Thermodynamics Properties

Question 1

What’s the principle of corresponding states?

Answer 1

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.

Question 2

How does the compressibility factor, Z, vary between gases?

Answer 2

Pv = ZRT

Z = 1 for ideal gas
Z < 1 for real gas
Z depends on T and P and chemical nature of the gas

Question 3

What’s acentric factor?

Answer 3

A measure of how non-spherical a molecule is. (Symbol = omega)

Zero would be given to spherical molecules e.g. argon

Question 4

What’s Amagat’s law of partial pressures?

Answer 4

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.

Question 5

What do ideal and real gases depend on?

Answer 5

Ideal - temperature

Real - temperature and pressure

Question 6

What’s a partial molar property?

Answer 6

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.

Question 7

What’s the Clausius-Claperyron equation?

Answer 7

(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.

Question 8

What’s enthalpy departure?

Answer 8

When enthalpy becomes dependent on pressure as well as temperature and behaves different to that of a real gas.

Question 9

How is enthalpy departure calculated?

Answer 9

dh is to be found between two state points.

1. Compute the enthalpy of departure between the real v1 and infinite volume at T1
2. Add the DhIdeal due to the DT from T1 to T2
3. Subtract the enthalpy of departure between the real v2 and infinite volume at T2

h2 – h1 = (h2 – h1)ideal – RTc (Zh2 – Zh1)

Question 10

What’s fugacity?

Answer 10

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

Question 11

How is the K value for VLE determined?

Answer 11

Ki = Yi /Xi (vapour/liquid mole fraction)

The greater the K value, the more volatile the substance.

Ki = v*gamma/Ø

Question 12

What is the equilibrium vaporisation ratio?

Answer 12

Ki = yi / xi = P*I/P = f(P,T)

It is the ratio of vapour to liquid mole fractions of a certain component.

Question 13

What is fugacity?

Answer 13

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.

Question 14

How is fugacity found for non-ideal gases, considering G, R and T?

Answer 14

dG = RT*ln f

Question 15

How is residual volume of a real gas determined (when considering fugacity)?

Answer 15

Residual volume = RT/P - V

Real gas at P = 0: RT/P-V is finite
Ideal gas at P = 0: RT/P-V = 0

Question 16

How can fugacity be related to entropy and enthalpy?

Answer 16

ln (f/p) = (H-H)/RT - [(S-S0)/R + ln (P/P0)]

Where f/p is the fugacitiy coefficient.

Question 17

What are the vapour and liquid phase fugacity coefficients?

Answer 17

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

Question 18

How is liquid phase activity coefficient determined? (gamma)

Answer 18

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

Question 19

What are the 3 coefficients (considering fugacity and thermodynamics) which describe non-deal behaviour?

Answer 19

ϕ - Vapour phase fugacity coefficient

v - liquid phase fugacity coefficient

γ - activity coefficient

Question 20

How can K be determined using fugacity?

Answer 20

K = v*γ/ϕ

= liquid phase fugacity coefficient * activity coefficient / vapour phase fugacity coefficient

Question 21

Under what conditions may you not assume the activity coefficient of a liquid mixture is 1

Answer 21

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.

Question 22

What is flash evaporation?

Answer 22

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.

Question 23

How is flash evaporation used for separations?

Answer 23

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

Question 24

How are bubble and dew point calculated?

Answer 24

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.

Question 25

How do you calculate bubble point?

Answer 25

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

Question 26

What is the Van dear Waals EoS?

Answer 26

P = RT / (v - b) - a / v^2

Where:
a = 27R^2*Tc^2 / 64Pc

b =RTc / 8Pc