Stepwise Method and Practice Problems for Equilibrium Concentration
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 How to Calculate Equilibrium Concentration in Chemistry
1. What is the main method for calculating equilibrium concentrations from initial values?
The most common method to calculate equilibrium concentrations is by using an ICE table. This involves a systematic, three-step approach:
- I (Initial): Write down the initial concentrations of all reactants and products.
- C (Change): Determine the change in concentration for each species as the reaction moves towards equilibrium. This change is typically represented by a variable, like 'x', and is based on the stoichiometric coefficients from the balanced chemical equation.
- E (Equilibrium): Calculate the equilibrium concentrations by adding the change (C) to the initial concentration (I) for each species. These expressions are then substituted into the equilibrium constant (Kc) expression to solve for 'x'.
2. What is an ICE table and what does each part stand for?
An ICE table is a simple organizational tool used in chemistry to solve equilibrium problems. It helps track the concentrations of reactants and products throughout the reaction. The acronym ICE stands for:
- I - Initial Concentration: The concentration of each substance before the reaction starts to move towards equilibrium.
- C - Change in Concentration: The amount by which each concentration changes to reach equilibrium. Reactants decrease (e.g., -x) and products increase (e.g., +x), with the change being proportional to the reaction's stoichiometry.
- E - Equilibrium Concentration: The final concentration of each substance once the system has reached equilibrium. It is calculated as (Initial + Change).
3. How are equilibrium concentrations typically represented or symbolised in chemistry?
In chemistry, the molar concentration of a substance at equilibrium is represented by enclosing its chemical formula in square brackets. For example, for a reaction involving nitrogen (N₂), hydrogen (H₂), and ammonia (NH₃), their equilibrium concentrations are denoted as [N₂], [H₂], and [NH₃] respectively.
4. How does changing the concentration of a substance affect a system at equilibrium?
According to Le Chatelier's Principle, if the concentration of a substance in a system at equilibrium is changed, the system will shift to counteract that change. Specifically:
- If you increase the concentration of a reactant, the equilibrium will shift to the right, favouring the formation of more products.
- If you increase the concentration of a product, the equilibrium will shift to the left, favouring the formation of more reactants.
The system adjusts its equilibrium concentrations to re-establish the equilibrium constant (Kc) ratio.
5. What are the typical units used for molar equilibrium concentration?
The standard unit for molar equilibrium concentration is moles per litre, which is commonly abbreviated as mol/L or M (Molarity). When using the equilibrium constant expression (Kc), all concentrations must be expressed in these units.
6. Why don't the concentrations of reactants and products have to be equal at equilibrium?
Equilibrium is a dynamic state where the rate of the forward reaction equals the rate of the reverse reaction, not a state where the amounts of substances are equal. The specific concentrations at which these rates become equal depend on the reaction's intrinsic properties, summarised by the equilibrium constant (Kc). For most reactions, this balance point is reached when concentrations of reactants and products are unequal.
7. What is the role of the reaction quotient (Qc), and how is it different from the equilibrium constant (Kc)?
The reaction quotient (Qc) is a measure of the relative amounts of products and reactants present in a reaction at any given time, not necessarily at equilibrium. The equilibrium constant (Kc) is the value of the reaction quotient specifically when the system is at equilibrium. By comparing Qc to Kc, we can predict the direction a reaction will shift:
- If Qc < Kc, the ratio of products to reactants is too small. The reaction will proceed to the right (towards products).
- If Qc > Kc, the ratio of products to reactants is too large. The reaction will proceed to the left (towards reactants).
- If Qc = Kc, the system is already at equilibrium.
8. In the ICE table method, what does the 'x' represent and why is it related to stoichiometry?
In an ICE table, 'x' represents the change in molar concentration of one of the reactants or products as the system moves towards equilibrium. It is directly related to stoichiometry because the balanced chemical equation dictates the mole ratio in which substances react and are formed. For example, in the reaction N₂(g) + 3H₂(g) ⇌ 2NH₃(g), if the change in [N₂] is -x, the change in [H₂] must be -3x, and the change in [NH₃] must be +2x, reflecting their stoichiometric coefficients.
9. Can you calculate equilibrium concentrations if the equilibrium constant (Kc) is not given?
Yes, it is possible under certain conditions. You can calculate the equilibrium concentrations of all species without Kc if you are provided with the initial concentrations of all substances and the equilibrium concentration of at least one substance. By knowing the initial and final concentration of one species, you can determine the change ('x'). Using stoichiometry, you can then apply this change to calculate the equilibrium concentrations of all other reactants and products.
10. How does the magnitude of the equilibrium constant (Kc) provide clues about the equilibrium concentrations?
The magnitude of Kc indicates the extent to which a reaction proceeds towards products at equilibrium:
- If Kc is very large (Kc >> 1), the equilibrium lies to the right. This means the equilibrium concentrations of the products will be much greater than the concentrations of the reactants. The reaction nearly goes to completion.
- If Kc is very small (Kc << 1), the equilibrium lies to the left. This means the equilibrium concentrations of the reactants will be much greater than the concentrations of the products. The reaction barely proceeds.
