Reaction Rates

## Putting Value on What Changes ## Contents

Concentration Dependance
Temperature Dependance
Energy & Predictions

Chemical reactions are at the heart of life.  But as reactions occur, they do so at rates that vary with the concentrations of reactants.  So description of each chemical reaction is complicated by values in flux.  (There are other important aspects in our lives that are similarly in flux.  The tools chemists have found for understanding reaction rates may be valuable for these other aspects as well).

The chemistry approach is to utilize understanding from theory (of the sub-microscopic) to come to understand the observable (macroscopic).

A RATE describes how fast something changes in time.  A chemical reaction rate describes how fast a reaction occurs.  But a reaction usually involves several different substances.  Typically chemists select one of the substances connected by the reaction to describe the reaction rate.

For example, for the idealized reaction where substance A reacts with B to make C
A + B → C
then the rate might be measured by
R1 = k  Δ[C] / Δt
where the Greek letter Δ (Delta) represents change in, the brackets [ ] represent concentration (customarily in units called Molarity), Δt is elapsed time (i.e., change in time), and k is a constant.  Constants are needed in most equations involving aspects of the real world because we wish to arbitrarily pick unrelated units for each variable.  In some cases (where one unit is defined by the other units and the equation), k may equal unity (exactly = 1).  But in many cases it is more practical to use a property such as color as a measure of concentration.  Then k will be the conversion factor to produce the desired rate units.

## Concentration Dependance

The key to understanding reaction rates is the realization that every chemical reaction occurs only when molecules come together: in short, molecules react only when they collide.  This implies that the concentration of each kind of constantly and randomly moving reactant determines the chance of the reaction occurring. Again using the idealized reaction where  substance A reacts with B to make C,
A + B → C
we often find the rate of reaction depends on the concentration of the reactants by
R1 = k1 [A] x [B]
where the brackets [ ] represent concentration (customarily Molar), and k1 is another constant.  So if [A] is doubled, and [B] tripled, the rate will be 6 TIMES faster.

Or, if in a second reaction where two identical molecules collide,
2D → E + F
i.e., D + D → E + F then R2 = k2 [D]2.
At first this may seem strange that 2D in the chemical reaction results in the squared relation.  But the relation is the direct consequence of the concentration of D determining both the chance of the first D colliding as well as the chance for the second D colliding, so that the rate of reaction, R2, depends on the first concentration TIMES the second concentration, that is [D]2.

It should be noted that while the concentration of each reactant may vary, there is a unique constant, k, for each reaction which distinguishes whether the reaction tends to be slow (small k) or fast (large k).

Often by determining the chemical equation and measuring the speed in one circumstance, chemists can predict the rate of reaction in other circumstances.

Fine Print: Many reactions occur by mechanisms involving numerous steps.  In such cases the concentrations involved in the slowest step governs the overall reaction rate.  Sometimes reaction rates are increased with assistance from catalysts causing other factors (such as geometry, surface area, or electron transfer rate) to govern reaction rate.  So a rate equation based on a balanced equation should be viewed as an educated first guess that should be verified at several concentrations.

## Temperature Dependance

Furthermore, the rate of reaction also depends on the temperature of the event.  Temperature has a duel role:

At higher temperature, molecules move faster, so they will arrive at the collision sooner.  Thus reactions are faster when the temperature is higher.  So our bodies are roused into action against an invading pathogen by a fever.

A reactions constant, k, increases with higher temperature.

Not all collisions between molecules cause reactions.  At slower speeds, collisions of molecules are gentler resulting in more rebounds and fewer breaking of bonds needed to cause reaction.  Below a certain characteristic temperature, the rate of reaction drops rapidly with virtually no reaction only a few degrees cooler.  It is a common observance that a match raises temperature enough to ignite a fire; but cooling by blowing or flooding will extinguish the flame.  Similarly the shelf live of food is prolonged from destructive spoilage reactions by refrigeration, and virtually preserved by freezing (except that evaporation continues creating freezer burn, the misnomer for freezer dehydration).

## Energy & Predictions

Scientists often use the physics concept of ENERGY to help understand and predict the effect of temperature on reaction rates.

Energy is defined by its ability to do WORK
W = f • d
where f is force and d is displacement (distance moved).  Many forms of energy are derived from this definition.  Here we are interested in the forces (bonds) maintaining the groups called molecules and the collision forces that break these bonds (causing reactions).  But such forces are difficult to measure directly, and also vary from moment to moment.  Using energy avoids those difficulties.

Physicists had carefully defined POTENTIAL ENERGY as energy stored in forces such a chemical bonds.  Chemists sometimes use the term enthalpy when describing potential energy stored in chemical bonds.  It requires a certain amount of energy to pull apart each chemical bond.  (We wont worry here about the precise formula for that relationship.)  But we can use a graph of potential energy (such as the reaction forming ammonia to the right→) to visualize the chemical forces and the effect of temperature on reaction rates. The reactants usually start with some potential energy (such as N2 and H2 on the left) depending on their initial chemical bonds.  (The potential energy for common bonds has been measured using reactions which form molecules with each kind of bond.  These are available in reference tables of Heats of Formation.  But note that if we are interested in the energy involved in the reaction, we may for our convenience choose to set the starting potential energies at zero, as we've done here.  Forming a bond usually releases potential energy in the form of heat.  The potential energy for molecules with multiple bonds can be summed from the known heats of formation to determine the potential energy of the entire molecule.Once a bond is formed, the atoms have less potential energy than when they were free and independent!  So potential energy must be added (increased) to break a bond.

In a collision causing a reaction, the initial potential energy of the molecule is increased (note peak on graph) as bonds are knocked apart.  The energy needed to do this is called ACTIVATION ENERGY.  Often this energy comes from the speed of the colliding molecules which depends on temperature.  (It could also come from light, higher energy radiation, or from other molecules such as ATP.)  If the collision has insufficient energy, the molecules rebound back to the reactant state (i.e., back to the left ← on the graph).  But if there is sufficient activation energy to break the bonds (and reach the peak), new bonds may form lowering the potential energy to that of the products (on the right side of the graph →).

The products may have more or less potential energy than the initial reactants.  If the potential energy is less (as is the case forming ammonia shown on this graph), the excess (difference) energy is usually released as heat.  (Alternatively it may be released as light or sound, or may be passed to other molecules such as ATP.)  Such a reaction that releases energy is described as EXOTHERMIC (Greek: heat exits); if the products have greater potential energy, more energy will have entered than left, and the reaction is called ENDOTHERMIC(Greek: heat into).  This usually results in the reaction mixture cooling itself.

Such heat of reaction, ΔH, can be measured in an insulated reaction vessel using the equation
ΔH = ΔT  m  C
where ΔT is the change in temperature, m is the mass of material, and C the heat capacity (i.e., a units conversion factor) for the substance.  Typically we arrange for the reaction to heat water which as a heat capacity, C = 4.18 Joules/g of water/°C.  Once measured, the heat of reaction can be used to predict heats for related reactions, determine the strength of bonds, or even predict if a reaction will occur!  And the rate of reaction is related to the activation energy.  High peaks require a lot of activation energy so tend to be slow reactions compared to reactions with lower energy peaks. 