Chemistry · General chemistry II · Concept

Chemical equilibrium, K and ICE tables

At equilibrium the forward and reverse reactions run at the same rate, so no concentration changes. The equilibrium constant K, written from the balanced equation, fixes the ratio of products to reactants at a given temperature. The reaction quotient Q uses the concentrations present now: comparing Q with K tells you which way a mixture shifts, and an ICE table finds where it ends up.

Dynamic equilibrium

In a closed flask a reversible reaction slows as its reactants are used up, while the reverse reaction speeds up as products build. Equilibrium is reached when the two rates are equal. Both reactions continue, but the concentrations stay constant.

The equilibrium constant

For aA + bB ⇌ cC + dD, the law of mass action gives Kc from the equilibrium concentrations, each raised to its coefficient. Pure solids and liquids are left out. For gases, Kp uses partial pressures instead. K depends on the temperature, not on the starting amounts.

K_{c} = \frac{{[C]}^{c} {[D]}^{d}}{{[A]}^{a} {[B]}^{b}}

What the size of K means

A K much greater than 1 means products dominate at equilibrium; a K much less than 1 means reactants dominate. When K is near 1, both are present in comparable amounts.

The reaction quotient Q

Q has the same form as K but uses the concentrations at any moment. If Q < K, the reaction proceeds forward, making products; if Q > K, it proceeds in reverse; if Q = K, the mixture is already at equilibrium.

ICE tables

To find equilibrium concentrations, list the Initial concentrations, the Change in terms of one unknown x, scaled by the coefficients, and the Equilibrium expressions. Substitute the equilibrium row into K and solve for x. Reject any root that makes a concentration negative.

Changing the equation changes K

Reversing an equation inverts K. Multiplying every coefficient by n raises K to the nth power. Adding two equations multiplies their constants.

K_{reverse} = \frac{1}{K} K_{sum} = K_{1} K_{2}

Le Châtelier’s principle

A disturbed equilibrium shifts to partly undo the disturbance, and only a temperature change alters K itself. The Le Châtelier’s principle page works through each kind of change with Q and K.

Common mistakes

Including pure solids or liquids in K.
Putting initial concentrations into K instead of equilibrium concentrations.
Forgetting the coefficients in the change row: for N₂O₄ ⇌ 2NO₂, when N₂O₄ falls by x, NO₂ rises by 2x.
Keeping a root of the quadratic that makes a concentration negative.
Expecting a catalyst to shift the equilibrium: it speeds up both directions equally, so K and the equilibrium mixture stay the same.

Key terms

Chemical equilibrium: The state in which the forward and reverse reactions run at the same rate, so the amounts of reactants and products stop changing. Their concentrations need not be equal.
Equilibrium constant: K, the ratio of products to reactants at equilibrium, each raised to its coefficient, for a given equation and temperature. Kc uses concentrations and Kp uses partial pressures.
Law of mass action: For a reaction at equilibrium, the products’ concentrations raised to their coefficients, divided by the reactants’ raised to theirs, equal the equilibrium constant K at that temperature. Pure solids and liquids are left out.
Reaction quotient: Q, calculated like K but with the current concentrations. If Q < K the reaction goes forward, if Q > K it goes in reverse, and if Q = K it is at equilibrium.
ICE table: A table of Initial amounts, Changes and Equilibrium amounts for a reaction. Writing the change as x turns the problem into one equation to solve with K.
Le Châtelier’s principle: When an equilibrium is disturbed, by adding a substance or changing pressure or temperature, it shifts in the direction that partly undoes the change.

Work through an example

At a certain temperature, Kc = 0.25 for N₂O₄(g) ⇌ 2NO₂(g). A flask starts with 1.00 M N₂O₄ and no NO₂. Find the equilibrium concentrations.

Solve an equilibrium with an ICE table →

Predict the direction of a reaction with Q →

Reverse, scale and combine equilibrium constants →

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