Where does Physical Chemistry fit into your course in Dentistry? Acidogenic bacteria in dental plaque can rapidly metabolise certain carbohydrates to acid endproducts. In the mouth, the resultant change in plaque ph over time is called a Stephan curve. (1) ph what is ph? Why is it so important? What effect will changes in ph have? (can act as a switch to activate/deactivate metabolites, enzymes etc. ) (2) Change in ph with time Rates of reaction - what governs how fast a reaction occurs? (3) Why does a reaction take place at all? Thermodynamics - Where does the energy come from? - free energy.
The mechanism by which bacteria can penetrate healthy dental enamel is ultimately related to the structure and properties of water within the spaces of the enamel. Change saliva ph level by drinking too many soft drinks is instrumental in the formation of cavities within teeth (Coke ph ~ 2 ). Water - its properties and role as a solvent. 75% of the earths surface 70% of human body weight 78% of blood Mammalian cells contain 70-75% water. Dental enamel has only 4% H 2 0 by weight, but important for diffusion processes. Water provides the ubiquitous environment, which surrounds and interacts with whole spectra of biological molecules. Indeed, most biochemical reactions take place within this aqueous environment. Saliva! This is a really complex mixture of water, ions and peptides, glycoproteins and enzymes. needs to be complex as it performs many functions.
Water as an ionising solvent -Excellent solvent -High dielectric constant Ideal medium for the dissociation of electrolytes [Charged molecules] But Water itself is ionised and a weak electrolyte. Conjugate Conjugate Acid Base Acid Base H 2 O + H 2 O H 3 O + + OH - Conjugate acid- base H-ion donor H-ion acceptor Pair (Acid) (Base) Definition Acid - Proton Donor Base - Proton Acceptor Water is Amphoteric - Can act as an ACID or BASE
Ionisation of Water From above we can write the EQUILIBRIUM CONSTANT, K [Products] [H + ]. [OH - ] K = = [Reactants] [H 2 O] where [ ] = the concentration of ion or molecule in moles per litre. H + H 3 O + From conductivity measurements :- [ H + ] = [ OH - ] = 1.0 x 10-7 M Only 1 water molecule in 10,000,000 is dissociated. [H 2 O] Can be considered constant. Hence, K w = [H + ]. [OH - ] = 1.0 x 10 14 at 25 C The equilibrium constant for water, Kw - is a constant at given temperature.
Strong Acids + Strong Bases - Dissociate completely in water. Change the equilibrium and hence [ H + ] and [ OH - ] in solution. e.g. What is the [ H + ] and [ OH - ] of 0.1 M HCl? * 2 Species Present HCl & H 2 O [ H + ] from HCl H + + Cl - [ H + ] from H 2 O H + + OH - Since solutions have no net charge :- OH - + Cl - = Anions H + = Cations [ H + ] = [ OH - ] + [ Cl - ] Now [ Cl - ] = 0.1 M ( since HCl = 0.1 M ) from K w [ OH - ] = K w / [ H + ] [ OH - ] = 1.0 x 10 14 / 1.0 x 10 7 = 1.0 x 10 7 M
[ H + ] = [ Cl - ] + [ OH - ] = 0.1 + 1 x 10-7 [ H + ] 0.1 M [ OH - ] = 1 x 10-13 M ( from K w ) For a STRONG ACID [ H + ] = [ Acid ] The same is true for strong bases e.g. 0.1 M NaOH [OH - ] = [Base] = 0.1 M and [ H + ] = 1 x 10-13 M Note :- The difference in concentrations even in these two cases is very LARGE. More convenient to use a logarithmic scale. ph scale introduced by Sorenson, 1909. ph = - log 10 [ H + ] * poh = -log 10 [ OH - ] = 14 - ph So what is the ph of our 0.1 M HCl solution? [ H + ] = [ Acid ] = 0.1 M
ph = -log 10 [ H + ] = 1.0 What about our 0.1 M NaOH solution? [ H + ] = 10-13 M remember only H + from water! ph = -log 10 [acid] = 13 this gives us a ph scale 1 7 14 Acidic Basic Often we are more interested in the reverse question. If a solution has a ph = 8.4, what is [ H + ] ph = -log 10 [ H + ] -8.4 = log 10 [ H + ] anti log (-8.4) = [ H + ] = 3.98 x 10-9 M. Warning If 1 x 10-2 M HCl ph = 2 and 1 x 10-3 M HCl ph = 3 Then 1 x 10-9 M HCl ph = 9 right? NO!!!! ph = 9 would be basic, which is illogical!
The solution has now become so dilute that we must consider the effect of [ H + ] from water. [ H + ] from water = 1 x 10-7 M [ H + ] = 1 x 10-9 + 1 x 10-7 = 1.01 x 10-7 M ph = 6.996 just the acid side of neutral.
Weak Acids and Weak Bases - MAJORITY of relevant ACIDS and BASES in Biochemistry. - They DO NOT dissociate completely in aqueous solution. Consider a weak acid, HA. HA H + + A - Equilibrium How do we define where the equilibrium lies? As an acid dissociation constant, K a. K a = [ H + ]. [ A - ] [ HA ] A Dilute solution contains H +, the anion A -, and the undissociated acid HA. How does this differ from the case of a strong acid? If there is a change in ph, i.e. [ H + ], then the relative concentrations of the other species i.e. A - and HA will change to restore the equilibrium.
e.g. (a) If a strong acid, HCl is added - [ H + ] increases, ph falls. HA H + + A - A - combines with the excess H + to form more HA. (b) If a strong base, NaOH is added [ OH - ] increase, ph rises. H + + OH - will form water so [ H + ] decreases. HA H + + A - HA dissociates and makes more H +. Solutions containing weak acids and weak bases, which are partially dissociated, resist changes in ph and are called BUFFERS. Buffer Solutions and their Effects * This is crucial in biological systems. A large variation in ph in biological systems is very undesirable!
e.g. ph of blood is 7.4 above ph 7.8 or below 7.0 Death! Lets consider some examples:- (i) Salts from a solution of a weak acid and a strong base. NaOH + CH 3 COOH CH 3 C00 - + H 2 O Strong weak acid conjugate conjugate base (acetic acid) base acid The conjugate base of a weak acid (acetic acid) is a strong base and will accept a proton (H + ) from water. CH 3 C00 - + H 2 O CH 3 COOH + OH - The result is an excess of OH - ions the ph is > 7 (ii) Salts from a solution of a strong acid and a weak base. e.g. Ammonium Chloride NH 3 + HCl NH 4 + + Cl - Weak strong conj. conj. Base acid acid base The conjugate acid of a weak base ( ammonia ) is a strong acid and will donate a proton ( H + ) to water.
NH 4 + + H 2 O NH 3 + H 3 O + The NH 4 + dissociates - donating a proton ph < 7 and is acidic. (iii) Salts from a solution of a weak acid and a weak base. e.g. Ammonium acetate, NH 4 + CH 3 COO - As the acetate ions accepts protons and the NH 4 + dissociates donating protons - ph ~ 7 Just like a strong acid + strong base??? NO! (a) Salts from Strong acids and bases e.g. NaCl HCl + NaOH Na + + Cl - + H 2 O are strong electrolytes i.e. dissociate 100%. H + and OH - react ( neutralise ) to form water ph = 7. (b) Salts formed from weak acids and bases can also be strong electrolytes. They only partially dissociate and can act as a buffer.
Consequences of weak acid weak base buffering action 1 drop (1 µl) of 1M HCl added to aqueous solutions will change the ph from 7 to 3. H 2 O isn t a buffer! If you added the same drop of 1M HCl to a solution containing a weak acid at ph 6.0, the ph will hardly change as it is a buffer. What happens if the ph was 9.0? would the ph still remain the same??? NO! So how do buffers work? We need to consider the equilibrium constant of the solution and the ph. K a = [ H + ]. [ A - ] [ HA ] Since the concentrations of these species can be very large or small so is the value K a. It is convenient to express K a on a logarithmic scale or as a pk a. pk a = -log 10 K a
* at 50% dissociation : [ H + ] = [ A - ] = [ HA ] ph = pk a A buffer works best at its pk a. Remember for weak acids and weak bases: HA H + + A - [ H + ]. [ A - ] [ A - ] K a = [ H + ]. [ HA ] [ HA ] take logs of both sides of the equation log 10 K a = log 10 [ H + ] + log [ A - ] / [ HA ] -pk a = -ph + log 10 [ A - ] / [ HA ] or ph = pk a + log 10 [ A - ] / [ HA ] ph depends on the ratio of the concentration of anion [ A - ] to undissociated acid [ HA ] and the pka.
This equation is the most important equation in solution chemistry and is known as the Henderson-Hasselbalch equation. The equation can be expressed as :- ph = pk a + log [ Conjugate base ] / [ Acid ] where conjugate base = salt = anions for acids or ph = pk a + log [ Base ] / [ Conjugate acid] where base = base and conjugate acid = salt for weak bases. Multiple Ionising Groups Polyprotic Acids/Bases Molecules which contain more than 1 ionisable group. e.g. carbonic acid H 2 CO 3, Phosphoric acid H 3 PO 4 This makes things more complicated! Phosphoric acid H 3 PO 4 has 3 protons three ionisations which we need to consider separately.
(1) H 3 PO 4 H + + H 2 PO 4 - K a1 = [ H + ]. [ H 2 PO 4 - ] [ H 3 PO 4 ] pk a1 = 2.12 (2) H 2 PO 4 - H + + HPO 4 2- K a2 = [ H + ]. [ HPO 4 2- ] [ H 2 PO 4 - ] pk a2 = 7.21 (3) HPO 4 2- H + + PO 4 3- K a3 = [ H + ]. [ PO 4 3- ] [ HPO 4 2- ] pk a1 = 12.32 What will be the ions in solution at the following ph values? 1.5 3.0 7.5 11.5 14.0
Remember the Henderson-Hasselbach equation allows you to calculate concentrations of species at any ph value. e.g. ph = pk a + log [ HPO 4 2- ] / [ H 2 PO 4 - ] Amino acids A simple example e.g Glycine. 2 pk a s 2.3 and 9.7 at ph < 2.3 2.3 < ph < 9.7 ph > 9.7 NH 3 + - CH 2 COOH NH 3 + - CH 2 COO - + H + NH 2 - CH 2 COO - + H + +ve + and -ve (Zwitterion) more complicated amino acids have more ionisable groups e.g. Histidine 3 pk a s 1.8 and 9.7 (as for Glycine ) and 6.0
Biological buffer systems There are many molecules in cells and tissues that act as weak acids and bases. These include proteins, nucleotides, amino acids and metabolites. These all help to buffer the ph. However phosphate and bicarbonate buffer systems are most important in biological systems. Phosphate buffer system -effective buffer in the ph range 6.4 to 7.4 H 2 PO 4 - H + + HPO 4 2- - PK a 6.8-7.0 In the mouth phosphate concentrations are not that high so it is not the main buffer. Doesn t increase with saliva Bicarbonate buffer system This plays a very important role both in buffering blood and in the mouth.
Three part equilibrium: H 2 O + CO 2 H 2 CO 3 HCO 3 - + H + Carbonic acid bicarbonate Important because CO 2 produced by every cell in your body. In blood the bicarbonate buffer maintains ph 7.4 This is due to the fact that H 2 CO 3 in the blood is in equilibrium with CO 2 in the air. [ CO 2 ] by limiting breathing and the blood will become more acidic. [ CO 2 ] by breathing too quickly (hyperventilation) the blood becomes more basic. Kidneys have to cope with these situations by absorption and excretion of bicarbonate ions. In the mouth the concentration of carbonic acid [ H 2 CO 3 ] stays remarkably constant at about 1.3mMol/L.
- Bicarbonate ions HCO 3 above 6.3. maintain the ph of saliva Two things do change in the mouth, 1) ph 2) bicarbonate concentration. Both are very important and central to how saliva protects teeth. 1. When acid is produced within dental plaque the increase in [ H + ] drives the equilibrium to the right. HCO 3 - + H + H 2 CO 3 H 2 O + CO 2 This will only happen if there is enough HCO 3 - present to interact with the hydrogen ions. 2. The concentration of bicarbonate in saliva is linked to the flow rate. As the rate of saliva production increases the more bicarbonate ion is produced as a by-product of cell metabolism. Important : During eating when saliva flow is raised that plaque acid is produced in highest quantities. The bicarbonate concentration varies with the flow can increase from 2mM (Low flow) to 30mM (Intermediate flow) and 60mM (High flow)
Remember: ph = pk a + log 10 [ HCO 3 - ] / [ H 2 CO 3 ] for the low flow case ph = 6.1 + log 10 [ 2 x 10-6 ] / [ 1.3 x 10-6 ] ph = 6.29 this is close to the ph of saliva at rest. Using the same equation for the other flow rates gives 30mM ph = 7.46 and 60mM ph = 7.76 Effect of ph on solubility Changes in ph can effect the solubility of partially soluble ionic compounds. e.g. Mg(OH) 2 Mg 2+ + 2 OH - solid ions in solution The equilibrium of the equation can be shifted by ph. At acid ph more Mg(OH) 2 dissolves as H + + OH - = H 2 0. Same is true for tooth enamel Ca 10 (PO 4 ) 6 (OH) 2 (hydroxyapatite) which dissolves in acid ph.
Osmosis & Osmotic Pressure Osmosis The flow of solvent through a semipermeable membrane into a solution or from a dilute solution into a more concentrated one. Semi-permeable membranes permit the free movement of solvent molecules but NOT solute molecules. e.g. Cellophane, many biological membranes e.g. fruit skin Solvent = H 2 O Solute = Sugar, Na +, Cl - etc. e.g. Pure solvent Concentrated sugar solution H 2 O H 2 O Semi-permeable membrane The system is inbalanced with a higher concentration of solvent on the left than on the right. The H 2 O solvent doesn t simply move one way BUT diffusion from solvent to solution is faster. This movement builds a pressure that can be measured.
Osmotic pressure ( Π ) is the minimum pressure that must be applied to a solution to prevent solvent flow. On what does Π depend? - For dilute solutions Π is proportional to the concentration of the solute. - When measurements are made for a given concentration, Π is proportional to the absolute temperature. Together this gives us van t Hoff s law Π = M.R.T where M = concentration of solute R = the gas constant T = absolute temperature in K ( kelvin )
The units of Π depend on the units of the gas constant. So Π can be in atmospheres or knm -2 (kilo Newtons per metre squared). R = 0.0821 L-atm mol -1 k -1 ( in atmospheres ) A Simple Calculation of Π What is the osmotic pressure of an aqueous solution containing 1.8g of glucose in 100ml at 15ºC? M r of glucose = 180 g number of moles of glucose = 1.8/180 = 0.01 moles 0.01 moles in 100mls (0.1 L) = 0.01/0.1 = 0.1 Molar 15ºC = 288.2 K so Π = MRT Π = 0.1 x 0.0821 x 288.2 Π = 2.4 atm. That the solute is glucose is not important the same concentration of any simple solute will give the same osmotic pressure.
Effect of ionisation on osmotic pressure. A solution of 0.1M NaCl in water has an osmotic pressure of 4.8 atm. A solution of 0.1M FeCl 3 in water has an osmotic pressure of 9.6 atm. Why are they so different from glucose? Strong electrolytes dissociate completely. NaCl Na + + Cl - (1mole) (2 moles of particles) 2x the osmotic pressure for glucose. FeCl 3 Fe 3+ + 3Cl - (1mole) (4 moles of particles) 4 x the osmotic pressure for glucose. To take this into consideration we can write van t Hoff s law as follows :- Π = i.m.r.t where i = observed number of particles number of particles if no dissociation obviously for non-electrolytes i = 1
Tonicity and Osmotic Pressure The concept of tonicity arises when considering osmotic effects in living cells. If a plant or animal cell is placed in a solution it will shrink or swell unless the osmotic pressure of the solution is equal to that in the cell. We must consider:- i) In biological systems membranes DO NOT separate pure solvent from solution containing a single solute. ii) Bio-membranes are not perfectly semi-permeable highly selective and discriminate between different molecules. e.g. some membranes discriminate between Na + but not K + ions, others between different sugars. The effective Π of a solution with respect to a particular membrane is called TONICITY. If two different solutions separated by a perfect semi-permeable membrane but have the same concentrations the Π = 0. They are ISOSMOTIC
If the two solutions have different concentrations but the same tonicity ( cells don t shrink or swell ) the effective Π = 0. They are ISOTONIC. Isotonic solutions are not necessarily isosmotic Lets take an example with a membrane that is permeable to urea and water but impermeable to sucrose. If there is no effective osmotic pressure the solutions are isotonic. If the concentration of particles in the solutions is the same they are isosmotic.