A Level Chemistry Entropy

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two possible arrangements. It can be in either the left-hand jar or the right-hand jar. We can write the number of possible arrangements for molecule 1 as W₁, and the number of possible arrangements for molecule 2 as W₂, and so on. As there are two possible arrangements for molecule 1, W₁ = 2. For molecule 2, W₂ = 2, and so on. With only 4 molecules - How many different arrangements of the molecules are there? Mathematically speaking it is W = W, +W,+W,...... W = 2¹ = 16 If we increase the number of molecules to 100, Wbecomes 2100, The left-hand gas jar would contain, all 100 molecules only once in every 3.2 x 10 years! We would have to wait for a very long time. indeed to see all 100 molecules in the left-hand jar! You can see that as the number of molecules increases, the number of possible arrangements also increases very rapidly. To make the numbers easier to work with we need to use an equation to help us. You do not need to remember the equation, but it helps us to see how the spreading out of the molecules is related to an increase in entropy where Wis the number of ways of arranging the molecules, k is a constant called the Boltzmann constant, with a value 1.38 x 10-2 JK and In is the natural logarithm (i.e. the logarithm to the base e). Entropy is measured in units of JK 'mol, Entropy measures the degree of randomness, so you would expect a gas to have a larger entropy than its liquid form, and a liquid to have a larger entropy than its solid form. The figures in table A show that this is the case for water vapour, water and ice. SUBSTANCE ENTROPY, S/JK mol water vapour 189 water 70 ice 48 table A Entropies of water vapour, water and ice. two possible arrangements for one molecule left or right for example for 4 molecules .. 4 left 0 right (0) .... 18 .: :: 3 left 1 right 8458: .. O left 4 right 2 left • 2 right 1 left 3 right 4 molecules 2 ↓ 2 arrangements left or right S-klnw no need to know this S=entropy = 16 distribution of energy. →spreading out of molecules in diffusion is an increase in entropy because the molecules become more randomly dispersed in the same way, the spreading out of heat energy also represents an increase in entropy → energy exists in packets called quanta → must be whole number distribution of quanta b/w molecules is random - more quanta there are = more ways there are of arranging them blw the molecules also, more molecules = more ways of sharing the quanta As an example, table B shows that there are five possible arrangements of four quanta between two molecules. Table C shows that there are six possible arrangements of five quanta between two molecules. Table D shows that there are 10 possible arrangements of three quanta between three molecules. table B MOLECULE 1 MOLECULE 2 4 3 2 1 0 0 1 2 3 4 table C MOLECULE 1 MOLECULE 2 5 4 3 2 1 0 table B 2 molecules, 4 quanta, 5 arrangements table C 2 molecules, 5 quanta, 6 arrangements table D 3 molecules, 3 quanta, 10 arrangements 0 1 2 3 4 5 table D MOLECULE 1 MOLECULE 2 MOLECULE 3 3 0 0 2 2 1 1 1 0 0 0 3 0 1 0 1 2 0 1 2 0 0 3 0 1 1 0 2 2 1 The higher the temperature, the more energy a substance has. The more energy a substance has, the more ways there are to distribute the energy. The more ways there are to distribute the energy, the higher the entropy. So, increasing the temperature will increase the entropy. from video it's not heat you need to run an engine →it's the difference in temperature entropy measure of how spread out energy is energy always increases - so it's always spreading out question → things to expect in a chemical reaction that increased entropy. increase in ways of arrangement more molecules = exothermic = Change of state energy is given out to surroundings ie-melting - increases spread entropy increased the second law of thermodynamics based on entropy and states that entropy tends to a maximum. infers that all chemical and physical changes involve an overall increase in entropy' CALCULATING ENTROPY standard molar entropy Sº de entropy per mole for a substance under standard conditions → generally, gases > liquids > Solids entropy increases as temperature increases = more energy to be distributed total entropy change, As total As AS + AS surroundings total 2 components = entropy change + entropy change of System of surroundings entropy change of the system ASS (products) 3= entropy GAS H₂O(g) H₂ 0₂ N Cl₂ CO NH₂ table A H₂O(g) H₂ 0₂ N₂ C₂ CO₂ NH, table A ENTROPY S /JK mol 188.7 1306 205.0 191,6 ENTROPY S 165.0 213.6 192.3 1887 130.6 205.0 191.6 165.0 213.6 192.3 system LIQUID H₂O(l) CH₂OH CH₂CH₂OH C₂H₂ LIQUID H₂O CH,OH CHICH,OH ENTROPY S /JK-¹ mol 69.9 239.7 160.7 172.8 calculating AS total ENTROPY S JK mol 69.9 239.7 1728 entropy change of surroundings AS surroundings ΔΗ SOLID S (reactants) = sum of SOLID H₂O(s) C(diamond) C(graphite) CaO CaCO H₂O(s) C(diamond) Cgraphite) Cao Q: calculate AS surroundings at 298k when one mole of hydrogen is burned in oxygen H₂(g) + O₂(g) → H₂O(l) 1 AS surroundings =-; AH = -286 kJ mol -1 -1 +0.960 kJ K mol -286 298 →in a perfectly ordered crystal at OK-> entropy is zero ENTROPY S /JK¹ mol-¹ 47.9 2.4 5.7 ENTROPY S 47.9 24 5.7 39.7 92.9 39.7 92.9 entropy is all about distribution. in a chemical reaction, the system is the species that are taking part in the reaction Surroundings = everything else (reaction vessel and air in lab) Q: calculate the entropy change for the system for the Synthesis of ammonia from nitrogen and hydrogen N₂ (g) + 3H₂(g) → 2NH3 (9) 192.3 = A: 191.6+ 391.8 (130.6 x 3) AS = 192.3 (191.6+391.8) = 583-4 Jk mol- OR +960 JK-1 -198-8 JK-1 → more the energy transferred to surroundings by an exothermic reaction LD larger the increase in entropy of surroundings mal -1 - Using the information in table A, calculate the total entropy change at 298 K for the following reaction: H₂(g) + O₂(g) → H₂O(1) AH = -286 kJ mol-¹ AS system = 69.9 AS total (130.6- (205-0/2)) -163-2 JK-1 mol-1 +960 JK 1 mol-1 AS total = +796-8 JK-1 mol-1 mol = -163-2 JK-mol- → for a given quantity of energy -D increase in entropy is greater when surroundings are cool rather than when they are hot -1 → reaction is only feasible when total entropy change is positive → most exothermic reactions tend to go be at around room temperature, the -AH/T value is much larger and more positive than AS system → So AS total is positive. → an endothermic reaction can be feasible - as long as the increase in AS system is greater than the decrease in AS surroundings →a reaction that doesn't tend to go to RTP may become feasible as temperature rises because AS surroundings decreases as T increases Summary AStotal will be positive if: both AS surroundings and AS AS surroundings is positive and AS of AS system system are positive system • AS surroundings is negative and AS of AS system- system is negative, but the magnitude of AS surroundings is positive, but the magnitude of ASSU > the magnitude surroundings the magnitude WHY ENTROPY CHANGES OCCUR changes of state EXAMPLE 1 When solid ammonium carbonate is added to pure ethanoic acid, bubbles of gas are rapidly produced. Despite its violent appearance, this is an endothermic reaction, as can be shown by placing a thermometer in the acid before the ammonium carbonate is added. The temperature falls considerably as the reaction takes place. 2CH₂COOH(1) + (NH₂)₂CO,(s) + 2CH,COONH,(aq) + H_O) + CO,{g) Since the reaction is endothermic. A.Sunding will be negative, However, there is a large increase in the entropy of the system, AS because a gas is produced from a liquid and a solid. The magnitude of AS is greater than that of AS and this makes AS positive, so the reaction is thermodynamically spontaneous examples EXAMPLE 1 EXAMPLE 2 EXAMPLE 3 Hydrated barium hydroxide reacts with solid ammonium chloride Magnesium burns in oxygen to form solid magnesium oxide: in a rapid endothermic reaction at room temperature: Mg(s) +O(g)- MgO(s) Ba(OH), 8H,O(s) + 2NH,C(s) + BaCi(s) + 10H,O) + 2NH (g) change in number of moles Increase in number of moles → increase in number of particles present → increases number of ways particles Cand their energy) can be arranged ->System entropy increases →AS system is positive So AS system is positive EXAMPLE 3 As in the previous example, the driving force of the reaction is ASystem which overcomes the negative value of ASoundings caused by the endothermic nature of the reaction. The reactants are solids and the products are a solid, a liquid and a gas. Mg(s) + O₂ → MgO(s) So AS system is negative 2CH₂COOH(1) + (NH₂)₂CO3(s) reactonts number of moles 3 →2CH₂COONH (s) + H₂O(l) + CO₂(g) products 4 number of moles So AS system is positive EXAMPLE 2 Ba(OH)2.8H₂O(s) + 2NH,Cl(s) reactants num. of moles 3 → BaCl,(s) + 10H,O(l) + 2NH,(g) products num of moles 13 reactant moles 1.5 The reaction is highly exothermic. so A.Surroundings will be positive. ASystem is negative since a solid and a gas are changing into a solid. However, the magnitude of the value of ASoundings is greater than that of AS making ASoal positive. So, the reaction is thermodynamically spontaneous. product dissolving ionic solids in water When an ionic solid dissolves in water, 2 changes happen: 1- lattice structure breaks down → 2- ion becomes hydrated breaking down of the lattice is endothermic results in an increased number of moles of particles present L increases entropy of the salt hydration of ions is exothermic LD water molecules become more ordered as they arrange themselves in an orderly manner around the positive and negative ions So water entropy decreases = total Lp since AS surroundings =- Lo this ordering of the water molecules is particularly significant when dissolving anhydrous solids in water why aren't all ionic solids soluble in water? Need to look at enthalpy and entropy changes. Solubility of ionic solid is determined by the total entropy change for the solid AS As + AS system Surroundings Asol H T the expression becomes AS =AS total System Asal H T ● value of AS - hence the solid's solubility → depend on the values of 3 factors 1- entropy change of system AS system 2- enthalpy change of solution Asal H 3- temperature (Kelvin) of water T example dissolving ammonium nitrate crystals in water at a temperature of 298K NH,NO (s) , NH, (aq) + NO₂ (aq) AH+25.8 kJ mol™¹ ASystem S[NH, (aq)] + S[NO, (aq)] - S[NH.NO,(s)] = +113.4+ 146.4-151.1 J K mol-1 = +108.7 J K¹ mol"! ASurroundings- AHol +25800 T 298 AStotal (+108.7-86.6)= +22.1 J K-¹ mol-¹ Since AStotal is positive, the dissolving of ammonium nitrate in water at 298 K is thermodynamically spontaneous. Since the activation energy for this process is very low, ammonium chloride is soluble in water at 298 K. We are now in a position think about the solubility in water of some other ionic solids. Table A shows the relevant thermodynamic data for some solids at a temperature of 298 K The values have been quoted to the nearest whole number IONIC SOLID AHKJ mol-¹ NaCl NH.CI AgCl MgSO CuSO CaSO table A +4 +15 +66 -91 -73 -18 =-86.6 J K-¹ mol-1 AS/JK-mol-¹ AS/JK-mol-¹ AS/JK mot -13 +56 +43 -50 +167 +117 -221 +33 -188 +305 -213 +245 -192 +60 -145 why does water freeze ? ice has lower entropy than liquid water → AS system is negative process is exothermic → AS surroundings is positive So if magnitude of AS surroundings > magnitude of AS system LD then AS total is positive and water will freeze at +5°C (2781) AS system - 6010 278 AS Surroundings the total entropy change is negative We will now calculate AStotal for the change of water into ice at +5°C and -5 °C using the following data. AH-6010 J mol-¹ H₂O(1)→ H₂O(s) • S(water) = 69.9 J K-¹ mol-¹ • So(ice) = 47.9J K-¹ mol-¹ at -5°C (268 K) As System AS Surroundings = +92 +53 -85 = (47.9 - 69.9) =-22.0 JK-₁ mol¹ +21.6 JK mol-1 (47.969.9) = - 6010 268 AS total = +0.4 JK mol-1 SOLUBILITY soluble soluble insoluble soluble soluble insoluble plenary →why does there is a change of state D AS total = -0.4 JK-1 mol-1 So the chonge is not thermodynamically spontaneous LD So the water will not freeze -22.0 JK-1 mol-1 -1 mol-1 +22.4 KJ the total entropy change is positive -> the change is thermodynamically spontaneous D water will freeze entropy change when... (gas) molecules arrangement become more (solid) or less ordered a solid ionic substance dissolves - crystalline solid going into solution. Solid highly ordered, solution disordered a reaction involves a change in number of moles → CH4 (g) +20₂ (g) → CO₂ (g) + 2H₂O (l) gas moles = 3 gas moles = 1 CuSO 4(S) + SH₂0 (1) -> CUSO4.5H₂O (8) Summary what is entropy ??? the measure of disordered particles basically the number of ways particles can arrange themselves Tood 1000 solid solld increasing entropy 2 another way of affecting entropy D5 moles of liquid incorporating into a crystal →→ 1808 = 069 liquid gas energy partides have energy → called quanta L more energy 3 more particles = higher the entropy liquid gas more ways of arrangement LD more ways of arranging lots of particles greater freedom to arrange particles 4D = entropy has increased entropy + temperature O melting boiling ↑ absolute zero temperature CK) higher entropy, a favourable process Clittle packers of energy) more ways these particles can arrange themselves. LD will obv move toward gaseous phase so higher energy particles increase the entropy volume bp mp -> > entropy values against temperature shows how entropy changes as we increase temperature Standard entropy. Se game for liquids BUT larger change solid partides start to move significantly rathe than just vibrating O temp & 0 entropy perfectly ordered crystal LD not entropically favourable underground' symbol tells that this is in standard conditions B increased number of moles = increased number of ways of arrangement change in num of gas moles but no overall change in moles tells that entropy is in a standard state 100 kPa (atmospheric pressure) 298 K C25°C room temperature) JK 1 mol 1 (units) entropy is given the letter s • type of energy that explains Why certain things diffuse entropically favourable involves change in disorder explanation particles in can are in liquid form the entropy value can change depending on the conditions 1-complexity of the molecule 2- physical State changes the value NO 2 = 240 NO=211 more complex = higher entropy be in ges particles have more ways of arrangement 8. BUT when we press the button. LD spreads out → turns into a gas turning into gas is favourable entropically L more ways of particle arrangement will spread out across the room →> temp ↑ = entropy ↑ i if we sprayed the deodorant →! U Stays in one area look for any of these 3 ideas 1- heating up = increased S 2- going from solid to gas asw (3- creating more moles dissolving is also entropically favorable H₂0 (1)=699 H₂O(g) = 189 gas = more entropy So when looking for Chemical reactions diffusion spreads out and diffuses partides gain energy = more ways of arrangement more significant increase in entropy volume entropy is basically the value of one mole per substance Sudden increases in entropy at mp and bp LD bigger increase at bp *Spontaneous endothermic reactions can only occur if the entropy values are favourable V more about this in Gibbs Free energy equations 3 equations 1-AS = system 2- AS surroundings 3-AS total for = AS S entropy S products AH KJ m01 system так + AS reactants surroundings enthalpy change if AH is negative if AH is positive exothermic endothermic if AH is in KJ make sure to Convert to J by X 10³ !!!