Rates of Reactions, Chemical Kinetics & Orders

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One of the most important things to note with chemical reactions is that the molar concentrations of the substrates are often proportional to the rate of the reaction.

So if we take the simplest rate constant for an equation:

A + B –> C

We could might find the rate law to be:

Rate = k[A][B]

The coefficient k is called the rate constant and is dependant on temperature – this is independant of the concentrations of the substrates; so the larger the value of k, the faster the rate of the reaction. Also important is that the units of k will convert the product of the concentrations into a rate – so change in concentration per unit of time, often expressed as mol.dm-3.s-1.

While temperature increases increase the rate constant and rate of reaction in most cases, reactions with a large activation energy will have small rate constants as considerable temperature rises may be required for the reaction to occur at all.

Consider this theoretical example:

Rate = k[A][B] where k = 5 dm3 mol^-1; [A] = 1 mol.dm-3; [B] = 2 mol.dm-3

Therefore Rate = 5 dm3.mol-1.s-1 x 2 mol^2.dm^-6

The units all cancel to leave us with a rate of: 10 mol.dm-3.s-1

So the units for k in that example were dm3.mol-1.s-1. In another rate law, eg: Rate = k[A] we would find the units for k to be simply s-1.

Once we know the rate law and rate constant for that reaction we can go on to predict the reaction rate for any concentration of substrates.

– The Order of a Reaction

Reactions can usually be defined as either zero order (0), first order (1) or second order (2). The order of a reagent or the overall reaction depends on the effect varying the concentrations of substrates has on the rate of the reaction. So:

  • Zero Order – rate is not related to reactant A – rate is proportional to [A]0
  • First Order – rate is doubled as concentration of reagent B doubles – rate is proportional to [B]1
  • Second Order – rate is quadrupled as concentartion of reagent C doubles – rate is proportional to [C]2

Combining the above information, rate is proportional to [A]0[B]1[C]2 – therefore Rate = k[B]1[C]2 – so the reaction is 3rd order ( 1+2=3). Third order tells us the reaction is made of several parts.

– Measuring Rate & Integrated Rate Equations

0. Zero Order:

As a zero order reaction has a rate which is independant of any reagents, we can assume that Rate = k.

To identify a zero order reaction plot concentration of a reagent against time and you would see a straight line. The integrated rate equation is:

Integrated Rate Equation - Zero Order

Which means that the gradient (from y=mx+c) equals -k. This allows us to determine k from the graph.

Another feature of a zero order reaction is a decreasing half life as the reaction continues. The half life equation for zero order reactions is:

Half Life Equation for Zero Order Reaction

Where [A]0 is the initial concentration. Shows a decreasing half life as concentration falls.

1. First Order:

First order reactions have a rate proportional to the concentration of only one reagent. Any other reagents present will not affect the rate.

To identify a first order reaction plot In(concentration) against time to give a straight line. The integrated rate equation is:

Half Life Equation for Zero Order Reaction

Which means that as with zero order, k is the -ve of the gradient.

The half life of a first order reaction is constant thoughout the reaction:

Half Life Equation for First Order Reaction

This half life is dependant only on k as the half life remains constant regardless of concentration.

2.Second Order:

Second order reactions have a rate proportional either to 1 or 2 reagents (eg 2 x first order reagents or 1 x second order reagents).

To identify a second order reaction, plot 1/concentration against time to give a +ve straight line. The integrated rate equation is:

Integrated Rate Equation for Second Order Reactions

Which means that k = gradient (so the opposite of what we find in zero and first order reactions).

The half life of a second order reaction increases throughout the reaction:

Half Life of a Second Order Reaction

Shows an increasing half life with decreasing concentration.

2(1). Psuedo First Order:

Psuedo first order approximation is used when carrying out some second order reactions. It is useful as it is difficult to effectively control the concentrations of more than one reagent at the same time, and the psuedo technique simply places one reagent in excess at a constant level; essentially limiting the reaction rate the other reagent (you only control the concentration of one reagent).

Rate Order of a Psuedo First Order Reaction

The equation above illustrates that by putting [B] in excess we have essentially removed it from the rate reaction, allowing us to calculate the psuedo rate constant k‘.

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