1. GOVERMENT ENGINEERING COLLEGE BHUJ PREPARED BY :- 140153105001 -Chaudhari Rashmi 140153105002 -Dhruv Divyesh 140153105003 -Dodiya Kuldeepsinh 140153105004 -Gohil Dilip Guided by S R B

2. PHASE RULE The number of variables that are set in independent form in a system in equilibrium is the difference between the total number of variables of the intensive system's state and the number of independent equations related to the variables. The intensive state of a PVT system with N chemical species and P phases in equilibrium is characterized by the intensive variables, temperature T, pressure P and N-1 mol fraction for any phase

3. number of variables given by phase rule is 2+(N-1)P The number of equations of the independent, phase equilibrium is (P-1) (N) The difference between the number of variables of phase rule and the independent equations that relate them is the number of variables that can be fixed independently.

4. They are known as degrees of freedom (F). F = 2 + (N - 1) (P) - (P - 1) (N). Simplyfing, F = 2 - P + N

5. Duhem Theorem It is similar to the phase rule. It is applied to closed systems in equilibrium, in which intensive and extensive states are kept as constant. The system state is completely determined and characterized not only by the 2 + (N - 1) P intensive variables.

6. obtained in the phase rule, if not also by the P extensive variables represented by the masses (or number of moles) of the phases. The total number of variables is 2 + N P - P N = 2 For any closed system formed by the know masses of the chemical species prescribed, the equilibrium state is determined fully when two independent variables are set.

7. These two independent variables are intensive or extensive. However, the number of independent intensive variables are known by the phase rule. So, when F=1, one of the variables must be extensive, and when F=0, both must be it.

8. Multipl Equilibrium Sometimes a series of chemical equilibrium are related, i.e., two or more reactions add up to a final reaction In this situation, the equilibrium constants are related If equilibrium reactions can be added to give a total reaction, then the equilibrium constant for the total reaction is equal to the product of the equilibrium constants for the contributing reactions.

9. Mathematically, this can be written as, A 1 (g) + B 1 (g) +... C 1 (g) + D 1 (g) +...K c1 A 2 (g) + B 2 (g) +... C 2 (g) + D 2 (g) +...K c2 A 3 (g) + B 3 (g) +... C 3 (g) + D 3 (g) +...K c3 etc. A 1 (g) + A 2 (g) + A 3 (g) + B 1 (g) + B 2 (g) + B 3 (g) +.....K ctotal C 1 (g) + C 2 (g) + C 3 (g) + D 1 (g) + D 2 (g) + D 3 (g) +. = K c1 ×K c2 ×K c3 ×...

10.  Example Find the equilibrium constant for the reaction:  2 N 2 O(g) + 3 O 2 (g) 4 NO 2 (g) given the following information:  N 2 O(g) + ½ O 2 (g) 2 NO(g) K c = 1.7×10 –13............... (1)  NO(g) + ½ O 2 (g) NO 2 (g) K c = 6.83×10 6................ (2)

11. THE GAMMA/PHI FORMULATION OF VLE DATA. Modified raoult’s law includes the activity coefficient to account for liquid-phase nonidealities. But it is limited by the assumption of vapor-phase ideality. For species i in vapor mixture is written as

12. f ̂ = yi ф ̂ P …………(1) Where, species i in the liquid phase, So that f ̂ = x ϒ f …………(2) Where, ф is refers to the vapor to phase and ϒ and f are liquid phase properties. Substituting for f by poynting factor gives y ф P = x ϒ P sat (i = 1,2,…) …………(3)

13. Where, ф =(ф ̂ /ф sat )exp[-v(p-p sat )/ RT] It’s omission introduce negligible error, and this equation is often simplified: ф = ф ̂ / ф i sat …………(4) Eq 3 called the gamma/phi formulation of VLE.

14. Thank you…