# Finding reaction rate

In previous lesson, we have obtained molar balance equations for different reactors. All of those equations contains rA (reaction rate). Two solve obtained equations, we have to find rA as a function of concentrations.

-rA = K(T)*f(CA , CB , .... )
rA - reaction rate of A
K - reaction rate constant which is a function of temperature
CA , CB , .... - concentrations of each constituents
We add - sign to rA because A is a reactant and it is reduced when reaction occurs.

## Find reaction rate constant - Arrhenius equation

Reaction rate constant(K) is given by Arrhenius equation.
K(T) = Ae(-E/RT)
A - frequency factor
E - Activation Energy(J/mol)
R - Gas constant = 8.314 J/mol.K = 1.987 cal/mol
T - absolute temperature(K)

We want to make a relation between absolute temperature(T) and reaction rate constant(K)
Take ln for both sides.
ln(K(T)) = ln(Ae(-E/RT))
ln(K(T)) = ln(A) + (-E/RT)

#### Plotting reaction rate constant against 1/(absolute temperature) #### Units of reaction rate constant

Units of K is depend on the units of function of concentrations (f(CA , CB , .... ) ).

## Write reaction rate equation

In this tutorials we are going to talk only about elementary reactions. Reaction rate(rA) is written by as follows.

Reaction rate is proportional to the product of the molar concentrations of reactants with each concentration term raises to the power equals to the stoichiometry number of respective reactants

Let's try some example for both irreversible reactions and reversible reactions

#### Write reaction rate equation for irreversible reactions

Write reaction rates for all reactants of following reaction.
A + 2B → C
In this reaction one A molecule is reacted with two B molecules and produce one C molecule. Therfore concentration of both A and B is reduced ( negative reaction rate) and C is increased (positive reaction rate).

rA = -K * CA * CB2
rB = -2 *K * CA * CB2
rB = K * CA * CB2

#### Examples of Rate laws of elementary irreversible reactions #### Write reaction rate equation for reversible reactions

Write reaction rate of A of following reversible reaction.
A + 2B ⇌ C
In this reversible reaction, one A molecule reacts with two B molecules and produce one C molecule (forward reaction). Also one C molecule produce one A molecule and two B molecules (backward reaction).
When we write reaction rate of A for forward reaction, A is reduced (disappearing). Therefore rection rate of A of forward reaction is negative. But A is formed by backward reaction from C. Therefore rection rate of A of backward reaction is positive.

rA|forward = -K1 * CA * CB2
rA|backward = K2 * CC
rA|net = -K1 * CA * CB2   +   K2 * CC when we write reaction rate equation, we should be careful about stoichiometry number of reactants. In the above reaction we can one hydrogen molecule and one iodine molecule react and produce two hydrogen iodide molecules.

Forward reaction: Reaction rate of producing HI is twice as reaction rate of consuming H2
Backward reaction: Reaction rate of producing H2 is half as reaction rate of consuming HI