Doc Brown's A Level Chemistry Advanced Level Theoretical Physical Chemistry AS A2 Level Revision Notes Basic Thermodynamics
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Part 3: ΔS Entropy Changes and ΔG Free Energy Changes
3.3b Entropy Changes & Feasibility of a Chemical Reaction
In Part 3.3a the total entropy change for the 'system' and its' surroundings' was considered and now applied to whether a chemical reaction is feasible i.e the criteria is a positive entropy is required. The entropy changes for thermal decomposition of limestone (a very endothermic reaction) and the burning of hydrogen in oxygen (a very exothermic reaction) are discussed in detail and in each case the feasibility of the reaction at different temperatures is discussed.
3.3b Entropy Changes and feasibility of a Chemical Change
ΔSθtot must be >0 for a chemical change to be feasible.
Example 3.3b1 Thermal decomposition of calcium carbonate (limestone)
This important industrial reaction for converting limestone (calcium carbonate) to lime (calcium oxide) has to be performed at high temperatures in a specially designed limekiln which these days, basically consists of a huge rotating angled ceramic lined steel tube in which a mixture of limestone plus coal/coke/oil/gas? is fed in at one end and lime collected at the lower end. The mixture is ignited and excess air blasted through to burn the coal/coke and maintain a high operating temperature.
ΔSθsys = ΣSθproducts ΣSθreactants
ΔSθsys = SθCaO(s) + SθCO2(g) SθCaCO3(s) = (40.0) + (214.0) (92.9) = +161.0 J mol1 K1
ΔSθsurr is ΔHθ/T = (179000/T)
ΔSθtot = ΔSθsys + ΔSθsurr
ΔSθtot = (+161) + (179000/T) = 161 179000/T
If we then substitute various values of T (in Kelvin) you can calculate when the reaction becomes feasible.
For T = 298K (room temperature)
For T = 500K (fairly high temperature for an industrial process)
For T = 1200K (limekiln temperature)
Now assuming ΔSθsys is approximately constant with temperature change and at room temperature the ΔSθsurr term is too negative for ΔSθtot to be plus overall. But, as the temperature is raised, the ΔSθsurr term becomes less negative and eventually at about 800900oC ΔSθtot becomes plus overall, so the decomposition is now chemically, and 'commercially' feasible in a lime kiln.
You can approach the problem in another more efficient way by solving the total entropy expression for T at the point when the total entropy change is zero. At this point calcium carbonate, calcium oxide and carbon dioxide are at equilibrium.
ΔSθtotequilib = 0 = 161 179000/T, 179000/T = 161, T = 179000/161 = 1112 K
Lime is actually formed at temperatures above 900oC (1173K) and a typical modern limekiln operating temperature range is 950980oC (from web). These calculations are approximate above 298K because it assumed that enthalpy and entropy values do not change with temperature. This is not true BUT the above calculations exemplify the sort of calculation you can do to calculate at what temperature becomes feasible.
In the next few examples I haven't bothered listing the entropy values, I've just slotted them into the entropy equations and the reaction enthalpy values are by the relevant chemical equation.
Example 3.3b2 The entropy change in forming water from hydrogen and oxygen
(i) Calculate the entropy changes ΔS for the combustion of hydrogen to form water vapour.
(ii) Calculate the entropy changes ΔS for the combustion of hydrogen to form liquid water.
Example 3.3b2 The entropy change in forming water from hydrogen ions and hydroxide ions neutralisation
Calculate the entropy change for the neutralisation reaction
summary to do
These theoretical calculations can be used for any reaction BUT there are limitations:
You cant say the reaction will definitely spontaneously happen (go without help!) because there may be rate limits especially if the reaction has a high activation energy or a very low concentration of an essential reactant.
However you can employ a catalyst, raise reactant concentrations or raise the temperature to get the reaction going! There is usually a way of getting most, but not all, feasible reactions to actually occur.
For more details on this last point see 3.6 Kinetic stability versus thermodynamic instability for a detailed discussion
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