Chemical Kinetics Theory

What question does chemical kinetics answer?

The rate of reaction as a function of concentration and temperature

How is the rate of disappearance of reactant A defined?

-r_A

r_A is the rate of reaction of species A
The negative sign indicates consumption of A

What are the typical units of reaction rate?

\text{mol m}^{-3}\text{s}^{-1}

What is the general form of a rate law for a single reactant?

-rA = k CA^n

k is the rate constant
C_A is the concentration of A
n is the reaction order with respect to A

What is the general rate law for multiple reactants?

-rA = k CA^a C_B^b

a,b are the reaction orders with respect to A and B

How is overall reaction order defined?

\text{Overall order} = a + b

What is the rate law for a first-order reaction?

-rA = k CA

What is the rate law for a second-order reaction in A?

-rA = k CA^2

What is the rate law for a mixed-order reaction?

-rA = k CA C_B

How is reaction order determined?

Reaction order is determined experimentally, except for elementary reactions

What defines an elementary reaction?

A single molecular step where the rate law follows stoichiometry

What is the rate law for the elementary reaction A + B → C?

-rA = k CA C_B

What defines a non-elementary reaction?

A multi-step reaction where the rate law cannot be inferred from stoichiometry

Why must most industrial rate laws be measured experimentally?

Because most reactions in reactors are non-elementary

What does the rate constant represent?

The proportionality factor linking reaction rate to concentration at a given temperature

Is the rate constant truly constant?

No, it depends strongly on temperature

What equation describes the temperature dependence of the rate constant?

k = A e^{-E_a/(RT)}

A is the pre-exponential (frequency) factor
E_a is the activation energy
R is the gas constant
T is absolute temperature

What physical meaning does activation energy have?

The minimum energy barrier molecules must overcome to react

How does temperature affect the reaction rate constant?

k \uparrow \text{ exponentially as } T \uparrow

Why does reaction rate increase rapidly with temperature?

Because the exponential Arrhenius term dominates

How does activation energy affect temperature sensitivity?

Higher Ea gives stronger sensitivity of k to temperature

What equation relates rate constants at two temperatures?

\ln\left(\frac{k2}{k1}\right) = -\frac{Ea}{R}\left(\frac{1}{T2} - \frac{1}{T_1}\right)

k1,k2 are rate constants

T1,T2 are temperatures

How does concentration affect reaction rate?

-rA \propto CA^n

What happens to rate when concentration doubles in a first-order reaction?

CA \to 2CA \Rightarrow -rA \to 2(-rA)

What happens to rate when concentration doubles in a second-order reaction?

CA \to 2CA \Rightarrow -rA \to 4(-rA)

Why do plug flow reactors often have higher initial rates than CSTRs?

-rA^{PFR} > -rA^{CSTR}

Because PFRs operate at higher inlet concentrations

How does reaction rate appear in reactor design equations?

V \propto \frac{1}{-r_A}

V is reactor volume

How does reaction rate affect reactor size?

-r_A \uparrow \Rightarrow V \downarrow

What reactor design variables are controlled by kinetics?

Reactor volume, residence time, and productivity

What does kinetics NOT determine?

Maximum conversion or thermodynamic feasibility

What does kinetics determine?

The time and reactor size required to reach a given conversion

How are kinetics and thermodynamics fundamentally different?

\text{Thermodynamics} \Rightarrow \text{maximum conversion}
\text{Kinetics} \Rightarrow \text{rate and reactor size}

One-sentence exam definition of chemical kinetics

Chemical kinetics determines reaction rate and therefore the reactor size and residence time required to achieve a desired conversion