7.3.3.P2

We’ve been grappling with the relationships between enthalpy *H*, entropy *S*, and Gibbs free energy *G. *In particular we’ve been especially interested in the *changes* in these quantities that take place when a particular system undergoes a particular process. As you now know, the relationship between these changes is given by:

∆*G* = ∆*H* - *T*∆*S*

In this problem we will explore where these thermodynamic quantities arise in the context of biological systems, and in the process try to make sense of of the conditions necessary for life.

1. Let’s think first just about Gibbs free energy changes, ∆*G*. As you’ve seen, the sign of ∆*G* tells us whether a process is spontaneous or not.

- Consider
**glycolysis** or **ATP hydrolysis**, two important biochemical processes in almost all animals. What is the sign of ∆*G* for these processes? Interpret/explain the sign of ∆*G* and its implications.
- Consider
*photosynthesis*, an important process in plants. What is the sign of ∆*G* for this process? Interpret/explain the sign of ∆*G* and its implications.
- What would it mean for ∆
*G* to equal ZERO for a biological organism?

2. Now let's think about entropic changes ∆*S*. As you've seen, the sign of ∆*S* tells us whether or not energy is spreading out evenly among a system's degrees of freedom. Equivalently, the sign of ∆*S* tells us whether the number of microstates for a given macrostate is increasing or decreasing.

- Consider the
**formation of a complex protein from its amino acid components**. What is the sign of ∆*S* for this process? Interpret/explain the sign of ∆*S*.
- Consider the
**formation of a lipid bilayer (or a micelle)**, as you did in recitation. What is the sign of ∆*S* for this process? Interpret/explain the sign of ∆*S*.
- In last week's HW problem
*Evolution and the Second Law, *you encountered the statement: **The theory of evolution says that life evolved from smaller inorganic molecules to larger organic molecules to simple one-celled organisms to more complex multicellular organisms, moving towards more complexity and organization**. If that statement is in fact correct (as it is), then what is the net overall sign of ∆*S *for evolving living systems?

3. Given that ∆*S* < 0 for many metabolic processes that create complex structure in organisms, what are the enthalpic conditions under which ∆*G* < 0 for those processes as well, i.e., *what are the conditions for *∆*H** under which such entropically unfavorable processes are still spontaneous*?

4. Give your result from Part 3, **what happens to the entropy of the system's environment during processes for which ∆***S* < 0 and ∆*G* < 0? Justify your answer in terms of what you said about ∆*H.* Does this help in reconciling the increasing complexity of evolving life with the 2nd Law of Thermodynamics (∆*S* > 0 for the universe ALWAYS)?

5. Can you make any general statements about the thermodynamic conditions necessary for life?

Ben Geller 2/4/12

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