Equilibrium Constant Notes

What K measures: the equilibrium constant tells us whether a reaction at a given temperature is likely to favor products or reactants once equilibrium is reached. It reflects the relative amounts of products and reactants at equilibrium.
Informal metaphor from the transcript: the idea of a "plateau" represents the state where the forward and reverse reaction rates are equal, so the overall concentrations stop changing.
Basic idea in one line: at a fixed temperature, the system settles into a balance where the ratio of product concentrations to reactant concentrations (each raised to its stoichiometric power) is constant and defined by K.

For a balanced chemical equation of the form
$aA + bB \rightleftharpoons cC + dD$
the equilibrium constant in terms of concentrations is
$K_c = \frac{[C]^c\,[D]^d}{[A]^a\,[B]^b}.$
The exponents are the stoichiometric coefficients from the balanced equation (a, b, c, d).
For gaseous reactions, the equilibrium constant in terms of pressures is
$Kp = \frac{PC^c\,PD^d}{PA^a\,P_B^b}.$
Relationship between Kc and Kp depends on the change in moles of gas; convert using standard state and the ideal gas law when needed.
Note on activities: the rigorous form uses activities; concentrations are often used as an approximation, which can introduce units unless activities (dimensionless) are used.

If K > 1, products are favored at equilibrium (the numerator dominates).
If K < 1, reactants are favored at equilibrium (the denominator dominates).
If $K \approx 1$ , neither side strongly dominates; significant amounts of both reactants and products are present.
Practical takeaway: K tells you the position of equilibrium at a given temperature, not the rate of approaching equilibrium.

K is temperature-dependent; changing temperature shifts the position of equilibrium.
The relationship is governed by the enthalpy change of the reaction, $\Delta H^\circ$ .
Van’t Hoff equation (detailed relationship):
$\frac{d\ln K}{dT} = \frac{\Delta H^\circ}{R\,T^2},$
where R is the gas constant.
Integrated form (useful for comparing two temperatures T1 and T2):
\ln\left(\frac{K2}{K1}{\right)} = -\frac{\Delta H^\circ}{R}\left(\frac{1}{T2} - \frac{1}{T1}\right).
If \Delta H^\circ > 0 (endothermic), increasing temperature generally increases K (more product-favored at higher T).
If \Delta H^\circ < 0 (exothermic), increasing temperature generally decreases K (more reactant-favored at higher T).
The transcript hints at specific temperatures (e.g., 250°C and 300°C) affecting whether equilibrium is observed or how much product forms, illustrating the core idea that K changes with temperature.

Step 1: Write the balanced equation and identify coefficients (a, b, c, d).
Step 2: Write the expression for $Kc$ (or $Kp$ if dealing with gases):
$K_c = \frac{[C]^c\,[D]^d}{[A]^a\,[B]^b}.$
Step 3: Substitute the equilibrium concentrations (or partial pressures) into the expression.
Step 4: Compute the numerical value of K.

Consider the reaction: $2A + B \rightleftharpoons 3C + D.$ Then
$K_c = \frac{[C]^3\,[D]}{[A]^2\,[B]}.$
Suppose at equilibrium: $[A] = 0.50\ \text{M},\; [B] = 0.30\ \text{M},\; [C] = 1.20\ \text{M},\; [D] = 0.40\ \text{M}.$ Then
$K_c = \frac{(1.20)^3\cdot(0.40)}{(0.50)^2\cdot(0.30)} = \frac{1.728\cdot 0.40}{0.25\cdot 0.30} = \frac{0.6912}{0.075} \approx 9.22.$
This numeric example shows a product-favored equilibrium (K > 1).

Define the reaction quotient Q with the same expression as for K but using instantaneous concentrations:
$Q = \frac{[C]^c\,[D]^d}{[A]^a\,[B]^b}.$
Compare Q to K:
- If Q < K, the reaction proceeds forward to form more products to reach equilibrium.
- If Q > K, the reaction proceeds in reverse to form more reactants.

Units and standard states: When using concentrations, K might appear to have units; using activities yields a dimensionless K. In practice, K is reported as a constant without units when activities are used.
Role of a catalyst: A catalyst changes the rate at which equilibrium is reached but does not change the position of equilibrium itself, i.e., it does not change the value of K.
Real-world relevance: Adjusting temperature to shift K is a common strategy in industrial synthesis to maximize yields; understanding K helps predict whether a reaction will favor products under specific conditions.
Foundational links: Equilibrium constants connect to broader themes in chemistry, including Le Châtelier’s principle, thermodynamics (ΔH°, ΔG°), and kinetics (rates toward equilibrium).

The instructor describes equilibrium constant as a measure of whether a reaction is likely to be brought in favor of products or reactants at a given temperature.
An informal metaphor is used: an equilibrium state resembles a plateau where the forward and reverse processes balance out.
There is discussion about “coefficients” as the numbers in front of chemical formulas in a balanced equation, which become the exponents in the K expression.
The transcript includes casual questions and clarifications about whether coefficients relate to moles or concentrations; the correct interpretation (in the K expression) is that coefficients are exponents, not simply mole amounts in the denominator or numerator.
The temperature-specific discussion in the transcript (e.g., references to 250 and 300, and a note about equilibrium) is used to illustrate that K can change with temperature, and that at certain temperatures an equilibrium position may be more or less favorable.
Aesthetic and anecdotal element: an anecdote about a printed copy being stolen and some students observing changes in the classroom environment; while not scientifically essential, it reflects the transcript’s informal tone and context in which the topic was introduced.

Links to Le Châtelier’s principle: Changing conditions (temperature, pressure, concentration) shifts the equilibrium to offset the change, which is reflected in changes to K with temperature.
Link to thermodynamics: The sign and magnitude of ΔH° influence how K shifts with temperature via the van’t Hoff relationship; ΔG° also relates to K through ΔG° = -RT ln K.
Link to kinetics: K tells the composition at equilibrium, while reaction rates determine how quickly equilibrium is reached.
Practical relevance: In industry, adjusting temperature to favor product formation is a common design strategy; catalysts are used to reach equilibrium faster but do not alter K.

The equilibrium constant K quantifies the balance between products and reactants at a given temperature for a chemical reaction.
Its value is determined by the stoichiometry of the balanced equation and the equilibrium concentrations (or activities) of the species.
Temperature changes shift K (and thus the equilibrium position) in a way that depends on the reaction’s enthalpy change.
K is related to the reaction quotient Q; comparing Q to K predicts the direction in which the system will proceed to reach equilibrium.
Understanding K enables prediction of yields, optimization of reaction conditions, and interpretation of how real-world conditions (like temperature) affect chemical equilibria.