Grade by Grade
E. Chemical Systems and Equilibrium · Chemical Equilibrium

The Reaction Quotient Q: Which Way Will It Shift?

E2.2 E2.4 E3.2 E2.1About 70 minutes
Learning goals
  • I can calculate the reaction quotient Q for any mixture.
  • I can compare Q with K to predict whether a system shifts forward, shifts in reverse, or is at equilibrium.
  • I can set up an ICE table with the correct signs when the reaction runs in reverse.
  • I can solve for equilibrium concentrations starting from any mixture of reactants and products.

Words to know

reaction quotient (Q)
The same ratio as K (products over reactants, coefficients as exponents) but calculated with the concentrations at any moment, not necessarily at equilibrium.
shift right (forward)
A net change in which reactants are used up and more products form; happens when Q < K.
shift left (reverse)
A net change in which products are used up and more reactants form; happens when Q > K.
Qp
The reaction quotient written with partial pressures, compared with Kp.

Is it there yet?

On a long drive, the question in the back seat is "Are we there yet?". For a reaction mixture, the question is "Is it at equilibrium yet, and if not, which way will it go?". You cannot always tell by looking. But if you know K, one quick calculation answers both questions: work out the reaction quotient, Q, and compare it with K.

Calculating Q

Q has exactly the same form as K, but uses the concentrations right now, whatever they are:

For aA + bB ⇌ cC + dD: Q = [C]ᶜ[D]ᵈ ÷ ([A]ᵃ[B]ᵇ) (any concentrations)

At equilibrium, and only then, Q = K. As a reaction runs, Q changes until it equals K.

Comparing Q with K

  • Q < K: the numerator (products) is too small. The system makes more products: it shifts right.
  • Q = K: the system is at equilibrium; no net change.
  • Q > K: the numerator is too big. Products turn back into reactants: the system shifts left.

A memory aid: the system always moves to bring Q toward K.

Q < Ktoo much reactant,too little product→shifts right (forward)Q = Kthe mixture isalready at equilibrium⇌no net changeQ > Ktoo much product,too little reactant←shifts left (reverse)
Comparing Q with K tells you the direction of the net reaction.
Worked example

Example 1: Predicting the direction

For H₂(g) + I₂(g) ⇌ 2 HI(g), K = 50.0 at a certain temperature. A flask contains [H₂] = 0.100 mol/L, [I₂] = 0.200 mol/L and [HI] = 0.800 mol/L. Is it at equilibrium? If not, which way will it shift?

  1. Q = [HI]² ÷ ([H₂][I₂]) = (0.800)² ÷ [(0.100)(0.200)] = 0.640 ÷ 0.0200 = 32.0.
  2. Compare: Q = 32.0 < K = 50.0.
  3. The product term is too small, so more HI will form.

Not at equilibrium; it shifts right (forward): [H₂] and [I₂] will decrease and [HI] will increase until Q = 50.0.

Worked example

Example 2: A reverse shift and an ICE table

For CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g), K = 4.00. A flask starts with [CO] = [H₂O] = 0.100 mol/L and [CO₂] = [H₂] = 0.300 mol/L. Find the equilibrium concentrations.

  1. Q = (0.300)(0.300) ÷ [(0.100)(0.100)] = 0.0900 ÷ 0.0100 = 9.00. Q > K, so the reaction shifts left.
  2. ICE with reverse signs: C row: CO +x, H₂O +x, CO₂ −x, H₂ −x.
  3. E row: 0.100 + x, 0.100 + x, 0.300 − x, 0.300 − x.
  4. Perfect square: (0.300 − x)² ÷ (0.100 + x)² = 4.00 → (0.300 − x) ÷ (0.100 + x) = 2.00.
  5. 0.300 − x = 0.200 + 2.00x → 0.100 = 3.00x → x = 0.0333.
  6. [CO] = [H₂O] = 0.133 mol/L; [CO₂] = [H₂] = 0.267 mol/L. Check: (0.267)² ÷ (0.133)² = 4.0 ✓.

[CO] = [H₂O] = 0.133 mol/L and [CO₂] = [H₂] = 0.267 mol/L. Using Q first told us which signs to put in the change row.

Signs in the change row

Decide the direction with Q before writing the C row.

  • Shift right: reactants −, products +.
  • Shift left: reactants +, products −.

If you guess wrong, the algebra will usually give a negative x or a negative concentration, which is a signal to recheck Q.

0255075100timeQK = 50start: Q = 10 < K, net forward reactionstart: Q = 95 > K, net reverse reactionboth reach Q = K
Two mixtures of the same reaction. One starts with Q below K and one above K; both change until Q equals K.
Worked example

Example 3: Q with a heterogeneous system

For CaCO₃(s) ⇌ CaO(s) + CO₂(g), K = [CO₂] = 0.010 at a certain temperature. A sealed container holds CaCO₃, CaO and [CO₂] = 0.025 mol/L. What happens?

  1. Q = [CO₂] = 0.025 (solids are left out).
  2. Q > K, so the reaction shifts left: CO₂ reacts with CaO to form CaCO₃.
  3. It continues until [CO₂] falls to 0.010 mol/L (as long as some CaO remains).

The system shifts left; [CO₂] drops to 0.010 mol/L and the mass of CaCO₃ increases.

Just for fun

Q is the most relatable letter in chemistry: it is never quite where it wants to be, but it always keeps moving toward its goal, K.

Hands-on activity

Q detective with the bean model

You need: 60 dried beans or buttons, two bowls labelled A and B, paper.

Use the bean model from the ICE Tables I lesson: each round, one third of the beans in A move to B and one sixth of the beans in B move to A (round to the nearest whole bean, halves up). For this model K = [B] ÷ [A] = 2.

  1. Start with A = 10 and B = 50. Calculate Q = B ÷ A and predict which bowl will gain beans.
  2. Run rounds until the counts stop changing. Was your prediction right? What is the final Q?
  3. Repeat with A = 50 and B = 10.

What to look for: in step 1, Q = 50 ÷ 10 = 5 > K, so you should predict a reverse shift (beans flow back into A). The counts go A 10 → 15 → 18 → 19 → 20 and stay at A = 20, B = 40, where Q = 2 = K. In step 3, Q = 0.2 < K, so beans flow into B until Q again settles near 2. Q always moves toward K.

Your turn

1

Write the expression for Q for 2 SO₂(g) + O₂(g) ⇌ 2 SO₃(g).

2

For H₂ + I₂ ⇌ 2 HI (K = 50.0), a mixture has [H₂] = [I₂] = 0.0500 mol/L and [HI] = 0.500 mol/L. Which way will it shift?

3

For N₂ + 3 H₂ ⇌ 2 NH₃, suppose K = 0.0579 at 500 °C. A mixture has [N₂] = 0.500 mol/L, [H₂] = 1.00 mol/L and [NH₃] = 0.100 mol/L. Predict the shift.

4

For PCl₅ ⇌ PCl₃ + Cl₂ (K = 0.0150), a mixture has [PCl₅] = 0.200, [PCl₃] = 0.0500 and [Cl₂] = 0.0600 mol/L. Is it at equilibrium?

5

If you remove some product from a system at equilibrium, what happens to Q, and which way does the system shift?

6

For H₂ + I₂ ⇌ 2 HI (K = 50.0), a flask starts with [HI] = 0.500 mol/L and [H₂] = [I₂] = 0.0100 mol/L. Find the equilibrium concentrations.

More practice: warm-up

1

How is Q different from K?

2

Q = 0.5 and K = 2.0. Which way does the system shift?

3

Q = 300 and K = 45. Which way does the system shift?

4

Q = K. What does that tell you?

5

A flask contains only reactants. What is Q, and which way must it shift?

More practice: on your own

1

For 2 SO₂ + O₂ ⇌ 2 SO₃, K = 180 at a certain temperature. A mixture has [SO₂] = 0.200, [O₂] = 0.100 and [SO₃] = 0.600 mol/L. Predict the shift and describe what happens to each concentration.

2

For N₂O₄(g) ⇌ 2 NO₂(g), Kp = 11.4 (kPa) at 25 °C. A sealed flask has P(NO₂) = 20.0 kPa and P(N₂O₄) = 50.0 kPa. Will the brown colour get darker or lighter?

3

For A(g) ⇌ 2 B(g), K = 0.50. A flask starts with [A] = 0.40 mol/L and [B] = 0.60 mol/L. Find the equilibrium concentrations.

4

For CO + H₂O ⇌ CO₂ + H₂ (K = 4.00), a mixture has 0.200 mol of each of the four gases in a 2.00 L flask. Predict the shift and find [CO₂] at equilibrium.

5

A student calculates Q = 0.0040 for a reaction with K = 0.0040 and writes "no reaction is happening". Correct the statement.

Challenge

1

For CaCO₃(s) ⇌ CaO(s) + CO₂(g), K = 0.010 at a certain temperature. 0.50 mol of CaCO₃ and no CO₂ are sealed in a 10.0 L container. How many moles of CaCO₃ decompose? What if the container were 100 L? 1000 L?

2

Show that adding an extra 0.100 mol/L of H₂ to an equilibrium mixture of H₂, I₂ and HI (K = 50.0) with [H₂] = [I₂] = 0.110 and [HI] = 0.780 mol/L makes Q < K. Which way will it shift?

3

A mixture of gases has Q = 2.0 × 10⁻⁶ for a reaction with K = 4.5 × 10³ at the same temperature, yet no change is seen after a week. Give a reason consistent with this lesson.

Check your understanding

Quiz

1.

If Q < K, the system will:

2.

For 2 NO₂ ⇌ N₂O₄ with K = 6.0, a mixture has [NO₂] = 0.50 and [N₂O₄] = 2.0 mol/L. Q is:

3.

For 2 NO₂(g) (brown) ⇌ N₂O₄(g) (colourless) with K = 6.0, a mixture has Q = 8.0. The system will:

4.

What is Q for a mixture that contains only products?

5.

A system with Q = K is:

6.

In an ICE table for a reaction that shifts left, the change row for the products is:

For parents and teachers

Big idea (E2.2, E2.4): Q is calculated like K but with the concentrations at any moment. Q < K → shift right; Q > K → shift left; Q = K → at equilibrium. Using Q first tells you the signs in the ICE table.

How to help: give your teen a K value and a few made-up mixtures; ask "which way will it go, and why?". They should answer by comparing numbers, not by guessing.

Common difficulties:

  • Inverting the ratio (reactants over products).
  • Forgetting coefficients as exponents in Q.
  • Using the wrong signs in the C row when the reaction runs in reverse.
  • Thinking Q = K means the reaction has stopped.

Looking ahead: in the next lesson, Q is the tool that explains Le Châtelier's principle.