In the second Blog aimed at supporting students taking Unit 16, Chemistry for Biology Technicians. There are three areas that I would like to address: Rates of Reaction, the principles of acids and bases in the form of pH measurements and finally a word or two about chemical equilibria. Having spent most of my PhD measuring the initial rates of glutamate dehydrogenase enzymes, I moved on to work with enzymes that are much more difficult to assay. It is important to choose the easiest and most robust enzymes for developing and testing kinetic ideas. Hence the work of Biochemists in the last century tended to feature focus on NAD(H)-linked enzymes or proteases, for which reliable and sensitive spectroscopic methods were widely available. However, our understanding of catalysis must be considered in the light of the "natural" tendency of a molecule to decompose or oxidise (for example) in the absence of any enzymes. Or, for two or more molecular species to unite to form new comopunds. In other words, before we can appreciate the catalytic power of enzymes, we need tobe able to understand the reactivity of molecules in the context of time. This is the field of reaction kinetics, which is of critical importance not only in Biology, but in all applications of chemistry from drugs to the synthesis of tonne quantities of plastics.
Take for example a solution of glucose (RHS) at neutral pH and room temperature (I will use pH as a defining parameter here, and will discuss the details below), and a solution of hydrogen peroxide. The image of glucose suggests that it forms a cyclic structure in solution. In fact glucose can adopt several conformations, but this is the most stable. However, it shows no tendency to decompose or pick up any other atmospheric atoms (eg oxygen). Which in principle poses a problem for living organisms where combustion of glucose in oxygen, provides us with the energy that we ultimately store as ATP. On the other hand, the concentration of hydrogen peroxide in a beaker left on the bench at 9am on Monday will have diminished overnight, owing to its tendency to release oxygen and form water. Therefore if we measure the release of oxygen at a series of specific times, from a solution of H2O2, we will obtain the rate of decomposition under a given set of conditions. These experiments can be carried out very easily and have given rise to the following graphical relationship for the decomposition of H2O2 (the data can be plotted either as H2O2 left in solution, or alternatively O2 released: the former will decline and the latter will rise).
The first thing to note is that the graph is not a straight line, but it does follow a a simple graphical trajectory that we call "exponential". If we start with 100 mmoles/litreof H2O2,
and we have 90 mmoles/litre after 10 minutes, and if the rate of decomposition was
linear, then how many molecules would we have after 40 minutes (sketch a simple graph)? If we
look at the graph in Figure 2,we start with 22.5 mmoles/litre and after 10 minutes, we have 14 mmoles/litre. What would this value be if there was a linear decomposition (try drawing a straight line between the first two data points in Fig. 2).
This tells us that the relationship between the rate of decomposition of H2O2 under these conditions follows a "first order" reaction pathway. This is a description of the mathematical relationship that provides us with the best fit to the observed rate of decomposition measured in our experiment.
I want to stress here, that nobody made the maths of reaction kinetics deliberately difficult (I am not a conspiracy theorist; well at least not yet): we simply make the measurements and find the best mathematical equation to fit the data. Physical chemist then try to attach physical phenomena to the algebraic terms consistent with the mathematical relationship (or model). This is a really important feature of Science in general. It is standard practice to use the simplest mathematical model to fit the experimental data. This model is then tested in order to establish its "robustness" for predictive purposes. You will all be familiar with one of the most complex mathematical models in common use: that describing the behaviour of British weather over time. The predictive powers of the model do not allow the Met Office to accurately forecast on more than a daily basis: long term forecasts are notoriously unreliable. However, as the Bard from Duluth Minnesota once commented so appositely: "You don't need a weatherman to know which way the wind blows".
Getting back to reaction kinetics. We have made one observation for H2O2, which sets it apart from glucose. Namely that the former molecule has a greater tendency to decompose compared with a solution of glucose (I should have added that the glucose must be kept sterile in these experiments. Why?). We now need to look at the rate equation that fits the data. The standard equation takes the form of
When there are two or more reactants, the equation is expanded as follows:
V is the measured rate, k is the rate constant (determined experimentally from the slope) and the indices (or exponents) refer to the order of the reaction. The terms [A] etc refer to the molar concentration of the reactant(s) at the start of the reaction and for a first order reaction, x = 1, etc. One consequence of this mathematical model, is that the rate of the reaction is dependent on the concentration of the reactants. For a first order reaction like the decomposition of H2O2, the rate of reaction is proportional to the concentration of the peroxide. This is readily seen by varying the starting concentration and measuring the rate of oxygen production. This approach forms the core of reaction kinetics. It is standard practice to measure product formation, or substrate depletion, with time in order to determine the value of rate constants. The units of reaction rates are expressed as Moles per second. Therefore the rate constant will have units of 1/second (or reciprocal time).
In the case of Glucose combining with a phosphate group (provided by ATP) in the first committed step of glycolysis, the reaction rate will be a function of both reactants:
it is sometimes necessary to fix one concentration (say [A]) and vary the second reactant ([B]). By systematically measuring the rates of reaction it becomes possible to construct "rate equations" which allow a reaction rate to be "forecast" under a given set of temperature, pressure, pH and reactant concentrations. This experimental method and the values obtained, forms the basis of determining whether a particular reaction pathway is likely to be operational in a Biological setting and in fact in any chemical process.
What makes one molecule decompose, oxidise or combine with another molecule? Reactivity is synonymous with molecular stability. It is related to the relative energies of the reactants and the products. In the case of H2O2, it rapidly dissociates into water and oxygen, largely as a result of the instability of the O-O peroxide bond, there are also differences when the molecule is dissolved in water, or neat (an old word meaning undiluted). In fact H2O2 can be used in rocket propulsion! However, when diluted down to a 1-5% solution, it can be used to produce that aesthetically appealing hair colour we refer to as bleached blond!
I will just add here that when a reaction is independent of the concentration of the reactant(s) it is said to be zero order. I will not discuss this further. When two or more molecules react, there is a requirement for collision; more precisely productive collision. I think it is pretty logical to appreciate that in order for two chemical groups on a molecule to combine and form a new bond (it could be the peptide bond in protein synthesis, for example), there will be an optimal geometry involved. Think lock and key.
Coming back to the issue of why do some reactants react readily (or we often say spontaneously) and others require heat (or in Life, an enzyme or two)? This BBC web site is worth a look if you need a refresher. In order for a reactant,or group of reactants to be transformed into products, there is finite amount of energy required to initiate the reaction, which then reaches a peak, beyond which the reaction accelerates to the formation of products. The "height"of this peak was termed "activation energy" by the famous physical chemist Arrhenius. In chemistry we generally drive the reactants over the activation energy barrier with heat: in Biology we deploy enzymes (just think of pushing a piano up the stairs and when you get to the top pushing it out of the bedroom window!). Acting as catalysts, enzymes (as you will be aware from the Biochemistry Unit) have evolved to overcome challenging activation energy barriers by breaking them down into several smaller steps; a little like walking around a mountain range to get to the other side, rather than climbing over the top.
Why then is a reaction dependent on the concentration of the reactants? It's simple: if two molecules need to collide productively in order to react, then the more there are in a given volume, the greater the frequency of productive collision. Equally, if the reactants are lazy, then by putting a little heat into the reaction vessel, makes them more agitated and therefore they make more collisions than at the lower temperature. Another factor that plays a role in determining the rate of a reaction is the size of the particles in the reaction vessel. This is not an issue that arises in Biology, but if you compare the rate at which a sugar cube dissolves compared with a spoonful of sugar (assuming the same mass), you'll get the idea straight away. It is that the greater the exposed "surface" of the reactant, the faster the reaction proceeds. So in summary, reactions proceed as a function of the intrinsic energy in the reactants and the products and this in turn means that some reactions are spontaneous, some require heat (or enzymes) and some are so slow, that they are effectively inert. Let's finish this section by putting all of this into the context of Equilibrium Constants.
If we write a reaction in the following form
Where A and B represent reactants and P and Q are the products, the reaction reaches an equilibrium when the reactants and products reach the end of the reaction. This governed by two rate constants: one for the forward reaction called k with the subscript f, + or sometimes just 1and the reverse reaction by k with the subscript r, - or 2. The equilibrium position is a reflection of the probability of the reactants converting to products, but in reality it is usually a dynamic process in which at the point of equilibrium the concentrations of A, B, P and Q are defined but the forward and reverse reactions proceed in a balanced way. We refer to this as a dynamic equilibrium at the molecular level.
The equation that defines the equilibrium constant, Keq, is conventionally written as
and this is equal to the ratio of the corresponding rate constants:
 |
| Figure 1 |
The first thing to note is that the graph is not a straight line, but it does follow a a simple graphical trajectory that we call "exponential". If we start with 100 mmoles/litreof H2O2,
and we have 90 mmoles/litre after 10 minutes, and if the rate of decomposition was
linear, then how many molecules would we have after 40 minutes (sketch a simple graph)? If we
look at the graph in Figure 2,we start with 22.5 mmoles/litre and after 10 minutes, we have 14 mmoles/litre. What would this value be if there was a linear decomposition (try drawing a straight line between the first two data points in Fig. 2). This tells us that the relationship between the rate of decomposition of H2O2 under these conditions follows a "first order" reaction pathway. This is a description of the mathematical relationship that provides us with the best fit to the observed rate of decomposition measured in our experiment.
I want to stress here, that nobody made the maths of reaction kinetics deliberately difficult (I am not a conspiracy theorist; well at least not yet): we simply make the measurements and find the best mathematical equation to fit the data. Physical chemist then try to attach physical phenomena to the algebraic terms consistent with the mathematical relationship (or model). This is a really important feature of Science in general. It is standard practice to use the simplest mathematical model to fit the experimental data. This model is then tested in order to establish its "robustness" for predictive purposes. You will all be familiar with one of the most complex mathematical models in common use: that describing the behaviour of British weather over time. The predictive powers of the model do not allow the Met Office to accurately forecast on more than a daily basis: long term forecasts are notoriously unreliable. However, as the Bard from Duluth Minnesota once commented so appositely: "You don't need a weatherman to know which way the wind blows".
Getting back to reaction kinetics. We have made one observation for H2O2, which sets it apart from glucose. Namely that the former molecule has a greater tendency to decompose compared with a solution of glucose (I should have added that the glucose must be kept sterile in these experiments. Why?). We now need to look at the rate equation that fits the data. The standard equation takes the form of
V = k[A]x
When there are two or more reactants, the equation is expanded as follows:
V = k[A]x[B]y[C]z
V is the measured rate, k is the rate constant (determined experimentally from the slope) and the indices (or exponents) refer to the order of the reaction. The terms [A] etc refer to the molar concentration of the reactant(s) at the start of the reaction and for a first order reaction, x = 1, etc. One consequence of this mathematical model, is that the rate of the reaction is dependent on the concentration of the reactants. For a first order reaction like the decomposition of H2O2, the rate of reaction is proportional to the concentration of the peroxide. This is readily seen by varying the starting concentration and measuring the rate of oxygen production. This approach forms the core of reaction kinetics. It is standard practice to measure product formation, or substrate depletion, with time in order to determine the value of rate constants. The units of reaction rates are expressed as Moles per second. Therefore the rate constant will have units of 1/second (or reciprocal time).
In the case of Glucose combining with a phosphate group (provided by ATP) in the first committed step of glycolysis, the reaction rate will be a function of both reactants:
V = k.[Glucose].[ATP]
it is sometimes necessary to fix one concentration (say [A]) and vary the second reactant ([B]). By systematically measuring the rates of reaction it becomes possible to construct "rate equations" which allow a reaction rate to be "forecast" under a given set of temperature, pressure, pH and reactant concentrations. This experimental method and the values obtained, forms the basis of determining whether a particular reaction pathway is likely to be operational in a Biological setting and in fact in any chemical process.
What makes one molecule decompose, oxidise or combine with another molecule? Reactivity is synonymous with molecular stability. It is related to the relative energies of the reactants and the products. In the case of H2O2, it rapidly dissociates into water and oxygen, largely as a result of the instability of the O-O peroxide bond, there are also differences when the molecule is dissolved in water, or neat (an old word meaning undiluted). In fact H2O2 can be used in rocket propulsion! However, when diluted down to a 1-5% solution, it can be used to produce that aesthetically appealing hair colour we refer to as bleached blond!
I will just add here that when a reaction is independent of the concentration of the reactant(s) it is said to be zero order. I will not discuss this further. When two or more molecules react, there is a requirement for collision; more precisely productive collision. I think it is pretty logical to appreciate that in order for two chemical groups on a molecule to combine and form a new bond (it could be the peptide bond in protein synthesis, for example), there will be an optimal geometry involved. Think lock and key.
Coming back to the issue of why do some reactants react readily (or we often say spontaneously) and others require heat (or in Life, an enzyme or two)? This BBC web site is worth a look if you need a refresher. In order for a reactant,or group of reactants to be transformed into products, there is finite amount of energy required to initiate the reaction, which then reaches a peak, beyond which the reaction accelerates to the formation of products. The "height"of this peak was termed "activation energy" by the famous physical chemist Arrhenius. In chemistry we generally drive the reactants over the activation energy barrier with heat: in Biology we deploy enzymes (just think of pushing a piano up the stairs and when you get to the top pushing it out of the bedroom window!). Acting as catalysts, enzymes (as you will be aware from the Biochemistry Unit) have evolved to overcome challenging activation energy barriers by breaking them down into several smaller steps; a little like walking around a mountain range to get to the other side, rather than climbing over the top.
Why then is a reaction dependent on the concentration of the reactants? It's simple: if two molecules need to collide productively in order to react, then the more there are in a given volume, the greater the frequency of productive collision. Equally, if the reactants are lazy, then by putting a little heat into the reaction vessel, makes them more agitated and therefore they make more collisions than at the lower temperature. Another factor that plays a role in determining the rate of a reaction is the size of the particles in the reaction vessel. This is not an issue that arises in Biology, but if you compare the rate at which a sugar cube dissolves compared with a spoonful of sugar (assuming the same mass), you'll get the idea straight away. It is that the greater the exposed "surface" of the reactant, the faster the reaction proceeds. So in summary, reactions proceed as a function of the intrinsic energy in the reactants and the products and this in turn means that some reactions are spontaneous, some require heat (or enzymes) and some are so slow, that they are effectively inert. Let's finish this section by putting all of this into the context of Equilibrium Constants.If we write a reaction in the following form
A + B = P + Q
Where A and B represent reactants and P and Q are the products, the reaction reaches an equilibrium when the reactants and products reach the end of the reaction. This governed by two rate constants: one for the forward reaction called k with the subscript f, + or sometimes just 1and the reverse reaction by k with the subscript r, - or 2. The equilibrium position is a reflection of the probability of the reactants converting to products, but in reality it is usually a dynamic process in which at the point of equilibrium the concentrations of A, B, P and Q are defined but the forward and reverse reactions proceed in a balanced way. We refer to this as a dynamic equilibrium at the molecular level.
The equation that defines the equilibrium constant, Keq, is conventionally written as
Keq = [Products]/[Reactants] or [P][Q]/[A][B]
and this is equal to the ratio of the corresponding rate constants:
kf/kr
You can read more about the concepts at the Chemwiki site here. I now want to look at the application of these concepts to understanding acids and bases and redox reactions. I am going to add this to the post over the next few days, so keep an eye out for updates!
Electron-half-equations
When magnesium reduces hot copper(II) oxide to copper, the ionic equation for the reaction is:
The equation identifies the positive charge on the Cu and Mg, but the electrons, whose departure from the metals, give rise to the charged state, are not shown. This is the convention, but it can also be written as
These two equations are "half equations" or "half reactions". Any redox reaction is made up of two half reactions: one defining the gain and the other the loss of electrons
Important to Remember:
Oxidation is a loss of electrons
Reduction is a gain of electrons
You can find a detailed account of the steps underlying the formalism for writing half reactions at this Chemguide site. It isnt necessary for me to reinvent this particular wheel when it is so clear!
Here is an example of how our understanding of Redox reactions allows us to reconcile the relationship between electron transfer reactions and the generation of energy in oxidative phosphorylation (this is for advanced level students).
Electron-half-equations
When magnesium reduces hot copper(II) oxide to copper, the ionic equation for the reaction is:
The equation identifies the positive charge on the Cu and Mg, but the electrons, whose departure from the metals, give rise to the charged state, are not shown. This is the convention, but it can also be written as
These two equations are "half equations" or "half reactions". Any redox reaction is made up of two half reactions: one defining the gain and the other the loss of electrons
Important to Remember:
Oxidation is a loss of electrons
Reduction is a gain of electrons
You can find a detailed account of the steps underlying the formalism for writing half reactions at this Chemguide site. It isnt necessary for me to reinvent this particular wheel when it is so clear!
Here is an example of how our understanding of Redox reactions allows us to reconcile the relationship between electron transfer reactions and the generation of energy in oxidative phosphorylation (this is for advanced level students).
Consider the overall reaction of the oxidation of NADH paired with the
reduction of O2: the potential can be calculated as shown below.
Reduction Potentials
|
ereduction
|
NAD+ + 2H+ + 2e- -->
NADH + H+
|
-0.32 V
|
(1/2) O2 + 2H+ +
2e- --> H2O
|
+0.82 V
|
NADH + H+ --> NAD+ +
2H+ + 2e-
|
eoxidation = 0.32 V
|
(1/2) O2 + 2H+ +
2e- --> H2O
|
ereduction = 0.82 V
|
net: NADH + (1/2)O2 + H+ -->
H2O + NAD+ |
erxn = 1.14 V
|
ΔG= -nFerxn
|
The
overall reaction is
The
electrical potential (erxn) is related to the free energy (ΔG) by
the following equation:
where
n is the number of electrons transferred (in moles, from the balanced
equation), and F is the Faraday constant (96,485 Coulombs/mole). (Using this
equation, ΔG is given in Joules; one Joule =1 Volt x 1 Coulomb.)
Hence
the overall reaction for the oxidation of NADH paired with the reduction of O2 has
a negative change in free energy (ΔG =-220
kJ); i.e., it is spontaneous.
Thus,
the higher the electrical potential of a reduction half reaction, the greater
the tendency for the species to accept an electron.
The importance of pH, I have decided warrants a separate Part, so look out for it in a few days. In the meantime, I came across a superb resource for real time visualisation of the manipulation of thermodynamic and kinetic equations at Scott Sinex's resource page in the USA.
The importance of pH, I have decided warrants a separate Part, so look out for it in a few days. In the meantime, I came across a superb resource for real time visualisation of the manipulation of thermodynamic and kinetic equations at Scott Sinex's resource page in the USA.
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