T is the absolute temperature (Kelvin, always positive) What it means: If ∆H is negative, this means that the reaction gives off heat from reactants to products
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T is the absolute temperature (Kelvin, always positive) What it means: If ∆H is negative, this means that the reaction gives off heat from reactants to products
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Intro Organic CHEM 2303 Page 1 David Birney, 2013 Equilibria, ∆G, ∆H and ∆S In a wide range of situations, we will see that understanding ∆G, ∆H and ∆S can help us understand where an equilibrium lies and often allow us to control whether the reactants or products are favored. For some of you, a little algebra might be helpful. (Or just skip to "What it means".) The relevant equations are: ∆G = - RT ln(Keq) ∆G = ∆H - T∆S or combining the two equations: ∆H - T∆S = - RT ln(Keq) Where: ∆G is the change in free energy Keq is the equilibrium constant (remember Keq = [products]/[reactants] ∆H is the change in enthalpy from reactants to products ∆S is the change in entropy (disorder) from reactants to products R is the gas constant (always positive) T is the absolute temperature (Kelvin, always positive) What it means: If ∆H is negative, this means that the reaction gives off heat from reactants to products. This is favorable. If ∆S is positive, this means that the disorder of the universe is increasing from reactants to products. This is also favorable and it often means making more molecules. Let's look at this f rom a qualit ative point of vie w. Consider a reaction that favors products at equilibri um. Doing the m ath, Keq > 1; the refore ln( Keq) > 0 (a posi ti ve number), and because R > 0 and T > 0, ∆G < 0 (a negative number). Therefore, if ∆G is a negative number, the reaction favors products. What must be true for ∆G to be negative and products to be favored? ∆G = ∆H - T∆S a) ∆H is negative and ∆S is positive (then both contribute to making ∆G negative), for example: C3H8 + 5 O2 à 3 CO2 + 4 H2O burning propane gives off heat and makes more molecules. b) ∆H is negative and ∆S is also negative but T is small enough, for example: waterlgas à waterliquid Liquid water is more ordered; condensing water releases heat (thunderstorms). c) ∆H is positive, but ∆S is positive and T is large enough. for example: CaCO3 à CaO + CO2 It requires adding heat limestone (heating to high temperatures) to drive off CO2, but it makes more molecules. For reaction type a, the reaction favors products and chemists cannot control it. For react ion of either type b or c, simpl y changing the temperat ure can change the position of the equilibrium. (But from experience, you knew this anyway!)
Intro Organic CHEM 2303 Page 2 David Birney, 2013 Let's look at a familiar example - the equilibrium between liquid water and water vapor. H
2 O liquid H 2 O gasmore stable less stable favored by ∆H favored by ∆S Above 100° C, at atmospheric pressure, the equilibrium is entirely to water vapor; that is what the boiling poi nt means. Bel ow the boiling point, bot h are in equi librium. Evaporation of water cools things off (think about swamp c oolers or sweat). Condensation of water warms things up (not so obvious, but this is where the energy in thunderstorms comes from, or why the temperature doesn't drop as much when there is dew in the morning, or why a glass of ice water warms up faster in a humid climate, when water condensed on it). All of these observations fit into the equilibrium picture. Now, imagine what happens to your skin, when there is an equilibrium between liquid water and water vapor, but the wind blows. The wind carries away those water molecules in the gas phase, and the system seeks to restore equilibrium (Le Chatlier's principle). To do this, it needs to take molecules from the liquid and turn then into vapor (favored by entropy - more disorder - ∆S > 0). But liquid water is held together by strong hydrogen bonds. To make vapor requires breaking them, taking heat from the environment (∆H > 0). This means that your skin cools off. O
H H O HH O HH O HH O HH O HH O HH O HH O HH O HH O HH O HH O HH O HH O HH liquid gas equilibriumnot equilibrium O HH O HH O HH O H H O HH O H H equilibriumNote that at higher temperature, the equilibrium will be shifted towards the gas (-T∆S becomes larger). Above 100° C and at atmospheric pressure, entropy wins and there is no liquid water at equilibrium. Consider the reverse - water vapor condensing in the clouds. What has to happen here is that as hydrogen bonds form, ∆H < 0, heat is given off. This heat is the source of the energy in thunderstorms.
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