Equilibrium constant and rate constant: How they are different?

The first question we would ask is [1] why a chemical reaction occurs, [2] when a chemical reaction occurs, and [3] how a chemical reaction occurs. Most chemical kinetics questions will be answered if we are clear on these three fundamental points.

The fundamental point is that energy always moves from a high to a low level according to the second law of thermodynamics. As a result, in every [forward] reaction, the products must be at a lower stable energy level than the reactants.

In most cases, if we leave a few molecules of reactants at room temperature, nothing would happen. Every substance has some internal energy [KE+PE] that is insufficient to cause molecular collisions and convert reactants into products. There is threshold energy for each reaction that must be met before the reaction can begin. The difference between threshold energy and internal energy is the activation energy.

The most important point is that just because a reaction has been started does not mean that it will proceed. If the products have a lower energy level than the reactants, the reaction will proceed spontaneously; otherwise, the reaction will reverse.

What exactly is Equilibrium?

Equilibrium is the state of an object in which two or more counter-influences, whether internal, external, or a combination of both, act on the body, canceling each other out to keep the object in the same state it was in before.

Chemical Equilibrium

Chemical equilibrium is linked to chemical reactions. The reactants in a chemical reaction react with each other to produce the products. When the products reach a certain concentration, they begin to decompose into reactants. At some point, the rate of product formation, known as the forward reaction, and the rate of product decomposition, known as the backward reaction, become the same. From this point forward, the concentration of both the reactants and the products remains constant. This is referred to as chemical equilibrium. The point to note is that at some stage every reaction becomes reversible.

Consider the following simple chemical reaction with species A and B:

A <-> B

The double arrow in the middle of A and B indicates that the reaction is going both ways. That is, reactants become product species, while products become reactant species.

Assume that whenever the temperature rises above room temperature, the A molecules begin to transform into B molecules. Consider placing a test tube containing only A molecules in an oven that maintains a constant temperature above room temperature. You'd expect some A molecules to start converting to B molecules. As time passes, more A molecules will transform into B molecules. Assume, however, that there is a backward tendency for B molecules to turn into A molecules over a wide temperature range, including the one in the oven. As a result, there will be a back-and-forth movement of product and reactant concentrations, with the possibility of a chemical equilibrium eventually being established. Chemical equilibrium is a state in which the forward reaction rate equals the reverse reaction rate.

Dynamic equilibrium

Dynamic equilibrium is defined as, when the rate of forward reaction (reactants chemically reacting with each other to produce the product) and the rate of backward reaction (products converting into reactants) become equal in a reversible reaction, and the ratio of reactants to products remains constant.

This means that after a certain period of time, the concentrations of species A and B will reach a stable state in which just as many A molecule as B molecules turn into A molecules. In other words, the reaction will reach equilibrium, which can be maintained indefinitely if all other factors remain constant, such as temperature.

Equilibrium constant

The equilibrium constant is a value that relates the ratio of product to reactant concentrations once the reaction has reached chemical equilibrium.

Consider a more general reaction to drive an equilibrium constant's point home. It goes like this:

aA + bB <-> cC + dD

In this equation, a, b, c, and d are integers, and A, B, C, and D represent the chemical species in question. The square brackets indicate that the concentration of a chemical species is being taken; for example, [A] is the concentration of A.

The equilibrium constant, denoted as Keq, can be calculated as follows:

Keq =([C]^c) ([D]^d )/( [A]^a) ([B]^b)

What exactly is the reaction quotient?

The equilibrium constant only describes the equilibrium conditions; it does not reflect the product to reactant ratio at any given time. The reaction quotient is used to represent those concentrations at a given time (Q). For those wondering, "What is reaction quotient?" it is the product to reactant ratio at a given point in time. If that moment occurs during equilibrium, Q = K. Otherwise, Q and K have different values.

Q is used to calculate the product-to-reactant ratio at a given time so that it can be compared to K. The system is in equilibrium if Q = K. If Q K, the value of Q in relation to the value of K determines whether the reaction proceeds forward or backward.

If Q K, the reaction will continue to produce more products.

If Q > K, the reaction will reverse to produce more reactants.

There will be no net change if Q = K.

Despite the fact that K and Q represent different concepts, they both use the same expression:

Q =([C]^c) ([D]^d )/( [A]^a) ([B]^b)

Equilibrium constant K and free energy ?G relation

K = e ^-?G/RT

ln K = - ?G/RT

Gibbs energy and the equilibrium

Explanation

Let's examine how this connection between free energy and the equilibrium constant takes shape. We shall first examine how to handle endothermic versus exothermic reactions. In these two scenarios, the free energy moves in opposite directions. To deal with opposites, we often assign one quantity a positive sign and the other a negative one. A positive value for the free energy of a reaction is assigned if the free energy rises. However, if free energy declines during the course of the reaction, we demonstrate this by using a negative number as the free energy value.

The exponent in the equation becomes positive if ?G is negative (because it is multiplied by -1 in the expression). Since e to positive power will usually be a number greater than one, the relationship suggests there are more products than reactants. That's because the reaction is exothermic, and we expect the reaction to go forward. The reaction will be more in favour of the product if ?G has a higher value.

Rate constant

The rate constant tells you ‘What is the reaction mechanism?' What reactants must be brought together in what concentrations to make the final product?

?For example, a reaction of A + B --> C has a rate of that below:

Rate = delta A / Time

The delta symbol above means 'change in.'

Fundamentally, k is the number of collisions that result in a reaction per second

The equation for the rate law is:

Rate = k[A]^m

A is the reactant

k is a constant called the rate constant

m is the reaction order

If m = 0, then the reaction is zero order, and the rate is independent of the concentration of A.

If m = 1, then the reaction is first order, and the rate is directly proportional to the concentration of A.

If m = 2, then the reaction is second order, and the rate is proportional to the square of the concentration of A.

Rate constant and activation energy

Arrhenius equation relates the rate constant with activation energy.

A common form of the equation is

K= A e^ - Ea/RT

K is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the universal gas constant and T is the absolute temperature.

K is the number of collisions that result in a reaction per second, A is the number of collisions (leading to a reaction or not) per second occurring with the proper orientation to react, and e^ - Ea/(RT) is the probability that any given collision will result in a reaction. Every collision does not result in a reaction. Only a small fraction of the collisions between reactant molecules convert the reactants into the products of the reaction. Another factor that influences whether the reaction will occur is the energy the molecules carry when they collide. Not all molecules have the same kinetic energy. This is important because the kinetic energy molecules carry when they collide is the principal source of the energy that must be invested in a reaction to get it started.

K as a function of the exponent –Ea /RT. K is rate constant. And what is the significance of this quantity? Recalling that RT is the average kinetic energy, it becomes apparent that the exponent is just the ratio of the activation energy Ea to the average kinetic energy. The larger this ratio, the smaller the rate (hence the negative sign). This means that high temperature and low activation energy favor larger rate constants, and thus speed up the reaction. Because these terms occur in an exponent, their effects on the rate are quite substantial.

Credit: Google