The Equilibrium Constant Kc – Part 1 (OCR A-Level Chemistry A): Revision Notes

The Equilibrium Constant Kc – Part 1

Understanding equilibrium position

In your previous studies, you learned that dynamic equilibrium is reached when the forward and reverse reactions proceed at the same rate. You also explored how changing conditions like concentration, temperature, and pressure can shift the position of equilibrium. However, these changes only tell us the direction of the shift, not the exact quantities of substances present at equilibrium.

This is where the equilibrium constant comes in. The equilibrium constant, represented by $K_c$, provides a precise mathematical way to describe the position of equilibrium. Rather than simply saying "equilibrium shifts to the right", we can calculate an actual value that tells us exactly how much product and reactant are present when equilibrium is established.

The size of the equilibrium constant is particularly useful because it indicates the relative proportions of reactants and products in the equilibrium mixture. A large Kc value tells us that products predominate, while a small Kc value indicates that reactants are more abundant at equilibrium.

The equilibrium law

The equilibrium law provides a mathematical relationship that allows us to work out the equilibrium constant for any reversible reaction. This law states that we can write an expression for $K_c$ using the equilibrium concentrations of all the substances involved in the reaction.

General expression for $K_c$

Consider a general reversible reaction:

$aA + bB \rightleftharpoons cC + dD$

where $a$, $b$, $c$, and $d$ are the balancing numbers (stoichiometric coefficients) in the balanced equation.

The equilibrium law defines $K_c$ as:

$K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} = \frac{\text{[products]}}{\text{[reactants]}}$

Understanding the notation

Several important points about this expression:

• Square brackets $[ \ ]$ are shorthand notation meaning "concentration of" (measured in $\text{mol dm}^{-3}$)
• The letters $A$, $B$, $C$, and $D$ represent the chemical species (reactants and products)
• The superscripts $a$, $b$, $c$, and $d$ are the balancing numbers from the chemical equation
• Equilibrium concentrations must be used - the expression only applies once equilibrium has been reached

Example: nitrogen and oxygen forming nitrogen monoxide

For the reaction:

$\ce{N2(g) + O2(g) \rightleftharpoons 2NO(g)}$

The equilibrium constant expression is:

$K_c = \frac{[\ce{NO(g)}]^2}{[\ce{N2(g)}] [\ce{O2(g)}]}$

Notice that:

• $\ce{NO}$ appears squared because its balancing number is 2
• $\ce{N2}$ and $\ce{O2}$ have no visible powers because their balancing numbers are 1
• All species are in the gas phase, indicated by (g)

Calculating $K_c$ from equilibrium concentrations

To find the value of an equilibrium constant, you need to know the equilibrium concentrations of all reactants and products. The calculation then follows a straightforward two-step process.

Worked example 1: the hydrogen iodide system

Worked example 2: the ammonia system

Interpreting $K_c$ values

The two examples above gave us very different $K_c$ values: 54.2 and 0.166. But what do these numbers actually tell us about the equilibrium systems? The size of $K_c$ provides crucial information about the relative proportions of reactants and products present at equilibrium.

What different $K_c$ values mean

The value of $K_c$ acts as an indicator of where the equilibrium position lies:

When Kc = 1: The equilibrium position is approximately halfway between reactants and products. This means there are roughly similar amounts of reactants and products present at equilibrium.

When Kc > 1: The equilibrium position lies towards the products. The larger the value above 1, the more the equilibrium favours product formation. For example, the value of 54.2 in worked example 1 tells us that the hydrogen iodide system contains predominantly products at equilibrium - there is much more $\ce{HI}$ than $\ce{H2}$ and $\ce{I2}$.

When Kc < 1: The equilibrium position lies towards the reactants. The smaller the value below 1, the more the equilibrium favours the reactants. For example, the value of 0.166 in worked example 2 indicates that, even at 400°C, the ammonia synthesis equilibrium contains more reactants than products - there is more $\ce{N2}$ and $\ce{H2}$ remaining than $\ce{NH3}$ produced.

The relationship between $K_c$ and equilibrium position

To summarize: the larger the value of Kc, the further the equilibrium position lies to the right-hand side of the equation. This means greater concentrations of products compared to reactants. Conversely, very small $K_c$ values indicate that the equilibrium mixture consists mainly of unreacted starting materials.

This relationship is particularly useful in industrial chemistry, where manufacturers want to maximize product yield. By measuring $K_c$, chemists can predict whether a reaction will be economically viable and what conditions might shift the equilibrium to produce more product.

Exam focus checklist

✓ Can you write a correct $K_c$ expression for any given reversible reaction?

✓ Do you understand that balancing numbers become powers, not multiplication factors?

✓ Can you substitute equilibrium concentrations correctly and calculate $K_c$?

✓ Can you interpret what a $K_c$ value tells you about the position of equilibrium?

✓ Do you know the difference between $K_c = 1$, $K_c > 1$, and $K_c < 1$?

✓ Can you work confidently with scientific notation in equilibrium calculations?

✓ Remember: only equilibrium concentrations are used in $K_c$ expressions, never initial concentrations