## Kinetics

The rate at which a reaction occurs depends on several factors including:

• the area of contact between reactants: Greater area of contact means more chances of particles colliding with each other with the right orientation for a reaction to occur.
• the temperature: Greater temperature means more reactant particles retaining the activation energy for a reaction to occur.
• the presence of a catalyst (which lowers the activation energy – see below).

# Rate Laws

A rate law is an equation which associates the reaction rate with concentrations of reactants. In general, for the equation

aA + bB → cC + dD

the rate law is:

r  =  k [A]a [B]b

Where:

• r is the rate at which the reaction occurs.
• k is the rate constant.
• a and b are known as the “orders” of their respective reactants. We can say, for instance, that this reaction is order a in respect to [A].
• [A] and [B] are the reactant concentrations.
• a+b is known as the order of the whole reaction. Reactions are thus known to be zero-order, first-order, second-order, and so on.

# Integrated Rate Laws

An integrated rate law allows the calculation of reactant concentrations given time values. The integrated rate law varies by the order of a reaction.

## Zero-th Order Reactions

For zero-th order reactions,

• A [Reactant] versus time graph yields a straight line with -k as the slope and the initial concentration as the y-intercept.
• The integrated rate law for zero-th order reactions is thus
• The half-life of a zero-th order reaction is related to both the current concentration of reactants and the rate constant:

## First Order Reactions

For first-order reactions,

• A ln[A] vs. time graph produces a straight line with a slope of -k and a y-intercept of ln[A]0.
• The integrated rate law for first order reactions is thus
• The half-life for a first-order reaction is dependent upon the rate constant, but not the current reactant concentration. Note this difference from zero-th and second order reactions’ half-life equations:

## Second Order Reactions

For second-order reactions,

• A 1/[A] vs. time graph yields a straight line with a slope of positive k and a y-intercept of 1/[A]0.
• The integrated rate law for second order reactions is thus
• The half-life of a second-order reaction, as if that of a zero-th order reaction, depends on both the current concentration as well as the rate constant of the reaction:

# Reaction Mechanisms

A reaction mechanism is the step by step sequence of elementary reactions by which overall chemical change occurs. For instance, the equation CO + NO2 → CO2 + NO may occur via the following reaction mechanism:

2 NO2 → NO3 + NO (slower)
NO3 + CO → NO2 + CO2 (faster)

In this case, the top step is slower is thus known as the rate-determining step. Note that nitrogen trioxide (NO3) appears in the products side of the top equation and in the reactants side of the bottom equation, but does not appear in the collective chemical equation. Thus, NO3 is known as an intermediate.

# Catalysts

A catalyst participates in a chemical reaction, but is not consumed by the reaction itself. A catalyst speeds up a chemical reaction by lowering the activation energy, while an inhibitor (also not consumed) raises the activation energy. A catalyst may lower the activation energy by changing which reaction mechanism is used and/or allowing for a better orientation of molecular collisions.