7.014 Section Problem: ThermodynamicsGiven the reversible chemical reaction: A + B¨ Æ æ C + D and the equation : DG = DG0+ RT ln[products][reactants]Ê Ë ˆ ¯ at 25oC, RT = 0.59kcalmol at 37oC, RT = 0.61kcalmola) If DG = 0, what does this mean?b) If DG° = 0, what does this mean?c) In the living cell at 25 °C, you observe the following concentrations:[A] = 50mM [B] = 30mM [C] = 1mM [D] = 10mMIf you allow a reaction mixture of only A, B, C, and D to come to equilibrium at 25 °C, youobserve these concentrations: [A] = 100mM [B] = 100mM [C] = 10mM [D] = 10mMi) What is DG° for this reaction?ii) What is DG° for the reaction C + D ¨ Æ æ A + B ?iii) What is DG for this reaction in the living cell?iv) How can you explain the difference between DG and DG°?Solutions to Thermodynamics The equation : DG = DG0+ RT ln[products][reactants]Ê Ë ˆ ¯ at 25oC, RT = 0.59kcalmol at 37oC, RT = 0.61kcalmolholds under all conditionsDG° is the free energy of the reaction under standard conditions: all []’s = 1MDG is the free energy of the reaction under any specified conditions; that is, where you’vespecified the []’s of all compounds involved in the reaction.a) In order to find DG, you must specify a set of conditions. If, under those specified set ofconditions, DG = 0, the reaction is at equilibrium at those conditions and no net formation ofproducts or reactants will occur. If DG < 0, net formation of products will occur; if DG > 0, netformation of reactants will occur.b) If DG° = 0, the reaction is at equilibrium at standard conditions; that is, when all []’s = 1M, itwill be at equilibrium. This is a possible, but unusual situation.c)i)In order to calculate DG°, you need to know the []’s at equilibrium; that is, whenDG=0. In that case, the above equation becomes: 0 = + RT ln[products][reactants]Ê Ë ˆ ¯ or : DG0= -RT ln[products][reactants]Ê Ë ˆ ¯ in our case : DG0= -RT ln[C][D][A][B]Ê Ë ˆ ¯ at equilibrium.DG0This relationship only applies at equilibrium (when DG=0), so we must use theequilibrium []’s: DG0= -RT ln10x10-6( )10x10-6( )100x10-6( )100x10-6( )Ê Ë Á ˆ ¯ ˜ = -0.59kcalmolln10-1010-8Ê Ë Á ˆ ¯ ˜ = +2.72kcalmolDG0This means that if all []’s = 1M, the reaction would spontaneously proceed to the left.ii) For the reverse reaction ( C + D ¨ Æ æ A + B), the sign of DG° is reversed (-2.72).Solutions to Thermodynamics, continuedc)iii) In the living cell, which is virtually never at equilibrium, you must use the completeDG equation: DG = DG0+ RT ln[products][reactants]Ê Ë ˆ ¯ . Substituting in our values gives :DG = +2.72kcalmol+ 0.59kcalmolln1x10-6( )10x10-6( )50x10-6( )30x10-6( )Ê Ë Á ˆ ¯ ˜ = +2.72kcalmol- 2.95kcalmol= -0.24kcalmolDG0This means that, in the living cell, the reaction proceeds spontaneously to the right.Often, living cells are able to drive unfavorable reactions by removing the products assoon as they are formed (thus lowering [products] and thereby lowering DG) orsynthesizing the reactants very rapidly (thus increasing [reactants] and therebylowering
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