General Chemistry Review
From Gen Chem to Organic Chem, Pt. 11 – The Second Law
Last updated: March 20th, 2021 |
Zeroth law of thermodynamics: you must play the game
1st law : you can’t win
2nd law: on a very cold day, you can break even
3rd law: it never gets that cold
The 2nd Law of Thermodynamics: Δ G = Δ H – T Δ S.
(I wrote a really long description of this law and realize that it is probably overkill. But I wrote it, so I’ll include it. If you’re already somewhat comfortable with thermodynamics, skip to the punchline at the end, “How the second law of thermodynamics applies to organic chemistry”).
We’ve talked about the concept of enthalpy (heat) and how certain reactions are exothermic (produce heat) and endothermic (absorb heat). For instance, one prominent example of an exothermic reaction is the combustion of hydrogen with oxygen to produce water. This gives off 276 kJ/mol.
Back in the earlier days of chemistry and physics, much attetion was given to the development of steam engines, where the combustion of wood or coal (another exothermic reaction) is used to boil water. In a closed system, the resulting high-pressure steam could be used to do work on a paddle wheel or some other contraption and the Industrial Revolution was born. [Recall that a mole of water (18 mL) occupies 22.4 L as a gas at room temperature and even more at 100° C – that’s a lot of pressure! ] Needless to say, explosions were common in the early days of steam.
Long story short: the work you receive out of these types of processes never equals the energy that goes in (1st law: “you can’t win”). It was in the 1870s that Gibbs (among others) determined that one must account for a certain amount of “non-useful” energy which is dissipated during these processes, which was later defined as “entropy”. The energy left over – which is available to do work – was termed the ‘free energy”, or as we call it now, the “Gibbs Energy“. Here’s the relevant equation:
Δ G = Δ H – T Δ S
This is the second law of thermodynamics, which has been written in many forms (see above) but in my favorite interpretation, goes: “Energy of all kinds in our material world spontaneously disperses or spreads out if it is not hindered from doing so”.
In organic chemistry it’s important to have an intuitive grasp of this equation and to understand it implications in certain types of reactions. While the effects of enthalpy changes are usually fairly easy to understand, it’s easy to get hung up on entropy and the Gibbs energy.
Remember that all matter is in constant motion, with particles constantly colliding with each other at high speed. Temperature is the measurement of how rapidly these molecules are in motion. And at absolute zero, all motion stops. A drop of dye placed in a glass of water will slowly fade to a lighter hue; air in car tires will slowly leak out to the atmosphere; an ice cube taken out of the freezer will slowly melt into a tiny puddle. All of these processes are the result of particles colliding with each other, exchanging energy in the process, and eventually reaching an equilibrium.
One of the interpretations of entropy (in a chemical sense) is the following:
“Entropy change measures the dispersal of energy: how much energy is spread out in a particular process, or how widely spread out it becomes (at a specific temperature).”
If you think about this in terms of forms of matter, it’s not hard to grasp intuitively that the entropy of a given compound will increase as it goes from solid to liquid to gas: the particles are spread out over a wider area (at a given temperature, of course).
Similarly, if you take a molecule such as H2 and split it into two molecules of H, the dispersal of energy will increase, since you will have twice as many particles colliding with each other than you did before. So this also leads to an increase in entropy.
So what the Second Law tells us is that if you account for the enthalpy of a process in addition to the entropy, you can calculate the Gibbs energy, ΔG.
In Gen Chem you learned how to apply this equation to figure out the Δ G of a process if you were given values for H and S. The sign of the Δ G tells you if the process happens spontaneously (if Δ G is negative) or if it requires work in order to occur (when Δ G is positive.)
However, the equation tells you nothing about rates. In chemistry, “spontaneous” means, “someday, but not necessarily right now”. The reaction of cellulose (wood) with oxygen to give CO2 and H2O (and heat) is highly spontaneous, but our forests survive because the chemical process of burning requires a certain activation energy to get started.
How the Second Law applies to organic chemistry
Here’s the key point. For any process that results in an increase in entropy, increasing the temperature will eventually cause it to become (thermodynamically) spontaneous. Because of the TΔS term, at high temperatures, any process that increases entropy is eventually going to dominate the Gibbs equation.
There are two types of process in Org1/Org2 where you will see this in action:
1) fragmentation reactions
2) reactions that form gases.
Let’s talk about fragmentation reactions first. Any process that increases the net number of chemical entities (fragmentation reactions, for instance) is going to have a positive Δ S, since the total number of intermolecular collisions (and therefore the entropy) will drastically increase. Fragmentation reactions are one particular example. Thermal cracking is a process used by the petrochemical industry to transform low-value long-chain hydrocarbons into higher value short chain hydrocarbons. It’s typically done at extremely high temperatures. For instance you can heat butane to obtain the smaller molecules methane and propene.
Another example is a reaction you’ll meet in Org 1 called the E2 reaction, which is when a base reacts with an alkyl halide to provide an alkene. Note that in this process we’ve gone from two entities to three, which will result in an increase in entropy.
One of the reactions it competes with is the SN2 reaction (which you’ll also meet later) which forms the other products. How many products are formed here? Two; there is no net change in the number of molecules.
Which of these two processes is going to have a higher entropy? The E2. Therefore, which will be favored at higher temperature? That’s right – the E2, since the TΔS term will start to dominate the equation.
Reactions that form gases are another example. A process which results in the formation of a gas from a liquid or solid will have a positive net entropy, and therefore be favored by high temperature.
One example is a reaction you’ll meet in Org 2 called decarboxylation. When you heat molecules like this malonate derivative (shown) to a high enough temperature in the presence of aqueous acid, they’ll spontaneously lose carbon dioxide gas to provide you with the carboxylic acid. This particular example is called the malonic ester synthesis. The formation of gas makes for a large value of the entropy term in this reaction. Note that this is also a fragmentation reaction, so it has that going for it as well.