Reaction Kinetics

What are reaction rates?

Simply, the time per unit volume it takes for a product to form (or for reactants to be consumed):

$Rate = - \frac{\downarrow in \ available \ reactants}{time} = \frac{\uparrow in \ accumulation \ products}{time}$

Note: The negative in front of the reactants side of the equation reflects the decrease in reactants that occurs in the formation of a product.

What are six factors that affect reaction rates?

1. Temperature
   • The reaction rate will increase as temperature increases. This is true until extremely high temperatures^37.1.
2. Concentration
   • Increasing the concentration increases the amount of interactions among reactants.
3. Pressure
   • Increasing the pressure is practically equivalent to increasing the concentration. This is really important for gases; however, reactants that do not involve gases are almost unaffected.
4. Presence of catalyst (more below)
   • Catalysts decrease the energy of activation ($E_{A}$) for a substance to change states.
   • Catalysts are not transformed or consumed in a reaction.
5. Order
   • The sum of the exponents of reactant concentrations. This reflects how quickly the reactants are consumed.

What is the rate law?

Because a reaction rate can be expressed as the disappearance of reactants - and assuming the reaction will only proceed in the forward direction - the general rate law for a reaction is equal to (1) the product of the reactant's concentration, (2) each raised to a certain power, and (3) multiplied by a constant ($k$):

$a A + b B \rightarrow c C + d D$

$Rate = k[A]^{x}[B]^{y}$

The powers $x$ and $y$ listed in the above rate law are derived by analyzing empirical data as we will see below.

What are the three rate laws that are most commonly observed?

1. Zero-order reaction
2. First-order reaction
3. Second-order reaction

What are the rate constants (and units) for each of the rate laws?

Table 36.1: Zero-, First- and Second- Order Reactions.

	Rate is equal to:	Units of the rate constant ($k$)	Description of the rate
Zero-Order Reaction	$rate = k$	$\frac{mole}{L\cdot sec}$	Rate of reaction is constant and independent to the amount of reactants.
First-Order Reaction	$rate = k[A]$	$\frac{1}{sec}$	Rate of reaction is directly proportional to the concentration of one of the reactants.
Second-Order Reaction	$rate = k[A]^{2}$ $rate = k[A][B]$	$\frac{L}{mole \cdot sec}$	Rate of reaction is directly proportional to the square of the concentration of one of the reactants or to both reactants.

Why do the units of the rate constants change?

The units change because the rate constants are different for each order of reactions.

Note: The unit for rate is always moles/(L)(sec) and the unit for concentration is always moles/L. Therefore, to maintain these ÒrigidÓ givens, the constant (k) is the scapegoat for being the flexible one and must adapt itself to have the appropriate units.

What is the rate determining step?

The slowest step in a set of reactions. Because it is the slowest, it sets the whole pace of the reaction. Think about a relay team for the 4x100m relay. If the third runner is the slowest (which actually is commonly the case), the overall time to race completion is dependent on that person's completion of her leg of the race.

How do kinetic and thermodynamic factors affect a reaction rate?

This is more of an organic chemistry topic, but let's talk about it a little. Reaction outcomes are influenced by two factors: (1) the relative stability of the products (aka thermodynamic factors), and (2), the rate of product formation (aka kinetic factors).

If a reaction is governed by thermodynamic factors, then the driving force will be to form the more stable product.

Conversely, if a reaction is governed by kinetic factors, then the driving force will be to form the product with the lowest activation energy.

How do temperature and time spans affect the type of control a reaction will be under?

Generally speaking, kinetic control is more often observed when reactions take place at lower temperatures and over shorter time spans; thermodynamic control is more often observed when reactions take place at higher temperatures and over longer time spans.

What are catalysts?

A substance that accelerates a reaction but is neither consumed nor transformed. Catalysts are added to reactions to facilitate their completion and are not considered reactants or products. This increased reaction rate is a result of a catalyst's ability to reduce activation energies. Consequently, this make reactions occur at lower temperatures or with less energy required:

Figure 36.1: $\Delta$G changes in a reaction with and without an enzyme: free energy changes, over time, in a reaction without an enzyme (upper, solid line) and with an enzyme (lower, dashed line).