Free Energy and Equilibrium

AP Chemistry Unit 9: Applications of Thermodynamics

Hello, future chemists and science enthusiasts! Ready to dive into the magical world of free energy and equilibrium? Imagine your chemistry exam is Thanos and we’re about to assemble the Avengers of knowledge to tackle it! Let's go!

In Unit 7, we explored equilibrium like archaeologists uncovering ancient treasures. Now, let’s connect those dots to spontaneity and ΔG (Gibbs Free Energy). Picture ΔG as the ultimate life coach, guiding chemical reactions on whether to proceed or chill.

When we first defined equilibrium, we used the kinetic definition. This is all about the rates of the forward and reverse reactions. Imagine a seesaw, where equilibrium means both sides balance perfectly, even though folks on either side are still moving.

Now, let's switch lenses to the thermodynamic definition. Here, equilibrium is the state of minimum free energy. It’s like finally finding the perfect napping spot where your energy is at its absolute minimum. As a reaction chugs along spontaneously, ΔG (note—no ° here, it’s just G without the star) is less than zero, indicating it’s losing free energy like a kid on a sugar high eventually crashing. Once equilibrium hits, ΔG becomes zero because the universe loves balance.

In the spirit of visuals, imagine graphs where the y-axis is free energy (G) and the x-axis shows the reaction’s journey from 100% reactants to 100% products.

1. The y-position isn't ΔG itself but the rate of change. If ΔG < 0, the graph descends faster than the popularity of fidget spinners. If ΔG > 0, the graph climbs up like our hopes every Monday morning.
2. Starting from 100% reactants (left side), we have ΔG = ΔG° of reactants. Over on the right side, 100% products mean ΔG = ΔG° of products.
3. If ΔG° of products is lower than reactants, we get a spontaneous reaction, with ΔG° = ΣnΔG°f (products) - ΣnΔG°f (reactants).

Think of a basketball rolling downhill (spontaneous) until it reaches the valley (equilibrium). From there, to roll it further, you gotta push it uphill (nonspontaneous).

Another graph might show ΔG° (products) greater than ΔG° (reactants). This is like trying to roll a ball uphill from the get-go — it’s a nonspontaneous reaction where reactants are couch potatoes, not racing to turn into products.

Let’s get a bit mathematical, but don’t worry, this isn’t rocket science… oh wait, it kind of is. Remember, ΔG tells us about free energy change under nonstandard conditions, and it’s closely related to Q (reaction quotient) and K (equilibrium constant).

To find Q, we use non-equilibrium concentrations or pressures in the mass action law (our trusty equilibrium formula). Here’s how our favorite constants fall into place:

[ ΔG = ΔG° + RT \ln(Q) ]

R is the gas constant (8.314 J/mol·K, like the Mr. Rogers of thermodynamics), and T is temperature in Kelvin (cue us thanking our eternal nerd crush, Lord Kelvin).

At equilibrium, ΔG = 0 and Q = K, giving us:

[ 0 = ΔG° + RT \ln(K) ]

Solving this:

[ ΔG° = -RT \ln(K) ]

[ K = e^{(-ΔG°/RT)} ]

If ΔG° is negative (reaction waits like an eager puppy), K > 1 indicating products favored. If ΔG° is positive (reaction more sluggish than Monday morning blues), K < 1 favoring reactants.

• 100% Products/Reactants: Imagine everyone at a costume party either fully dressed as products or reactants.
• Concentrations: Measures of product and reactant partygoers at any point.
• Direct Relationship: If ΔG° is negative, K loves making products. If positive, reactants are the reigning party champions.
• Equilibrium: The nerdy version of a perfectly balanced party where neither products nor reactants steal the show.
• Equilibrium Point: The magical point where reactants and products are in a forever-tied volleyball match.
• Forward Reaction: Reactants putting on their product costumes.
• Free Energy Change at Nonstandard Conditions: ΔG adjusts like your Netflix recommendations based on how nonstandard your binging conditions are.
• Gas Constant (R): The ever-reliable BFF of thermodynamics.
• Kinetic Definition of Equilibrium: Rates of forward and reverse reaction are equal, like synchronized swimming.
• Law of Mass Action: The OG guide for reaction rates.
• Minimum Free Energy: The ultimate chill zone where the system can't get any more comfortable.
• Mole Fraction: The flavor proportion in a jazzed-up soda.
• Nonspontaneous Reaction: Needs energy like a car needs gas.
• Qualitative Relationship: Fancy term for non-numerical comparisons.
• Reaction Quotient (Q): Measures how close a reaction is to reaching the party equilibrium.
• Reverse Reaction: Products putting on their reactant Halloween costumes again.
• Reversible Reaction: Reaction can go either way, like a boomerang.
• Spontaneity: Will this reaction Netflix and chill without help?
• Temperature in Kelvin (T): Mr. Kelvin's chill scale, starting from cool as ice.
• Thermodynamic Definition of Equilibrium: Balancing the energy books.
• ΔG < 0: Reaction on an enthusiastic roll.
• ΔG°: The grand master guide predicting spontaneity when the universe is at standard conditions.

So there you have it, your chemistry superhero cape is now fully equipped! Remember, equilibrium is like balancing on a tightrope, governed by the laws of kinetic and thermodynamic awesomeness. ΔG, Q, and K are your mighty tools, guiding you through the mystical lands of reactions.

Now go ace that chemistry exam with the confidence of Iron Man bench-pressing a car! 🚀

Note: Images and graphs not included. Keep practicing those equations, and may the ΔG be ever in your favor!