How to Calculate the Equilibrium Constant Kc from Initial Concentrations and Equilibrium Data

The Problem

Find the equilibrium constant Kc:

For the reaction: N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

Initially, 0.500 mol of N₂ and 0.800 mol of H₂ are placed in a 2.00 L container. At equilibrium, the concentration of NH₃ is found to be 0.150 M.

Calculate the equilibrium constant Kc for this reaction at this temperature.

This is one of those classic equilibrium problems that shows up on every chemistry exam. You've got initial concentrations, you've got one equilibrium concentration, and you need to find Kc. It looks straightforward, but there are a lot of places to mess up.

The trick here is the ICE table. You need to track how concentrations change from initial to equilibrium, and that means keeping track of stoichiometry. One wrong coefficient and your whole answer is off. If you're stuck on a similar problem, you can always generate a custom video solution on Torial.

Understanding Equilibrium Constants

Chemical equilibrium diagram showing forward and reverse reactions

The equilibrium constant Kc tells you how far a reaction goes at equilibrium. For a general reaction:

aA + bB ⇌ cC + dD

Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ

Important things to remember:

Key points about Kc:

Only equilibrium concentrations go into Kc. Not initial concentrations.
Products in numerator, reactants in denominator. Always.
Concentrations are raised to their stoichiometric coefficients. That's where students mess up.
Kc has no units (technically, but we'll ignore that for now).
Pure solids and liquids don't appear in the expression. Only gases and aqueous solutions.

For our problem, the equilibrium expression is Kc = [NH₃]² / ([N₂][H₂]³). Notice how the coefficients become exponents. That 3 in front of H₂? It becomes a 3 in the exponent. If you need more help visualizing equilibrium, check out other chemistry videos in our library.

Setting Up the ICE Table

ICE stands for Initial, Change, Equilibrium. This is where you track how concentrations change. Let's break it down step by step.

Step 1: Calculate initial concentrations

We're given moles and volume. Convert to molarity:

[N₂]₀ = 0.500 mol / 2.00 L = 0.250 M

[H₂]₀ = 0.800 mol / 2.00 L = 0.400 M

[NH₃]₀ = 0 M (not present initially)

Step 2: Set up the ICE table

We know [NH₃] at equilibrium is 0.150 M. Since it started at 0, the change must be +0.150 M.

Species	Initial (M)	Change (M)	Equilibrium (M)
N₂	0.250	-x	0.250 - x
H₂	0.400	-3x	0.400 - 3x
NH₃	0	+2x	2x = 0.150

💡 Key Insight: The stoichiometry determines the change. For every 1 mole of N₂ that reacts, 3 moles of H₂ react, and 2 moles of NH₃ form.

Since 2x = 0.150 M, we get x = 0.075 M. Now we can find all equilibrium concentrations.

This is where a lot of students get tripped up. They forget that the change depends on the stoichiometric coefficients. If NH₃ increases by 0.150 M, and the coefficient is 2, then x = 0.075 M. But N₂ decreases by x (0.075 M), and H₂ decreases by 3x (0.225 M).

Finding All Equilibrium Concentrations

Now that we know x = 0.075 M, let's calculate all the equilibrium concentrations.

Equilibrium concentrations:

[N₂] = 0.250 - x = 0.250 - 0.075 = 0.175 M

[H₂] = 0.400 - 3x = 0.400 - 3(0.075) = 0.400 - 0.225 = 0.175 M

[NH₃] = 2x = 2(0.075) = 0.150 M ✓ (matches given)

⚠️ Check your work: Make sure all concentrations are positive. If you get a negative concentration, you probably messed up the signs in your ICE table.

Notice how both N₂ and H₂ ended up at the same concentration (0.175 M) even though they started different. That's just a coincidence from the numbers. Don't assume that always happens. Want to see more worked examples? Browse through hundreds of chemistry solutions on Torial.

Alternative Method: Solving the Quadratic

Sometimes you won't be given an equilibrium concentration directly. Instead, you might need to solve a quadratic equation. Let's see how that works.

If we didn't know [NH₃] at equilibrium:

We'd set up the equilibrium expression with x:

Kc = [NH₃]² / ([N₂][H₂]³)

Kc = (2x)² / [(0.250 - x)(0.400 - 3x)³]

Kc = 4x² / [(0.250 - x)(0.400 - 3x)³]

This would require solving a quartic equation, which is why problems usually give you one equilibrium concentration.

Most textbook problems are set up so you can avoid the messy algebra. They give you enough information to solve for x directly, like we did. But if you ever see a problem that requires solving a higher-order equation, check if you can use the quadratic formula or if there's a simplifying assumption you can make.

Calculating Kc from Equilibrium Concentrations

Equilibrium constant calculation with concentrations plugged into formula

Now we have everything we need. Plug the equilibrium concentrations into the Kc expression.

The equilibrium expression:

Kc = [NH₃]² / ([N₂][H₂]³)

Substituting our values:

Kc = (0.150)² / [(0.175)(0.175)³]

Kc = 0.0225 / [(0.175)(0.00536)]

Kc = 0.0225 / 0.000938

Kc = 23.99 ≈ 24.0

Final Answer:

Kc = 24.0

The equilibrium constant for N₂(g) + 3H₂(g) ⇌ 2NH₃(g) at this temperature is 24.0.

What this tells us:

Kc > 1 means products are favored at equilibrium
The reaction goes pretty far to the right under these conditions
At equilibrium, there's more NH₃ than you might expect from the initial amounts
This is the Haber process, used industrially to make ammonia

Notice how we kept three significant figures throughout, then rounded the final answer. That's good practice. Also, Kc has no units because we're using concentrations, but if you were using partial pressures (Kp), the units would cancel out the same way.

Common Mistakes to Avoid

Here are the mistakes that cost students the most points. Learn them now so you don't make them on test day. If you want personalized help avoiding these errors, create a custom study video for your specific problem.

❌ Mistake #1: Using Initial Concentrations in Kc

Plugging [N₂]₀, [H₂]₀, and [NH₃]₀ directly into the Kc expression. Kc only uses equilibrium concentrations, not initial ones.

Fix: Always use the equilibrium row from your ICE table. Never use the initial row.

❌ Mistake #2: Forgetting the Stoichiometric Coefficients

Writing Kc = [NH₃] / ([N₂][H₂]) instead of Kc = [NH₃]² / ([N₂][H₂]³). The coefficients become exponents.

Fix: Look at the balanced equation. The coefficient in front of each species becomes the exponent in Kc.

❌ Mistake #3: Messing Up the ICE Table Signs

Putting +x for reactants or -x for products. Reactants decrease (negative change), products increase (positive change).

Fix: Reactants always have negative changes, products always have positive changes. Always.

❌ Mistake #4: Not Accounting for Stoichiometry in Changes

Writing -x for H₂ instead of -3x. If 1 mole of N₂ reacts, 3 moles of H₂ must react too.

Fix: The change is always coefficient × x. If the coefficient is 3, the change is 3x.

❌ Mistake #5: Forgetting to Convert Moles to Molarity

Using moles directly in the ICE table instead of dividing by volume first. Kc uses concentrations, not amounts.

Fix: Always convert to molarity (mol/L) before setting up your ICE table.

❌ Mistake #6: Arithmetic Errors in the Final Calculation

Making calculation mistakes when plugging numbers into the Kc expression. Especially with the exponents and multiplication.

Fix: Work step by step. Calculate [H₂]³ first, then multiply by [N₂], then divide [NH₃]² by that result. Don't try to do it all at once.

❌ Mistake #7: Not Checking That Concentrations Make Sense

Getting negative concentrations or concentrations larger than initial amounts and not catching it.

Fix: Always check that 0 ≤ [equilibrium] ≤ reasonable max. If [N₂] = 0.250 initially, it can't be more than 0.250 at equilibrium.

Practice Problems with Video Solutions

Best way to get good at this? Practice. Try these similar problems and check your work with video solutions. You can also generate instant video explanations for any equilibrium problem you're working on.

Practice Problem 1: Different Reaction

For the reaction: 2NO(g) + O₂(g) ⇌ 2NO₂(g)

Initially, 0.200 mol NO and 0.150 mol O₂ are placed in a 1.00 L container. At equilibrium, [NO₂] = 0.080 M. Calculate Kc.

Hint: Set up your ICE table. Notice the coefficients are different from the main problem. Your answer should be around 8.5.

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Practice Problem 2: Reverse Direction

For the reaction: PCl₅(g) ⇌ PCl₃(g) + Cl₂(g)

Initially, 0.500 mol PCl₅ is placed in a 2.00 L container. At equilibrium, [PCl₃] = 0.100 M. Calculate Kc.

Hint: This one starts with only reactant. The ICE table will look different. Kc should be around 0.025.

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Practice Problem 3: With Initial Product

For the reaction: CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g)

Initially, [CO] = 0.100 M, [H₂O] = 0.200 M, and [CO₂] = 0.050 M in a 1.00 L container. At equilibrium, [H₂] = 0.080 M. Calculate Kc.

Hint: When products are present initially, your change might be negative for products. Think carefully about which direction the reaction goes. Kc ≈ 0.64.

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Practice Problem 4: Finding Initial Concentrations

For the reaction: H₂(g) + I₂(g) ⇌ 2HI(g), Kc = 50.2 at 448°C.

If 0.200 mol HI is placed in a 1.00 L container, what are the equilibrium concentrations? Then calculate Kc to verify.

Hint: This time you're working backwards. You'll need to solve a quadratic. The answer should give you Kc = 50.2 when you check.

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When to Use ICE Tables vs. Direct Calculation

Should you always set up an ICE table, or can you sometimes calculate Kc directly?

✓ Use ICE Tables When:

You're given initial concentrations and one equilibrium concentration
You need to find how much something changed
The problem asks for Kc from experimental data
You're working with a reaction that hasn't reached equilibrium yet

✓ Calculate Directly When:

You're given all equilibrium concentrations
The problem just asks you to plug numbers into the Kc expression
You're verifying a Kc value you already calculated
You're working backwards from Kc to find concentrations

For this problem? ICE table is essential. We had initial amounts and one equilibrium concentration, so we needed to track the changes. Without the ICE table, you'd have no way to figure out what the other equilibrium concentrations are. When you're juggling multiple concepts, it helps to have a step-by-step video walkthrough that shows exactly when to use each method.