Homework 3 Thermodynamics. Read Chapter 3 1. Calculate the entropy change for a reversible reaction of 1 mol an ideal gas from 1L to 10L at 27 °C. Hint dS =qrev/T and dQ = -dW Thus dS=-dW/T since –dW=PdV then dS =PdV for one mole PV=RT then dS = RT/T(dV/V) = R(dV/V) integrating ?S = R?_v1^v2¦dV/V R = 1.99cal K-1 mol-1 2. Calculate the entropy change accompanying the melting of 9 g of ice to water at 0 °C. The heat of melting is 5.98 kJ/mol b) by what factor would the same molar quantity of an ideal gas have to expand to achieve the same increase in entropy? 3. The standard free energy and enthalpy of hydrolysis of the “high energy” compound ATP are approximately -8 and -4 kcal/mol. What is the magnitude and sign of the standard entropy change at 25 °C for this reaction? ATP +H2O ? ADP + Pi What are the reasons for the magnitude and sign of the changes of ?H° and ?S°. 4 If one would try to measure the ?G° of ATP hydrolysis , it would be difficult because the Keq is so large. How much ATP is present at equilibrium starting with only 1 mM ATP if the Keq at pH 8 is 1 x 106? 5 Consider a proton symport mechanism operating for transport of a divalent (z=-2) anion into E. coli or right side out vesicles with a negative internal membrane potential. Assume 2H+( n=2) transported per one anion. What is the accumulation ratio for a ?????-59 mV and a ?pH =1 (inside=8,outside =7)? What is the accumulation ratio of an uncharged solute under the same conditions? 6. Consider transport of Cl- into inside –out membrane vesicles, ??positive inside. Derive an expression for logSi/So according to a uniport mechanism. By how much does the accumulation ratio change when a ?? is increased from +59 to +177 mV? 7. Historically, the ?G°’ of ATP was measured using tow coupled reactions to be -7.7 and -6.9 kcal/mol using (a) hexokinase reaction (glucose +ATP ? glucose-6-phosphate + ADP with a ?G°’ = -4.4 kcal/mole, and the (b) galactokinase reaction (gal + ATP ? gal-1-phosphate a+ ADP with a ?G°’ of -1.9 kcal/mol) Determine the reaction that should be coupled to a and b as well as the expected ?G°’. 8. The fraction, ?, of oligo nucleotide molecules in a hairpin, as compared to a coil, state at temperature T can be determined spectrophotometrically from the absorbance at 260 nm which is greater in the coil conformation. Calculate ?G° as a function of temperature for the hairpin-coil transition of an 11 mer with the melting profile for the traction of molecules, ?, in the hairpin state at equilibrium shown in the figure on the next page. Solve for several above and below 50 °C.