Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales License   The...
Thermochemistry <ul><li>Enthalpy changes in chemical reactions (+ video) </li></ul><ul><li>Enthalpy Diagrams </li></ul><ul...
Energy and Chemistry <ul><li>Petrol bombs </li></ul><ul><li>What does this show? </li></ul><ul><li>How to ensure your bonf...
Energy and Chemical Reactions <ul><li>Formation of new substances  </li></ul><ul><ul><li>Redox reactions </li></ul></ul><u...
Reaction 2 Energy products<reactants so energy flows as heat from the system to the surroundings  Temperature (surrounding...
Enthalpy level diagrams For You To Do Draw diagrams for the reactions on the previous slide You will need to write balance...
Thermochemical Equations <ul><li>A   thermochemical equation   is the  chemical equation  for a reaction  (including  stat...
Thermochemical Equations <ul><li>Why do we need state symbols? </li></ul><ul><li>In a   thermochemical equation   it is im...
<ul><li>Two important rules  </li></ul>Thermochemical Equations <ul><ul><li>When a thermochemical equation is  multiplied ...
<ul><li>What is the enthalpy change of reaction for the formation of 1 mole and 6 moles of water? </li></ul><ul><li>-285.9...
Using Thermochemical Equations <ul><li>Consider the reaction of methane, CH 4 , burning in the presence of oxygen at const...
Coffee-cup calorimeter <ul><li>Measuring enthalpy changes is called  calorimetry </li></ul><ul><li>Carry out the reaction ...
Need to know Specific Heat Capacity <ul><li>Definition </li></ul><ul><li>The amount of energy required to raise the temper...
An Example: 25 cm 3  of 2.00 mol dm -3  HCl(aq) is mixed with 25 cm 3  of 2.00 mol dm -3  NaOH(aq). The temperature rises ...
An Example continued For 1 mol of HCl and NaOH
Now Try This One 0.327 g of Zinc powder is added to 55 cm 3  of aqueous copper sulfate solution at 22.8  o C. The copper s...
Limitations of this method ?? Coffee-cup calorimeter HCl(aq) NaOH (aq) Thermometer 2 polystyrene coffee cups
A bomb calorimeter How can we accurately measure enthalpy changes  of combustion reactions? Needle Gas inlet Insulated jac...
Bomb Calorimetry- measurements Some heat from reaction warms “bomb”  q bomb  = heat capacity x ∆T  Total heat evolved, q t...
<ul><li>Calculate enthalpy of combustion of octane.  </li></ul><ul><li>C 8 H 18(l)   +  25/2 O 2(g)   8CO 2(g)   +  9H 2 O...
Step 1 : energy transferred from reaction to water. q = (4.184 J g -1 K -1 )(1200 g)(8.20 K) =  41170 J Step 2 : energy tr...
Video Click to link to “Thermochemistry” video
A case study- Self-heating cans Water Can Insert Quicklime Foil separator Button
The Chemistry <ul><li>CaO (s)  + H 2 O (l) Ca(OH) 2(s) </li></ul><ul><li>quicklime slaked lime </li></ul><ul><li>Water and...
How much quicklime is needed to heat up a coffee can? <ul><li>Think about what information you need to know for the calcul...
FRS1027 Introductory Chemistry <ul><li>Hess’s law </li></ul><ul><li>Standard enthalpy of formation </li></ul><ul><li>Calcu...
Hess’s Law <ul><li>The enthalpy change on going from reactants to products is independent of the reaction path taken </li>...
Hess’s Law & Energy Level Diagrams <ul><li>Reaction can be shown as a single step or in a two steps.  </li></ul><ul><li>∆ ...
Standard enthalpy values (  H o ) <ul><li>Initial  and  final  species are in their  standard states </li></ul><ul><li>Th...
Standard Enthalpy of Formation ∆ f H o  (298 K) = standard  molar enthalpy of formation  at 298 K enthalpy change when 1 m...
Standard enthalpies of formation and Hess’s Law can be used to calculate unknown ∆ r H o   ∆ r H o  =  ∆H f o   (products...
Calculate ∆ c H o  for methanol Standard state of methanol at 298 K is liquid CH 3 OH(l) + 3/2O 2 (g) CO 2 (g) + 2H 2 O(l)...
Video Link to “Hess’s Law” video
Some Other Problems to do
Describe the reaction
The enthalpy of reaction for black powder <ul><li>Black powder is a mixture of potassium nitrate (75%), charcoal (13%) and...
The reaction of barium hydroxide with ammonium chloride <ul><li>Equation </li></ul><ul><li> f H o  values/ kJ mol-1 </li>...
Calculate the standard enthalpy of combustion of octane at 298 K <ul><li> f H o  (octane)= -249.9 kJ mol -1 </li></ul>
FRS1027 Introductory Chemistry Bond Dissociation Enthalpies
Definition <ul><li>The bond dissociation enthalpy (  diss H) for an X-X diatomic molecule refers to the process: </li></u...
D and  D <ul><li>CH 4 (g) CH 3 (g) + H(g)    H=436 kJ mol -1 </li></ul><ul><li>CH 3 (g) CH 2 (g) + H(g)    H=461 kJ mol ...
Enthalpy Changes in Chemical Reactions <ul><li>Enthalpy difference between products and reactants because different chemic...
Now have a go at the bond enthalpy problems and set up as an Excel spreadsheet. Can you set it up so that you only need to...
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales License   Ack...
Upcoming SlideShare
Loading in …5
×

of

Chemical Reactions: Thermochemistry Slide 1 Chemical Reactions: Thermochemistry Slide 2 Chemical Reactions: Thermochemistry Slide 3 Chemical Reactions: Thermochemistry Slide 4 Chemical Reactions: Thermochemistry Slide 5 Chemical Reactions: Thermochemistry Slide 6 Chemical Reactions: Thermochemistry Slide 7 Chemical Reactions: Thermochemistry Slide 8 Chemical Reactions: Thermochemistry Slide 9 Chemical Reactions: Thermochemistry Slide 10 Chemical Reactions: Thermochemistry Slide 11 Chemical Reactions: Thermochemistry Slide 12 Chemical Reactions: Thermochemistry Slide 13 Chemical Reactions: Thermochemistry Slide 14 Chemical Reactions: Thermochemistry Slide 15 Chemical Reactions: Thermochemistry Slide 16 Chemical Reactions: Thermochemistry Slide 17 Chemical Reactions: Thermochemistry Slide 18 Chemical Reactions: Thermochemistry Slide 19 Chemical Reactions: Thermochemistry Slide 20 Chemical Reactions: Thermochemistry Slide 21 Chemical Reactions: Thermochemistry Slide 22 Chemical Reactions: Thermochemistry Slide 23 Chemical Reactions: Thermochemistry Slide 24 Chemical Reactions: Thermochemistry Slide 25 Chemical Reactions: Thermochemistry Slide 26 Chemical Reactions: Thermochemistry Slide 27 Chemical Reactions: Thermochemistry Slide 28 Chemical Reactions: Thermochemistry Slide 29 Chemical Reactions: Thermochemistry Slide 30 Chemical Reactions: Thermochemistry Slide 31 Chemical Reactions: Thermochemistry Slide 32 Chemical Reactions: Thermochemistry Slide 33 Chemical Reactions: Thermochemistry Slide 34 Chemical Reactions: Thermochemistry Slide 35 Chemical Reactions: Thermochemistry Slide 36 Chemical Reactions: Thermochemistry Slide 37 Chemical Reactions: Thermochemistry Slide 38 Chemical Reactions: Thermochemistry Slide 39 Chemical Reactions: Thermochemistry Slide 40 Chemical Reactions: Thermochemistry Slide 41 Chemical Reactions: Thermochemistry Slide 42 Chemical Reactions: Thermochemistry Slide 43 Chemical Reactions: Thermochemistry Slide 44
Upcoming SlideShare
Thermochemistry Presentation
Next
Download to read offline and view in fullscreen.

13 Likes

Share

Download to read offline

Chemical Reactions: Thermochemistry

Download to read offline

Lecture materials for the Introductory Chemistry course for Forensic Scientists, University of Lincoln, UK. See http://forensicchemistry.lincoln.ac.uk/ for more details.

Related Audiobooks

Free with a 30 day trial from Scribd

See all

Chemical Reactions: Thermochemistry

  1. 1. This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales License Thermochemistry University of Lincoln presentation
  2. 2. Thermochemistry <ul><li>Enthalpy changes in chemical reactions (+ video) </li></ul><ul><li>Enthalpy Diagrams </li></ul><ul><li>Thermochemical Equations </li></ul><ul><li>Calorimetry and measuring enthalpy changes </li></ul>
  3. 3. Energy and Chemistry <ul><li>Petrol bombs </li></ul><ul><li>What does this show? </li></ul><ul><li>How to ensure your bonfire burns! </li></ul><ul><li>Why does this happen? </li></ul>
  4. 4. Energy and Chemical Reactions <ul><li>Formation of new substances </li></ul><ul><ul><li>Redox reactions </li></ul></ul><ul><ul><li>Acid-base reactions </li></ul></ul><ul><ul><li>Precipitation reactions </li></ul></ul><ul><li>Energy released/absorbed </li></ul><ul><ul><li>Light (chemiluminescence) </li></ul></ul><ul><ul><li>Electrical energy (electrochemistry) </li></ul></ul><ul><ul><li>Heat (thermochemistry) </li></ul></ul>
  5. 5. Reaction 2 Energy products<reactants so energy flows as heat from the system to the surroundings Temperature (surroundings) increases - Exothermic e.g. NaOH(aq) and HCl(aq). Reaction 1 Energy products>reactants so energy is absorbed from the surroundings Heat is lost from the surroundings so Temperature (surroundings) decreases - Endothermic e.g. Ba(OH) 2 .8H 2 O(s) and NH 4 Cl(s) (video) Endothermic Exothermic S u r r o u n d I n g s S u r r o u n d I n g s System System Heat Heat Heat Heat
  6. 6. Enthalpy level diagrams For You To Do Draw diagrams for the reactions on the previous slide You will need to write balanced chemical equations first. For reaction1 assume that the products are NH 3 (g), H 2 O(l) and BaCl 2 (s) and that  r H = +135 kJ mol -1 Reaction 2 is a straightforward neutralisation with a  r H = -55 kJ mol -1 The reaction between sodium metal and water – metal floats on water – effervescent reaction moves metal around- yellow flame above the metal- no solid residue 2 mol Na(s) + 2 mol H 2 O(l) Enthalpy, H (kJ) 2 mol NaOH(aq) + 1 mol H 2 (g) Δ H = -367.5 kJ (367.5 kJ of heat is released
  7. 7. Thermochemical Equations <ul><li>A thermochemical equation is the chemical equation for a reaction (including state symbols ) and the enthalpy of reaction for the molar amounts as given by the equation written directly after the equation. </li></ul>
  8. 8. Thermochemical Equations <ul><li>Why do we need state symbols? </li></ul><ul><li>In a thermochemical equation it is important to note state symbols because the enthalpy change depends on the physical state of the substances. </li></ul>
  9. 9. <ul><li>Two important rules </li></ul>Thermochemical Equations <ul><ul><li>When a thermochemical equation is multiplied by any factor , the value of  H for the new equation is obtained by multiplying the DH in the original equation by that same factor. </li></ul></ul><ul><ul><li>When a chemical equation is reversed , the value of DH is reversed in sign . </li></ul></ul>
  10. 10. <ul><li>What is the enthalpy change of reaction for the formation of 1 mole and 6 moles of water? </li></ul><ul><li>-285.9 kJ mol -1 ; -1715.1 kJ mol -1 </li></ul><ul><li>What is the enthalpy change for the splitting of 1 mole of water into hydrogen and oxygen gas? </li></ul><ul><li>+285.9 kJ mol -1 </li></ul>Using Thermochemical Equations
  11. 11. Using Thermochemical Equations <ul><li>Consider the reaction of methane, CH 4 , burning in the presence of oxygen at constant pressure. Given the following equation, how much heat could be obtained by the combustion of 10.0 grams CH 4 ? </li></ul>Combustion of methane gives 55.6 kJ g -1 1 g of methane would give 10 g of methane would give
  12. 12. Coffee-cup calorimeter <ul><li>Measuring enthalpy changes is called calorimetry </li></ul><ul><li>Carry out the reaction in a calorimeter and measure the temperature change . </li></ul><ul><li>Calculate the energy transferred during the reaction from the temperature change. </li></ul><ul><li>Also require the mass of the substance and the specific heat capacity </li></ul><ul><li>Assumptions </li></ul><ul><li>All the energy change is transferred to the solution (water) </li></ul><ul><li>No losses of heat to the other surroundings </li></ul>Measuring enthalpy changes HCl(aq) NaOH (aq) Thermometer 2 polystyrene coffee cups
  13. 13. Need to know Specific Heat Capacity <ul><li>Definition </li></ul><ul><li>The amount of energy required to raise the temperature of a specified mass of an object (substance) by 1 degree kelvin (K) </li></ul><ul><li>units </li></ul><ul><li>J g -1 K -1 or J kg -1 K -1 </li></ul><ul><li>Important example </li></ul><ul><li>Water 4.184 J g -1 K -1 </li></ul>
  14. 14. An Example: 25 cm 3 of 2.00 mol dm -3 HCl(aq) is mixed with 25 cm 3 of 2.00 mol dm -3 NaOH(aq). The temperature rises from 22.5 o C to 34.5 o C. Find the enthalpy change for the reaction 2508 J of heat is transferred from the reaction of 0.05 mol HCl with 0.05 mol NaOH
  15. 15. An Example continued For 1 mol of HCl and NaOH
  16. 16. Now Try This One 0.327 g of Zinc powder is added to 55 cm 3 of aqueous copper sulfate solution at 22.8 o C. The copper sulfate is in excess of that needed to react all the zinc. The temperature rises to 32.3 o C. Calculate  H for the following reaction:
  17. 17. Limitations of this method ?? Coffee-cup calorimeter HCl(aq) NaOH (aq) Thermometer 2 polystyrene coffee cups
  18. 18. A bomb calorimeter How can we accurately measure enthalpy changes of combustion reactions? Needle Gas inlet Insulated jacket Steel bomb + - O 2 Thermometer Current for ignition coil Stirrer Ignition coil Graphite sample
  19. 19. Bomb Calorimetry- measurements Some heat from reaction warms “bomb” q bomb = heat capacity x ∆T Total heat evolved, q total = q water + q bomb Total heat from the reaction =qtotal Needle Gas inlet Steel bomb Some heat from reaction warms water q water = mc∆T Insulated jacket + - O 2 Thermometer Current for ignition coil Stirrer Ignition coil Graphite sample
  20. 20. <ul><li>Calculate enthalpy of combustion of octane. </li></ul><ul><li>C 8 H 18(l) + 25/2 O 2(g) 8CO 2(g) + 9H 2 O (l) </li></ul><ul><li>Burn 1.00 g of octane </li></ul><ul><li>Temp rises from 25.00 to 33.20 o C </li></ul><ul><li>Calorimeter contains 1200 g water </li></ul><ul><li>Heat capacity of bomb = 837 J K -1 </li></ul>Calculating enthalpy changes from calorimetry data
  21. 21. Step 1 : energy transferred from reaction to water. q = (4.184 J g -1 K -1 )(1200 g)(8.20 K) = 41170 J Step 2 : energy transferred from reaction to bomb. q = (bomb heat capacity)(∆T) = (837 J K -1 )(8.20 K) = 6860 J Step 3 :Total energy transferred 41170 J + 6860 J = 48030 J Heat of combustion of 1.00 g of octane = - 48.0 kJ For 1 kg = -48 MJ kg -1  H=-48 kJ x 114 g mol -1 =-5472 kJ mol -1 Calculating enthalpy changes from calorimetry data
  22. 22. Video Click to link to “Thermochemistry” video
  23. 23. A case study- Self-heating cans Water Can Insert Quicklime Foil separator Button
  24. 24. The Chemistry <ul><li>CaO (s) + H 2 O (l) Ca(OH) 2(s) </li></ul><ul><li>quicklime slaked lime </li></ul><ul><li>Water and quicklime packaged separately </li></ul><ul><li>When mixed, exothermic reaction takes place and the temperature of the water increases </li></ul><ul><li>Heat transferred to the drink </li></ul><ul><li> r H = -65.1 kJ mol -1 </li></ul>
  25. 25. How much quicklime is needed to heat up a coffee can? <ul><li>Think about what information you need to know for the calculation before doing the calculation – do some research and find approximate values </li></ul><ul><li>Homework </li></ul><ul><li>Draw an enthalpy level diagram for the reaction </li></ul><ul><li>Do the calculation </li></ul>
  26. 26. FRS1027 Introductory Chemistry <ul><li>Hess’s law </li></ul><ul><li>Standard enthalpy of formation </li></ul><ul><li>Calculating enthalpy changes </li></ul>
  27. 27. Hess’s Law <ul><li>The enthalpy change on going from reactants to products is independent of the reaction path taken </li></ul><ul><li>Can be used to calculate enthalpy changes </li></ul>
  28. 28. Hess’s Law & Energy Level Diagrams <ul><li>Reaction can be shown as a single step or in a two steps. </li></ul><ul><li>∆ H total is the same no matter which path is followed. </li></ul> ∆ H reaction path 1=  ∆H reaction path 2 C(s) + O 2 (g) Energy CO 2 (g) CO(g) + ½ O 2 (g) Δ H 3 = Δ H 1 + Δ H 2 = -393.5 kJ Δ H 2 = -283.0 kJ Δ H 1 = -110.5 kJ
  29. 29. Standard enthalpy values (  H o ) <ul><li>Initial and final species are in their standard states </li></ul><ul><li>The standard state of a substance at a specified temperature is its pure form at 1 bar (100 kPa). T is usually 298 K (25 o C) but not always </li></ul><ul><li> r H o (298 K) is the standard enthalpy of reaction at 298 K </li></ul><ul><li>Some Physical States at 298 K </li></ul><ul><li>C = graphite; O 2 = gas; CH 4 = gas; H 2 O = liquid </li></ul>
  30. 30. Standard Enthalpy of Formation ∆ f H o (298 K) = standard molar enthalpy of formation at 298 K enthalpy change when 1 mole of compound is formed from elements in their standard states at 298 K (These are available from data books) H 2 (g) + 1/2O 2 (g) H 2 O(g) ∆ f H o (H 2 O, g) = -241.8 kJ mol -1 ∆ f H o is zero for elements in their standard states.
  31. 31. Standard enthalpies of formation and Hess’s Law can be used to calculate unknown ∆ r H o ∆ r H o =  ∆H f o (products) -  ∆H f o (reactants) Enthalpy of reaction = sum of the enthalpies of formation of the products (correct molar amounts) – sum of the enthalpies of formation of the reactants (correct molar amounts) Why is this an application of Hess’s law? Calculating Enthalpy Changes using standard enthalpies of formation
  32. 32. Calculate ∆ c H o for methanol Standard state of methanol at 298 K is liquid CH 3 OH(l) + 3/2O 2 (g) CO 2 (g) + 2H 2 O(l) ∆ c H o =  ∆H f o (products) -  ∆H f o (reactants) = {∆H f o (CO 2 ) + 2 ∆H f o (H 2 O)} - {3/2 ∆H f o (O 2 ) + ∆H f o (CH 3 OH)} = {(-393.5 kJ) + 2 (-285.8 kJ)} - {0 + (-238.9 kJ)} ∆ c H o (298K)= -726.2 kJ mol -1 Now try the problems on the separate sheet Calculating Enthalpy Changes
  33. 33. Video Link to “Hess’s Law” video
  34. 34. Some Other Problems to do
  35. 35. Describe the reaction
  36. 36. The enthalpy of reaction for black powder <ul><li>Black powder is a mixture of potassium nitrate (75%), charcoal (13%) and sulfur (12%). </li></ul><ul><li>A simplified equation is: </li></ul> f H o values/kJ mol -1 KNO 3(s) -494.6 K 2 S (s) -380.70 CO 2(g) -393.51 Calculate the enthalpy of reaction in kJ mol -1 and kJ kg -1 of black powder.
  37. 37. The reaction of barium hydroxide with ammonium chloride <ul><li>Equation </li></ul><ul><li> f H o values/ kJ mol-1 </li></ul><ul><li>Ba(OH) 2 .8H 2 O (s) -3345 </li></ul><ul><li>NH 4 Cl (s) -314 </li></ul><ul><li>NH 3(g) -46 </li></ul><ul><li>H 2 O (l) -286 </li></ul><ul><li>BaCl 2(s) -859 </li></ul><ul><li>Calculate  r H o </li></ul>
  38. 38. Calculate the standard enthalpy of combustion of octane at 298 K <ul><li> f H o (octane)= -249.9 kJ mol -1 </li></ul>
  39. 39. FRS1027 Introductory Chemistry Bond Dissociation Enthalpies
  40. 40. Definition <ul><li>The bond dissociation enthalpy (  diss H) for an X-X diatomic molecule refers to the process: </li></ul><ul><li>X 2 (g) 2X(g) </li></ul><ul><li>at a given temperature (often 298 K) </li></ul><ul><li> diss H = D(X-X) is the bond enthalpy for a specific process (a particular bond in a molecule) </li></ul><ul><li>Breaking bonds is an endothermic process </li></ul>
  41. 41. D and D <ul><li>CH 4 (g) CH 3 (g) + H(g)  H=436 kJ mol -1 </li></ul><ul><li>CH 3 (g) CH 2 (g) + H(g)  H=461 kJ mol -1 </li></ul><ul><li>CH 2 (g) CH(g) + H(g)  H=428 kJ mol -1 </li></ul><ul><li>CH(g) C(g) + H(g)  H=339 kJ mol -1 </li></ul><ul><li>D depends on the bond </li></ul><ul><li>D is an average value and is obtained from </li></ul><ul><li>CH 4 (g) C(g) + H(g)  H=1664 kJ mol -1 </li></ul><ul><li>D (C-H) = 416 kJ mol -1 </li></ul>
  42. 42. Enthalpy Changes in Chemical Reactions <ul><li>Enthalpy difference between products and reactants because different chemical bonds are formed. </li></ul><ul><li>Enthalpy change can be estimated from the chemical bonds that are broken and made. </li></ul><ul><li>Breaking bonds is an endothermic process and making bonds is an exothermic process </li></ul><ul><li>Only an estimate because </li></ul><ul><ul><li>Bond enthalpies are mean values </li></ul></ul><ul><ul><li>All species are in the gaseous state </li></ul></ul><ul><li>A Hess’s law problem </li></ul>
  43. 43. Now have a go at the bond enthalpy problems and set up as an Excel spreadsheet. Can you set it up so that you only need to enter the number of C and H atoms to calculate the enthalpy change ??? -818 Tota enthalpy change of combustion kJ mol -1     -3466 Total energy out/kJ mol -1 2648 Total energy in/kJ mol -1       -1856 4 0 0 464 O-H 0 0 996 2 498 O=O -1610 2 0 0 805 C=O 0 0 1652 4 413 C-H 0 0 0 0 347 C-C Energy out KJ mol -1 Number made Energy in KJ mol -1 Number broken Bond energy Bond type   CH 4 Compound   Enthalpy changes of combustion for hydrocarbons
  44. 44. This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales License Acknowledgements <ul><li>JISC </li></ul><ul><li>HEA </li></ul><ul><li>Centre for Educational Research and Development </li></ul><ul><li>School of natural and applied sciences </li></ul><ul><li>School of Journalism </li></ul><ul><li>SirenFM </li></ul><ul><li>http:// tango.freedesktop.org </li></ul>
  • MangokatombiokAguek

    Apr. 10, 2018
  • mahfuzahyusoff

    Jan. 13, 2018
  • muhammadzakir25

    Jul. 29, 2017
  • Tuktamekkhala

    Jan. 22, 2017
  • ayanmohammed7

    Nov. 14, 2016
  • Mizsa98

    Oct. 4, 2016
  • 100003541117285

    Nov. 23, 2015
  • JoshuaLewa

    Nov. 22, 2015
  • VeronikaRoseline

    Aug. 25, 2015
  • leeratomampai

    Aug. 4, 2014
  • kassim1234

    Jan. 4, 2014
  • erasyafera

    Oct. 15, 2013
  • ningcao666

    Sep. 18, 2012

Lecture materials for the Introductory Chemistry course for Forensic Scientists, University of Lincoln, UK. See http://forensicchemistry.lincoln.ac.uk/ for more details.

Views

Total views

19,731

On Slideshare

0

From embeds

0

Number of embeds

466

Actions

Downloads

513

Shares

0

Comments

0

Likes

13

×