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Molecular Modeling & Drug Discovery

9. Thermodynamic Equilibrium:

Chemical equilibrium, kinetics, and thermodynamics

1st law of thermodynamics

The first law of thermodynamics is a thermodynamic adaptation of the law of conservation of energy that distinguishes between three types of energy transfer: heat, thermodynamic work, and energy associated with matter transfer.

It also relates each type of energy transfer to a property of a body's internal energy.

It is common to formulate the first law for a thermodynamic process without a transfer of substance as follows:

ΔU=Q-W

Q > 0: system take up heat
Q < 0: system releases heat
W > 0: system does work
W < 0: work is done to the system
ΔU > 0: system takes up energy
ΔU < 0: system loses energy

A thermodynamic system's enthalpy, which is one of its properties, is calculated by adding the system's internal energy to the product of its pressure and volume.

The pressure-volume concept describes the effort needed to create space for the system by displacing its surrounds in order to determine its physical dimensions.

Enthalpy, then, serves as a stand-in for energy in chemical systems; bond, lattice, solvation, and other properties that we refer to as "energies" in chemistry are actually differences in enthalpy.

Enthalpy as a state function depends simply on the ultimate arrangement of internal energy, pressure, and volume, not on the procedure followed to get there.

ΔH = ΔU + pΔV

(by changing Q in U = Q - W to H)

Enthalpy H is a state function with the following definition: H=U+pV.

2nd Law of Thermodynamics

"The entropy will rise in a spontaneous (naturally occurring) process"

We must always take the environment and system entropy changes into account.

ΔS_tot = ΔS_sys + ΔS_env

Gibbs Free energy

ΔS_env = ΔH/T

ΔS_tot = ΔS_sys -ΔH/T

TΔS_tot = TΔS_sys-ΔH

Substitute ΔG for -TΔS : ΔG = ΔH-TΔS_sys

ΔG = ΔH-TΔS changes in gibbs free energy

G = H-TS gibbs free energy

Meaning of ΔG :

G is like H and S- a state function ΔG = G₂-G₁

Finally, the Gibbs free energy function allows us to determine whether a process will occur spontaneously under specific conditions (temperature and pressure constant)

ΔG > 0 reaction will not happen spontaneously.

ΔG = 0 System is in thermodynamic equilibrium.

ΔG < 0 reaction will happen spontaneously.

Chemical Equilibrium

The majority of chemical processes and reactions are reversible.

Thermodynamic equilibrium is the end stage of all reversible processes.

Equilibrium is established in a chemical reaction when the two opposing reversible reactions happen at the same reaction rate.

When a reaction happens, the opposite reaction will also happen:

N₂(g) + 3H₂(g) =====> 2NH₃(g)
2NH₃(g) ====> N₂(g) + 3H₂(g)

A double arrow is used to denote this.

N₂(g) + 3H₂(g) <====> 2NH₃(g)

When the two opposing reversible reactions happen at the same rate, equilibrium has been attained.

A₂(g) + X₂(g) = 2AX(g)

The change in substance concentration over time is referred to as the rate of a chemical reaction, or r.

r=dc(X)/dt

All substances have a constant concentration while a chemical reaction is in equilibrium.

Due to the equal rates of the forward and backward reactions, there is no overall change in the reactions.

There is a dynamic equilibrium in the system.

equilibrium

Figure 1. Reactant and product concentrations in a equilibrium reaction.

We may calculate the forward and reverse reaction's rates as follows if they are single steps:

r₁ = k_f*c(A₂).c(X₂)
r₁ = k_r * c₂(AX)

In the state of equilibrium :

r₁= r_r

k_f* c(A₂) * c(X₂) = k_r*c₂(AX)

c₂(AX)/c(A₂) * c(X₂) ====> k_f/k_r

Equilibrium constant

The Law of Mass Action

aA+eE = xX+zZ

k=c^x(X) * c^z(Z)/c^a(A)*c^c(C)

The ratio between the product of the product concentrations and the product of the reactant concentrations is constant.

The Equilibrium Constant K_c

The law of mass action is stated for concentrations for reactions of gases and in solutions. The index c in 'K_C' indicates this.

The composition of the system at equilibrium in terms of educts and products is shown by the value of "K_C"

Net substance changes will continue until the ratio Q of products to byproducts equals K_C, at which point the system will have attained equilibrium.

Q < K_c: net foward reaction will occur
Q = K_c: equilibrium
Q > K_c: net reverse reaction will occur

The Equilibrium Constant K_p

The ideal gas law links concentration and (partial) pressure.

p = n/V . RT = cRT

As a result, we can formulate the law of mass action with partial pressures for reactions that only involve gases:

aA(g) + eE(g) = xX(g) + zZ(g)

Kp=p^x(X).p^z(Z)/p^a(A).p^e(E)

Le Chatelier’s Principle

If a chemical reaction is at equilibrium and experiences a change in pressure, temperature, and concentration of product or reactant, the equilibrium shifts in the direction that tends to undo the change.

1. effect of concentration :

If we increase the reactant, the reaction will proceed to produce more product, hence it will move in the forwarding direction.
If we increase the product, the reaction will proceed to produce more reactants, hence it will move in the backward direction.

2. effect of pressure :

As pressure is directly proportional to the number of moles
As we increase pressure, the reaction will move where there are fewer moles.

3. effect of addition of inert gas:

At constant pressure: equilibrium will shift towards more number of gas moles as it will increase the vessel`s volume
At constant volume: it will not affect the equilibrium.

4. effect of temperature:

On increasing, temperature equilibrium will shift towards an endothermic reaction.
Exothermic reactions are favored at low temperature
Endothermic reactions are favored at high temperature

5. effect of catalyst :

It doesn't affect the equilibrium
It only increases the rate of reaction and decreases the activation energy of a reaction.

eg:

H₂+I₂⇒ 2HI+ heat

1. If we increase the product concentration , the reaction will move in the backward direction.

2. If we increase the pressure, the reaction will have no effect as the number of moles on both sides is equal.

3. If we increase the temperature, the exothermic reaction will move in a backward direction producing more reactants.

4. If we add a catalyst, the equilibrium will not change.

A new equilibrium is established when a system in equilibrium is subjected to an imposed change in concentration, temperature, volume, or partial pressure.

Example:

2S0₂(g) + 0₂(g) <===> 2S0₃(g)

Since 3 moles of gas are reduced to 2 moles under higher pressure, the fon/vard reaction is more favorable.

If there is an exothermic reaction and a rise in temperature, how do you think the equilibrium will change?

Temperature-Dependence of Equilibrium Constants

Le Chatelier's idea is quantitatively expressed in the previously mentioned standing equation.

The expression on the right side of the equation is negative if T2 > T1 and the reaction is exothermic (ΔH <O).

K2 <K1 as a result, and with the higher temperature T2, the reactant side is where the equilibrium is now.

Thermodynamics vs. Kinetics

The study of energy changes using thermodynamics.

Science of kinetics that examines the motions/velocities of particles and accompanying forces.

Thermodynamics predicts whether a chemical reaction will take place under specific circumstances, while kinetics assesses the rate of this reaction.

While kinetics evaluates the speed at which states shift, thermodynamics analyzes the energy of various system process stages.

When chemical equilibrium is created, thermodynamics and kinetics collide.

Chemical Equilibrium

Differences in free energy between states are used in thermodynamics to establish equilibrium concentrations (reactants vs. products)

Boltzmann distribution : Probability as a function of energy of a specific state (substance)

Pofential Energy Surface

A potential energy surface, often known as a PES, is a mathematical or visual representation of the relationship between a molecule's energy and shape.

reaction coordinate