Equilibrium Position: Relative Amounts at Equilibrium
What is a Reversible Reaction?
Imagine a busy playground with a seesaw. Children are constantly getting on and off, making the seesaw tip back and forth. A reversible chemical reaction is similar. It is a reaction that can go in both the forward direction (reactants turning into products) and the reverse direction (products turning back into reactants).
A general reversible reaction is written as:
Here, A and B are reactants, C and D are products, and the double arrow ($\rightleftharpoons$) indicates the reaction is reversible. The lowercase letters (a, b, c, d) are the stoichiometric coefficients[1].
Initially, only reactants are present, so the forward reaction is fastest. As products form, the reverse reaction begins and speeds up. Eventually, the rate[2] of the forward reaction equals the rate of the reverse reaction. At this point, the reaction has reached dynamic equilibrium. The amounts of each substance stop changing, but the reactions haven't stopped—they are still happening at equal rates.
Defining the Equilibrium Position with K
The equilibrium position is quantitatively described by the equilibrium constant, K. It is a number that compares the concentrations of products to reactants at equilibrium.
For our general reaction $aA + bB \rightleftharpoons cC + dD$, the equilibrium constant expression is:
$K = \frac{[C]^c [D]^d}{[A]^a [B]^b}$
The square brackets [ ] represent the molar concentration (in mol/L) of each substance at equilibrium. The concentrations are raised to the power of their coefficients from the balanced equation.
The magnitude of K tells us about the equilibrium position:
- K >> 1 (K is very large): The numerator (products) is much larger than the denominator (reactants). At equilibrium, there are mostly products. We say the equilibrium position "lies to the right" or "favors the products."
- K << 1 (K is very small): The denominator (reactants) is much larger than the numerator. At equilibrium, there are mostly reactants. The equilibrium position "lies to the left" or "favors the reactants."
- K ≈ 1: The amounts of products and reactants are comparable at equilibrium.
Critical Point: The value of K depends only on temperature. It does not change if you change the starting amounts of reactants or add a catalyst. A catalyst only helps you reach equilibrium faster; it does not change the final relative amounts.
How Starting Conditions Affect Final Amounts
While K is constant, the actual equilibrium concentrations of each substance depend on what you start with. Think of K as a fixed target ratio. You can reach that target ratio from different starting points.
Let's use a simple example: $H_2 + I_2 \rightleftharpoons 2HI$. Suppose at a certain temperature, K = $64$.
The equilibrium expression is: $K = \frac{[HI]^2}{[H_2][I_2]} = 64$.
The table below shows how different initial mixtures all converge to meet this K = 64 ratio, but the final amounts (equilibrium concentrations) are different.
| Initial Concentrations (mol/L) | Equilibrium Concentrations (mol/L) | Check K = [HI]2/([H2][I2]) |
|---|---|---|
| [H2] = 1.0, [I2] = 1.0, [HI] = 0 | [H2] = 0.2, [I2] = 0.2, [HI] = 1.6 | (1.6)2 / (0.2 * 0.2) = 2.56 / 0.04 = 64 |
| [H2] = 2.0, [I2] = 0.5, [HI] = 0 | [H2] = 1.56, [I2] = 0.06, [HI] = 0.88 | (0.88)2 / (1.56 * 0.06) = 0.7744 / 0.0936 ≈ 64 |
| [H2] = 0, [I2] = 0, [HI] = 2.0 | [H2] = 0.23, [I2] = 0.23, [HI] = 1.54 | (1.54)2 / (0.23 * 0.23) = 2.37 / 0.0529 ≈ 64 |
Notice that no matter what we start with, the final concentrations always satisfy K = 64. However, the absolute amount of HI at equilibrium is different in each case. This shows the difference between the equilibrium constant (K, which is fixed) and the equilibrium concentrations (which are variable but always related by K).
Shifting the Position: Le Chatelier's Principle
What happens if we disturb an equilibrium system? French chemist Henri Le Chatelier gave us a rule: If a stress[3] is applied to a system at equilibrium, the system will shift in a direction that relieves that stress.
This "shift" changes the relative amounts of reactants and products temporarily until a new equilibrium is established. Importantly, the value of K only changes if the temperature changes. For other stresses, K stays the same, but the system finds new equilibrium concentrations that still equal that same K.
Common stresses and how the equilibrium position shifts:
- Changing Concentration: Adding more reactant causes the system to shift toward products to use up the extra reactant. Adding more product causes a shift toward reactants.
- Changing Pressure (for gases): Increasing pressure by decreasing volume shifts the equilibrium toward the side with fewer moles of gas. Decreasing pressure shifts it toward the side with more moles of gas.
- Changing Temperature: This is the only change that alters K. For an endothermic reaction (absorbs heat), increasing temperature shifts equilibrium toward products (K increases). For an exothermic reaction (releases heat), increasing temperature shifts equilibrium toward reactants (K decreases).
Applying Equilibrium: The Haber Process for Ammonia
A classic real-world application is the Haber Process, which produces ammonia $(NH_3)$ from nitrogen and hydrogen gas. This ammonia is vital for fertilizers.
The reaction is: $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)} + \text{heat}$
This equation tells us key facts: 1) It's reversible, 2) It's exothermic (releases heat), and 3) The left side has 4 moles of gas (1 $N_2$ + 3 $H_2$), while the right side has 2 moles of gas (2 $NH_3$).
Chemists use Le Chatelier's Principle to maximize the yield of ammonia (shift equilibrium to the right):
- Pressure: Use high pressure (~200 atmospheres). This favors the side with fewer gas moles—the product side—shifting the equilibrium position to the right, producing more $NH_3$.
- Temperature: The reaction is exothermic, so low temperature would favor the product side. However, too low a temperature makes the reaction extremely slow. A compromise temperature (~450°C) is used to get a reasonable reaction speed while still getting a decent yield.
- Concentration: Continuously removing the ammonia product as it forms shifts the equilibrium to the right to make more. Also, using an excess of the less expensive reactant (hydrogen) helps drive the reaction forward.
This process perfectly illustrates the practical manipulation of the equilibrium position to achieve a desired relative amount of product.
Important Questions
Q1: If the equilibrium constant K is very large, does that mean there are zero reactants left at equilibrium?
No. A very large K means the concentration of products is much, much greater than the concentration of reactants. However, there are always some reactants present due to the dynamic nature of equilibrium. The reverse reaction never completely stops, so a tiny, often immeasurable, amount of reactants will always exist.
Q2: Does adding a catalyst change the equilibrium position or the value of K?
No. A catalyst speeds up both the forward and reverse reactions by the same factor. It helps the system reach equilibrium faster but does not change the final relative amounts of reactants and products. Therefore, it does not change the equilibrium position or the value of the equilibrium constant K.
Q3: Can you have different equilibrium positions for the same reaction?
You must be careful with terminology. The "equilibrium position" is often spoken of qualitatively (e.g., "it favors products"). In that sense, for a given temperature, there is only one K, so one fundamental position. However, the actual amounts or concentrations at equilibrium can vary widely depending on the starting concentrations, as shown in the HI example table. So while the ratio defined by K is fixed, the specific point where the system lands on that ratio can be different.
Footnote
[1] Stoichiometric coefficients: The numbers written in front of chemical formulas in a balanced equation. They show the ratio in which molecules react and are formed.
[2] Rate: The speed of a chemical reaction, often measured as how quickly the concentration of a reactant decreases or a product increases over time.
[3] Stress (in Le Chatelier's context): A change imposed on a system at equilibrium, such as a change in concentration, pressure, or temperature.