How to find equilibrium concentration using ICE table and Kc formula with examples
When we talk about a balanced chemical reaction, we mean that each element has an equal number of atoms on both sides of the equation. These balanced chemical reactions form the basis for the concept of equilibrium concentration. We say that a chemical is in an equilibrium concentration when the products and reactants do not change as time moves on. In other words, chemical equilibrium or equilibrium concentration is a state when the rate of forward reaction in a chemical reaction becomes equal to the rate of backward reaction. At the same time, there is no change in the products and reactants, and it seems that the reaction has stopped.
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It can be understood from the graph above, that initially, the concentration of the product is zero. Still, with time, the concentration of the product increases and the concentration of the reactant decreases as it is getting consumed. After some time, the concentration does not change any further. Then it is said that the reaction is in equilibrium concentration. We will now see how to calculate equilibrium concentration using the equilibrium concentration equation.
Equilibrium Constant Kc
To understand how to calculate equilibrium concentration using the equilibrium concentration equation, you need to know the formula for equilibrium constant Kc. When the chemical is in equilibrium, the ratio of the products to the reactants is called the equilibrium constant.
Consider a chemical reaction,
aA +bB cC + dD
For this equation, the equilibrium constant is defined as:
\[K_{c}\] = \[\frac{[c]^{c} [D]^{d}}{[A]^{a} [B]^{b}}\]
The ICE Table
The simplest way of finding the equilibrium concentration equation is by adopting the ICE table. It is an organised table to identify what quantity of products and reactants are given and what quantity needs to be found. The equilibrium constant and table will be very beneficial when we look at how to calculate equilibrium concentration.
‘I’ stands for initial concentration.
‘C’ stands for the change in concentrations.
‘E’ stands for equilibrium concentration.
Steps to Calculate Equilibrium Concentration
There are a few steps that need to be carried out to find the equilibrium concentration of a chemical reaction. The steps are as below.
The first step is to write down the balanced equation of the chemical reaction. aA +bB cC + dD
The second step is to convert the concentration of the products and the reactants in terms of their Molarity.
The third step is to form the ICE table and identify what quantities are given and what all needs to be found.
ICE Table
Now using the formula for equilibrium constant, we will obtain an equation in terms of the unknown variable ‘x’.
\[K_{c}\] = \[\frac{[c]^{c} [D]^{d}}{[A]^{a} [B]^{b}}\]
The last step is to solve the quadratic equation to find the value of ‘x’.
Now that you know how to calculate equilibrium concentration let’s look at some solved problems for better understanding.
Solved Problems
Question 1) Find the equilibrium concentration of 6 moles of PCl5 is kept in a 1L vessel at 300K temperature. Assume Kc to be equal to 1.
Answer 1) the first step is to write the chemical reactions
PCl5PCl3+Cl2
PCl5 = 6 moles
Concentration of PCl5 = 6 moles / 1L = 6 M
Using Kc formula, we get,
\[K_{c}\] = \[\frac{[c]^{c} [D]^{d}}{[A]^{a} [B]^{b}}\]
\[K_{c}\] = \[\frac{[PCI_{3}][Cl_{2}]}{[PCI_{5}]}\]
1 = \[\frac{x * x}{(6 - x)}\]
\[x^{2}\] + x - 6 = 0
Upon solving the quadratic equation, we get, x = 2, and x = -3.
X cannot be a negative number, therefore x = 2.
Substituting the value of x we get,
[PCl5] = 6 – x = 6 – 2 = 4M
[PCl3] = [Cl2] = x = 2M
Question 2) Find the concentration for each substance in the following reaction.
C2H4 + H4 C2H6
Using Kc formula, we get,
\[K_{c}\] = \[\frac{[c]^{c} [D]^{d}}{[A]^{a} [B]^{b}}\]
\[K_{c}\] = \[\frac{[C_{2} H_{6}]}{[C_{2}H_{4}][H_{2}]}\]
0.98 = \[\frac{x}{(0.33 - x)(0.53-x)}\]
0.98 = \[\frac{x}{x^{2} - 0.86x\: +\: 0.1749}\]
0.98(\[x^{2}\] - 0.86x + 0.1749) = x
0.98\[x^{2}\] - 1.8428x + 0.1714 = 0
Upon solving the quadratic equation, we get, x = 1.78, and x = 0.098.
Let x = 1.78,
[C2H4] = 0.33 – 1.78 = -1.45,
The concentration cannot be negative; hence we discard x = 1.78.
Let x = 0.098,
[C2H4] = 0.33 – 0.098= 0.23,
Therefore, we get the following equilibrium concentration,
[C2H4] = 0.23M
[H2] = 0.43M
[C2H6] = 0.098M.
FAQs on Calculating Equilibrium Concentration in Chemical Reactions
1. What is equilibrium concentration in chemistry?
The equilibrium concentration is the constant concentration of reactants and products in a reversible reaction when the system has reached dynamic equilibrium. At this point:
- The forward and reverse reaction rates are equal.
- The concentrations of all species remain constant over time.
- The reaction has not stopped; it is in dynamic equilibrium.
2. How do you calculate equilibrium concentration using an ICE table?
You calculate equilibrium concentration using an ICE table (Initial, Change, Equilibrium) by expressing concentration changes with a variable and solving using the equilibrium constant expression.
- I: Write initial concentrations.
- C: Represent changes using +x or −x based on stoichiometry.
- E: Add changes to initial values.
- Substitute equilibrium values into the Kc expression and solve for x.
3. What is the formula for calculating equilibrium concentration?
The formula for calculating equilibrium concentration comes from the equilibrium constant expression (Kc), which is the ratio of product concentrations to reactant concentrations, each raised to their stoichiometric coefficients.
- For aA + bB ⇌ cC + dD
- Kc = [C]c[D]d / [A]a[B]b
4. How do you calculate equilibrium concentration from Kc?
To calculate equilibrium concentration from Kc, substitute the equilibrium expressions (from an ICE table) into the Kc formula and solve for the unknown variable.
- Write the balanced equation.
- Set up an ICE table.
- Express equilibrium concentrations in terms of x.
- Substitute into the Kc expression.
- Solve for x and calculate final concentrations.
5. How do you find equilibrium concentration from initial concentration?
You find equilibrium concentration from initial concentration by using stoichiometric changes and the equilibrium constant expression.
- Start with initial molar concentrations.
- Use stoichiometric ratios to define changes (±x).
- Write equilibrium concentrations.
- Substitute into Kc and solve for x.
6. Can you give an example of calculating equilibrium concentration?
Yes, equilibrium concentration can be calculated using an ICE table and the equilibrium constant expression.
- Reaction: N2O4(g) ⇌ 2NO2(g)
- Suppose initial [N2O4] = 1.0 M, [NO2] = 0 M, and Kc = 4.0.
- ICE: N2O4: 1.0 − x; NO2: 2x
- Kc = (2x)2 / (1.0 − x) = 4.0
- Solve: 4x2 / (1.0 − x) = 4.0
7. What is the difference between initial concentration and equilibrium concentration?
The initial concentration is the amount of reactant or product present before the reaction proceeds, while the equilibrium concentration is the constant amount present when the system reaches dynamic equilibrium.
- Initial concentration: measured at time zero.
- Equilibrium concentration: measured after forward and reverse rates are equal.
- Values usually differ unless the system starts at equilibrium.
8. How does Le Chatelier’s principle affect equilibrium concentration?
According to Le Chatelier’s principle, a system at equilibrium shifts to oppose any imposed change, altering equilibrium concentrations.
- Adding reactant shifts equilibrium toward products.
- Increasing pressure favors the side with fewer gas moles.
- Increasing temperature favors the endothermic direction.
9. Do solids and liquids affect equilibrium concentration calculations?
Pure solids and liquids do not appear in the equilibrium constant expression and therefore do not affect equilibrium concentration calculations.
- Their concentrations are constant.
- Only gases (g) and aqueous (aq) species are included in Kc.
10. What are common mistakes when calculating equilibrium concentration?
Common mistakes when calculating equilibrium concentration include incorrect stoichiometry, forgetting exponents in K expressions, and including solids or liquids in the equilibrium constant.
- Not balancing the chemical equation first.
- Using wrong powers in Kc (must match coefficients).
- Ignoring units (usually mol·L−1).
- Failing to check approximation validity when simplifying quadratic equations.
