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==Thermodynamics== Chemical reactions are determined by the laws of [[thermodynamics]]. Reactions can proceed by themselves if they are [[exergonic]], that is if they release free energy. The associated free energy change of the reaction is composed of the changes of two different thermodynamic quantities, [[enthalpy]] and [[entropy]]:<ref>[[#Atkins|Atkins]], pp. 106β108</ref> :; <math>\Delta G = \Delta H - T \cdot \Delta S</math>. :: <small> {{mvar|G}}: free energy, {{mvar|H}}: enthalpy, {{mvar|T}}: temperature, {{mvar|S}}: entropy, {{math|Ξ}}: difference (change between original and product) </small> Reactions can be [[Exothermic reaction|exothermic]], where Ξ''H'' is negative and energy is released. Typical examples of exothermic reactions are [[combustion]], [[Precipitation (chemistry)|precipitation]] and [[crystallization]], in which ordered solids are formed from disordered gaseous or liquid phases. In contrast, in [[endothermic]] reactions, heat is consumed from the environment. This can occur by increasing the entropy of the system, often through the formation of gaseous or dissolved reaction products, which have higher entropy. Since the entropy term in the free-energy change increases with temperature, many endothermic reactions preferably take place at high temperatures. On the contrary, many exothermic reactions such as crystallization occur preferably at lower temperatures. A change in temperature can sometimes reverse the sign of the enthalpy of a reaction, as for the [[carbon monoxide]] reduction of [[molybdenum dioxide]]: :<chem>2CO(g) + MoO2(s) -> 2CO2(g) + Mo(s)</chem>; <math>\Delta H^o = +21.86 \ \text{kJ at 298 K}</math> This reaction to form [[carbon dioxide]] and [[molybdenum]] is endothermic at low temperatures, becoming less so with increasing temperature.<ref name="ReacWeb">{{Cite web|url=https://www.crct.polymtl.ca/reacweb.htm|title=F*A*C*T - REACTION-Web|website=www.crct.polymtl.ca}}</ref> Ξ''H''Β° is zero at {{val|1855|ul=K}}, and the reaction becomes exothermic above that temperature. Changes in temperature can also reverse the direction tendency of a reaction. For example, the [[water gas shift reaction]] :<chem>CO(g) + H2O({v}) <=> CO2(g) + H2(g)</chem> is favored by low temperatures, but its reverse is favored by high temperatures. The shift in reaction direction tendency occurs at {{val|1100|u=K}}.<ref name="ReacWeb" /> Reactions can also be characterized by their [[internal energy]] change, which takes into account changes in the entropy, volume and [[chemical potential]]s. The latter depends, among other things, on the [[activity (chemistry)|activities]] of the involved substances.<ref>[[#Atkins|Atkins]], p. 150</ref> :; <math>{d}U = T\cdot {d}S - p\cdot {d}V + \mu\cdot {d}n</math> :: <small> {{mvar|U}}: internal energy, {{mvar|S}}: entropy, {{mvar|p}}: pressure, {{mvar|ΞΌ}}: chemical potential, {{mvar|n}}: number of molecules, {{mvar|d}}: [[differential calculus|small change sign]] </small>
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