Unit 7 Beta

Equilibrium: the one-page sheet

7.1 Introduction to Equilibrium

In a closed container, a reversible reaction slows as reactants are used, while the reverse reaction speeds up as products build. When the two rates are equal, the system is at chemical equilibrium: every concentration is constant, but not equal, and both reactions keep running. Concentration changes follow the coefficients, and the same equilibrium is reached from either direction.

Chemical equilibrium: the forward and reverse rates are equal, so all concentrations are constant.
Constant does not mean equal. Equilibrium concentrations can be very different from each other.
Equilibrium is dynamic: both reactions continue. It is reached from either direction and only in a closed system.
On a concentration-time graph, equilibrium is where every curve becomes flat; changes before that follow the coefficients.

only the forward reaction can run at first, at its fastest rate the forward rate falls and the reverse rate rises each species is made as fast as it is used, so every concentration stays constant the equilibrium is dynamic: molecules still react, but the composition does not change

chemical equilibrium: The state of a reversible reaction in a closed system when the forward and reverse rates are equal, so the concentrations of all species stay constant (but are usually not equal).

7.2 Direction of Reversible Reactions

A mixture of reactants and products has a net reaction in the direction of the faster reaction: forward when the forward rate is larger, reverse when the reverse rate is larger, and none when they are equal. Each rate depends on the concentrations of the species it uses, so a net reaction pulls the rates together until equilibrium. Adding or removing a species changes one rate first and starts a net reaction; a catalyst speeds both equally.

The net reaction goes in the direction of the faster reaction: forward if forward > reverse, reverse if reverse > forward.
Each rate depends on the concentrations of the species that react in that direction.
A net reaction always moves the rates toward each other, so a closed system heads to equilibrium.
Adding or removing a species changes one rate first; the system then has a net reaction until the rates match again. A catalyst speeds both rates equally and causes no net change.

there is a net forward reaction: reactants fall and products rise the forward rate falls and the reverse rate rises the net reaction stops and the system is at equilibrium the rate of the reaction that uses it changes first, so a net reaction runs until the rates are equal again

net reaction: The overall change in a reversible reaction when the forward and reverse reactions run at different rates: a net forward reaction turns reactants into products overall, a net reverse reaction the opposite.

7.3 Reaction Quotient and Equilibrium Constant

The equilibrium constant expression puts products over reactants, each raised to its coefficient, and leaves out pure solids and liquids; K c uses concentrations and K p partial pressures. The reaction quotient Q has the same expression filled in with the current amounts. If Q is less than K the net reaction goes forward, if Q is greater than K it goes in reverse, and when Q equals K the system is at equilibrium.

K = products over reactants, each to the power of its coefficient, at equilibrium. Leave out pure solids and liquids.
K_c uses molar concentrations in brackets; K_p uses partial pressures (no brackets).
Q has the same expression, filled in with the amounts present now.
Q < K: net forward. Q > K: net reverse. Q = K: at equilibrium.

products over reactants, each raised to its coefficient, with pure solids and liquids left out you get Q, a snapshot of where the mixture is now the forward rate is larger, so products form and Q rises toward K the reverse rate is larger, so reactants form and Q falls toward K the system is at equilibrium and the concentrations stop changing

equilibrium constant: K: the value of products over reactants, each raised to the power of its coefficient, for a system at equilibrium at a given temperature. Kc uses molar concentrations, Kp partial pressures; pure solids and liquids are left out.
reaction quotient: Q: the same expression as K, filled in with the concentrations or pressures present at any moment. Q < K means net forward reaction, Q > K net reverse, Q = K equilibrium.

7.4 Calculating the Equilibrium Constant

To calculate K, substitute equilibrium concentrations (or partial pressures for K p ) into the expression; every equilibrium mixture at one temperature gives the same value. Pure solids and liquids stay out of K even in a heterogeneous equilibrium. When only starting amounts and one equilibrium value are known, an ICE table writes each change as x times its coefficient, the measured value fixes x, and the equilibrium row goes into K.

K is calculated from equilibrium concentrations or pressures only.
Every equilibrium mixture of a reaction at one temperature gives the same K.
In a heterogeneous equilibrium (more than one phase), pure solids and liquids still drop out of K.
An ICE table (Initial, Change, Equilibrium) writes each change as x times the coefficient, so one measured value gives them all.

their concentrations differ, but K = products over reactants (with exponents) comes out the same an ICE table writes every change as x times a coefficient every equilibrium concentration follows from Initial + Change you get the value of K, with no units and the data’s significant figures

heterogeneous equilibrium: An equilibrium with species in more than one phase, such as a solid and a gas; pure solids and liquids are left out of its K. A homogeneous equilibrium has every species in one phase.
ICE table: A table with rows for Initial, Change and Equilibrium concentrations of each species. The change row is x times each coefficient, so one known value gives all the others.

7.5 Magnitude of the Equilibrium Constant

Because K is products over reactants at equilibrium, its size describes the equilibrium mixture. K much greater than 1 means product-favored (mostly products), K much less than 1 means reactant-favored (mostly reactants, a little product), and K near 1 means appreciable amounts of both. A small K lets you estimate product amounts by treating the reactant concentration as unchanged. K says how far a reaction goes, not how fast.

K ≫ 1: product-favored; mostly products at equilibrium.
K ≪ 1: reactant-favored; mostly reactants, but some product forms.
K near 1: appreciable amounts of both reactants and products.
K tells you how far a reaction goes, never how fast.

its size tells you which side dominates the equilibrium mixture the mixture is mostly products: product-favored the mixture is mostly reactants, with a little product: reactant-favored it gives no information about how fast equilibrium is reached

product-favored: Product-favored: a reaction with K much greater than 1, whose equilibrium mixture is mostly products. Reactant-favored: K much less than 1, mostly reactants with a little product.

7.6 Properties of the Equilibrium Constant

K belongs to one equation written one way. Reversing the equation gives 1/K, multiplying every coefficient by n gives Kⁿ, and adding equations multiplies their K values, because K is built from products of concentration terms. For a given equation, K changes only with temperature: adding substances, changing the volume or adding a catalyst changes Q or the rates, never K.

Reverse an equation: K_new = 1/K.
Multiply all coefficients by n: K_new = Kⁿ (n = ½ means a square root).
Add equations: multiply their K values.
For a given equation, K depends only on temperature. Concentration, pressure, volume and catalysts do not change it.

its K expression turns upside down, so K becomes 1/K every exponent in K is multiplied by n, so K becomes Kⁿ multiplying their expressions cancels the shared species, so K = K₁ × K₂ K takes a new value; at a fixed temperature nothing else changes it

combining equilibrium constants: Rules for K when an equation is changed: reversing it gives 1/K, multiplying all coefficients by n gives K to the n, and adding equations multiplies their K values.

7.7 Calculating Equilibrium Concentrations

To find equilibrium concentrations from K, compare Q with K to get the direction, build an ICE table with changes of ±x times each coefficient, substitute the Equilibrium row into K and solve for x. A perfect-square expression is solved by a square root. When K is small compared with the starting concentration, x can be dropped from (initial − x) but never set to zero elsewhere, and the result must pass the 5% check; otherwise use the quadratic formula.

Always find the direction first by comparing Q with K; it sets the signs in the Change row.
Changes are ±x × coefficient. Equilibrium = Initial + Change. Use molarities.
Perfect square: take the square root of both sides. Small K: drop x only from (initial − x), never x standing alone.
Check the small-x approximation: the change must be under about 5% of the starting value; otherwise solve exactly.

you know which side is used up and which forms every equilibrium concentration is written with one unknown you get one equation in x x can be dropped from (initial − x), and a 5% check confirms it every equilibrium concentration follows from Initial + Change

small-x approximation: A shortcut for ICE-table problems with a small K: x is dropped where it is added to or subtracted from a starting concentration, then checked; the change should be under about 5% of the starting value.

7.8 Representations of Equilibrium

Equilibrium shows up in a particle diagram as counts that stop changing and on a concentration-time graph as flat lines. To get K c , convert counts to moles and divide by the volume; raw counts work only when the gas coefficients are equal on both sides. Changes follow the coefficients, and a mixture reacts until Q equals K, not until a reactant runs out.

An equilibrium particle diagram shows a composition that no longer changes; look for identical counts over time.
Convert counts → moles → mol/L before using K_c. Counts work directly only when gas moles are equal on both sides.
On a concentration-time graph, equilibrium is where curves go flat; changes follow the coefficients.
An equilibrium mixture is not a limiting-reactant problem: it stops changing when Q = K.

the system is at equilibrium you have the molar concentrations K c needs the volume cancels, so raw counts give the right Q or K you can predict and draw the equilibrium mixture, conserving atoms

equilibrium particle diagram: A particle diagram of a system at equilibrium: its counts of each species stay the same over time. Converted to concentrations, the counts give K.

7.9 Introduction to Le Châtelier's Principle

Le Châtelier’s principle: a system at equilibrium that is disturbed shifts to partly counteract the change. Adding a species shifts the equilibrium away from it and removing one shifts toward it; decreasing the volume of a gas mixture shifts toward fewer gas moles. These changes leave K unchanged. A temperature change alters K, favoring the endothermic direction on heating. Catalysts, inert gases at constant volume and extra solid cause no shift.

Le Châtelier’s principle: a disturbed equilibrium shifts in the direction that partly counteracts the change.
Add a species: shift away from it. Remove a species: shift toward it. Solids and pure liquids do not count.
Smaller volume: shift toward fewer gas moles. No shift if gas moles are equal, for a catalyst, or for an inert gas at constant volume.
Temperature changes K: heating favors the endothermic direction.

it is no longer at equilibrium, and a net reaction starts the system shifts toward products, partly undoing the change the system shifts toward the side with fewer gas moles K changes: up for an endothermic reaction, down for an exothermic one, and the system shifts to match no shift: the equilibrium mixture stays the same

Le Châtelier's principle: When a system at equilibrium is disturbed by a change in concentration, volume or temperature, it shifts in the direction that partly counteracts the change.

7.10 Reaction Quotient and Le Châtelier's Principle

Every Le Châtelier shift can be justified by comparing Q with K. Changing a concentration, the volume or the pressure changes Q but not K; changing the temperature changes K but not Q at that instant. If Q is then less than K the net reaction goes forward, if greater it goes in reverse, until Q equals K again. Full-credit answers name what changed, give the comparison and the direction.

Concentration and volume changes move Q; K stays fixed.
Temperature changes move K; Q is unchanged at that instant.
Then compare: Q < K net forward; Q > K net reverse; until Q = K.
A volume change shifts the equilibrium only if the gas exponents on the top and bottom of Q differ.

Q changes while K stays the same K changes while Q stays the same at that instant the net reaction goes forward the net reaction goes in reverse Q moves until Q = K again at a new equilibrium

Q vs K: Justifying a shift by comparing the reaction quotient with the equilibrium constant: Q < K means net forward reaction, Q > K net reverse, until Q = K. Concentration and volume changes move Q; temperature changes move K.

7.11 Introduction to Solubility Equilibria

A slightly soluble salt reaches a dynamic equilibrium with its ions in a saturated solution. K sp is the product of the ion concentrations, each raised to its coefficient, with the solid left out. Writing each ion as s times its coefficient links K sp to the molar solubility s (s² for a 1 : 1 salt, 4s³ for a 1 : 2 or 2 : 1 salt). Compare K sp values directly only for salts with the same ion ratio; Q above K sp means a precipitate forms.

K_sp is the product of the ion concentrations in a saturated solution, each raised to its coefficient; the solid is left out.
Molar solubility s: mol of salt dissolved per liter. 1 : 1 salt: K_sp = s². MX₂ salt: K_sp = s(2s)² = 4s³.
Rank solubility by K_sp only for salts with the same ion ratio.
Q > K_sp: precipitate forms. Q < K_sp: more can dissolve.

ions leave the solid, and some return to it the saturated solution is at equilibrium, with K sp = product of ion concentrations every ion concentration is s times its coefficient you can solve for s, or calculate K sp from a measured s solid precipitates until Q = K sp

solubility product: Ksp: the equilibrium constant for a slightly soluble salt dissolving, equal to the product of its ion concentrations in a saturated solution, each raised to its coefficient. The solid is left out.
molar solubility: The number of moles of a salt that dissolve per liter of saturated solution (mol/L), often written s.

7.12 Common-Ion Effect

The common-ion effect: a salt is less soluble in a solution that already contains one of its ions. The common ion raises Q above K sp , so the salt precipitates until Q = K sp again; K sp is unchanged and only the solubility drops. To calculate the new solubility, write the shared ion as common ion plus a small term, drop the small term, solve K sp for s and check the 5% rule.

The common-ion effect: an ion already in solution lowers the solubility of a salt that contains it.
Justify it with Q: the common ion raises Q above K_sp, so solid forms until Q = K_sp. K_sp does not change.
In calculations, the shared ion is (common ion + coefficient × s) ≈ common ion. Count ions per formula unit; check the 5% rule.
An ion that is squared in K_sp has a larger effect.

Q rises above K sp the slightly soluble salt precipitates until Q = K sp less of the salt is dissolved: its molar solubility is lower K sp is the same; only the solubility changed

common-ion effect: The lowering of a salt’s solubility in a solution that already contains one of its ions: the common ion raises Q above Ksp, so less salt dissolves. Ksp itself does not change.