Entropy and Gibbs Free Energy

Equations not on formula sheet:

• S = k_B ln(W)

• ΔS = q_rev / T

• K_p = K_c(RT)^Δn

• K_w + [H₃O⁺][OH^-] = 1 × 10^-14

• p(X)=-log(X)

• pH + pOH = 14

• % ionization = [H₃O⁺]_{equilibrium /} [HA]_initial × 100

• K_w = K_b × K_a

• K_a = 10^-pKa

• K_b = 10^-pKb

• pKa + pKb = 14

• 5% check

S = k_B ln(W)

what does each variable represent?

S = entropy

k_B = 1.38 × 10^-23

W = “ways” the system can be arranged

W = Xⁿ

X = number of outcomes

n = number of trials

• ΔS = q_rev / T

What does each variable represent?

• ΔS = change in entropy (J/K)

• q_rev = removed (J)

• T = temperature (K)

Relationships between Q and K

Q < K the reaction will shift towards products

Q =  the reactions is in equilibrium

Q > K the reaction will shift towards reactants

Difference between Q and K

• When you use Q you are using the concentrations at ANY moment (whether it be initial, halfway through, etc.)

• When you use K you are using concentrations at equilibrium

Le Chatelier’s Principle (What happens when you increase/decrease moles, temperature, pressure, or volume)

Moles

• Increase moles on one side → reaction shifts to the other side

• Decrease moles on one side → reaction shifts towards the side that had the decrease

Temperature

• Endothermic reaction → reaction shifts to products

• Exothermic reaction → reaction shifts to reactants

Pressure

• Increase pressure → shifts towards fewer moles

• Decrease pressure → shifts towards more moles

Volume

• Increase volume → shifts towards more moles

• Decrease volume → shifts towards fewer moles

How can you tell if a reaction will be spontaneous or nonspontaneous?

Reference: 𝛥𝐺 =𝛥𝐻 − 𝑇𝛥𝑆

• ΔG < 0→ spontaneous

• ΔG = 0 equilibrium

• ΔG > 0 → non-spontaneous

Spontaneous: naturally favored by the universe

• ice melting

Non-spontaneous: needs energy input to keep going

• water freezing

How to know if a reaction is endothermic or exothermic

• Exothermic (ΔH < 0)

• Endothermic (ΔH > 0)

What conditions would increase/decrease ΔS

When ΔS increase

• Solid → liquid → gas

• increase in moles of gas

  • liquid and solids have an effect too but way less

• Dissolving solid in water

• Increasing temperature

• Increasing volume → more space → more disorder

• decreasing pressure → more freedom → more disorder

When ΔS decreases

• Gas → liquid → solid

• fewer gas moles produced

• dissolving gas in liquid

• lowering temperature

• decreasing volume → less space → more order

• Increasing pressure → less fredom → more order