temperatures, you know composition of the vapour and need to calculate the unknown composition of the liquid (xi) You know that the overall liquid satisfies the condition and you need to solve for the unknown xi , to find out how much of your component of interest is left in the liquid.
How do you calculate bubble point?
To calculate bubble point, you can use the mass balance to come up with an expression that is only in terms of xi (mole fraction of your desired component i in the liquid) and Zi which are known from your feed composition and Ki.
You get starting values for Ki from the DePriester tables, by taking a starting guess at what the bubble point temperature would be and looking up the Ki values at that temperature.
At the bubble point, V is close to zero (i.e. everything is a liquid, but about to boil) so the expression reduces to:
xi = zi
What is the Van dear Waals EoS?
P = RT / (v - b) - a / v^2
Where:
a = 27R^2*Tc^2 / 64Pc
b =RTc / 8Pc
