AP Chemistry 7.3: Equilibrium Concentrations and ICE Tables

Many equilibrium problems do not give the equilibrium concentrations directly. Instead, you may know the initial concentrations and K, then need to determine how much the reaction changes before reaching equilibrium.

• The most common tool is an ICE table.
• ICE stands for:
• Initial
• Change
• Equilibrium
• Khan Academy's current Unit 7 explicitly uses equilibrium concentration and pressure calculations based on initial conditions.

Consider:

• A ⇌ B
• Suppose initially:
• [A] = 1.00 M
• [B] = 0
• and:
• Kc = 4.00
• Set up:

Why −x for A?

• Because A is consumed.
• Why +x for B?
• Because B forms.
• Now use:
• Kc = [B]/[A]
• Substitute equilibrium expressions:
• 4.00 = x/(1.00−x)
• Solve:
• 4.00(1.00−x) = x
• 4.00 − 4x = x
• 4.00 = 5x
• x = 0.800 M
• Therefore:
• [A]eq = 1.00 − 0.800 = 0.200 M
• [B]eq = 0.800 M

Suppose:

• A ⇌ 2B
• If A decreases by x:
• A change = −x
• but B increases by:
• +2x
• because one mole of A produces two moles of B.
• The table becomes:

The coefficients in the balanced equation control the change row.

Consider:

• N₂(g) + 3H₂(g) ⇌ 2NH₃(g)
• If the reaction shifts right by x:
• N₂ changes by:
• −x
• H₂ changes by:
• −3x
• NH₃ changes by:
• +2x
• So:

This is why balancing the reaction correctly is essential.

Sometimes products and reactants are both initially present.

• Then you may not know whether the system will shift right or left.
• Calculate Q first.
• If:
• Q < K
• shift right.
• Your ICE changes should consume reactants and form products.
• If:
• Q > K
• shift left.
• Your signs reverse because products are consumed and reactants form.

Some equilibrium expressions produce quadratic equations.

• Example:
• A ⇌ 2B
• with:
• [A]₀ = 1.00 M
• [B]₀ = 0
• Then:
• [A]eq = 1−x
• [B]eq = 2x
• If:
• Kc = [B]²/[A]
• then:
• Kc = (2x)²/(1−x)
• which may create a quadratic equation.
• You may need to use factoring or the quadratic formula.

In some equilibrium problems where K is extremely small, only a tiny amount of reactant changes.

• If:
• A₀ − x
• appears and x is very small compared with A₀, you may sometimes approximate:
• A₀ − x ≈ A₀
• This can simplify the algebra.
• However, do not use this approximation automatically.
• After solving, check whether x really was small relative to the initial concentration. A common chemistry guideline is that the approximation is reasonable when the change is only a few percent of the original amount.
• If not, solve the full equation.

ICE tables can also use gas partial pressures.

• Instead of concentrations:
• [A]
• you may use:
• PA
• The same stoichiometric logic applies.
• For example:
• PCl₅(g) ⇌ PCl₃(g) + Cl₂(g)
• If PCl₅ decreases by x atm:
• PCl₅: −x
• PCl₃: +x
• Cl₂: +x
• Then substitute equilibrium pressures into Kp.

After calculating equilibrium values, verify:

• no concentration or pressure is negative;
• stoichiometric relationships are correct;
• substituting the values back into the equilibrium expression gives K;
• the direction of change agrees with Q vs. K if that was determined.

Do not place initial concentrations directly into K unless the system is already at equilibrium.

Do not use identical x changes when coefficients are different.

Do not let an equilibrium concentration become negative.

Do not use a small-x approximation without checking whether it is valid.

ICE tables follow:

• Initial → Change using coefficients → Equilibrium → substitute into K → solve x

For a reaction such as:

• A + 2B ⇌ 3C
• construct:

Then:

• Write K.
• Substitute the equilibrium row.
• Solve for x.
• Calculate each equilibrium concentration.

Check your answer.

• If the system shifts left, reverse the change signs.