Writing $K_p$ expressions

10 minAS Level7.1.6

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can write a $K_p$ expression from a balanced gas equation, work out its units, and evaluate it from partial pressures.

The same idea, measured differently

Concentrations work well for solutions. For gases, though, the pressure of each gas is what a chemist usually measures and controls.

So there is a second equilibrium constant, $K_p$ , built from partial pressures. It has exactly the same structure as $K_c$ — only the quantity in the brackets changes.

Definition

Equilibrium constant, $K_p$

For the gas equilibrium

$a\text{A}(g) + b\text{B}(g) \rightleftharpoons c\text{C}(g) + d\text{D}(g)$

the equilibrium constant in terms of partial pressures is

$K_p = \frac{p_{\text{C}}^{\,c}\, p_{\text{D}}^{\,d}}{p_{\text{A}}^{\,a}\, p_{\text{B}}^{\,b}}$

Here $p$ means the equilibrium partial pressure of that gas, in $\text{atm}$ or $\text{Pa}$ (or $\text{kPa}$ ).

Working out the units

$K_p$ usually has units, because pressures have units and they appear to different powers on the top and bottom. Treat the units exactly like algebraic symbols.

For the Haber equilibrium:

$K_p = \frac{p_{\text{NH}_3}^{\,2}}{p_{\text{N}_2}\, p_{\text{H}_2}^{\,3}}$

$\text{units} = \frac{\text{atm}^2}{\text{atm} \times \text{atm}^3} = \frac{\text{atm}^2}{\text{atm}^4} = \text{atm}^{-2}$

For $2\text{SO}_2(g) + \text{O}_2(g) \rightleftharpoons 2\text{SO}_3(g)$ :

$K_p = \frac{p_{\text{SO}_3}^{\,2}}{p_{\text{SO}_2}^{\,2}\, p_{\text{O}_2}} \qquad \text{units} = \frac{\text{atm}^2}{\text{atm}^3} = \text{atm}^{-1}$

When the powers on top and bottom are equal, as in $\text{H}_2 + \text{I}_2 \rightleftharpoons 2\text{HI}$ , the units cancel and $K_p$ has no units.

Worked example: Worked example: $K_p$ for the Haber equilibrium

At $700\ \text{K}$ an equilibrium mixture of nitrogen, hydrogen and ammonia has partial pressures

$p_{\text{N}_2} = 2.0\ \text{atm} \qquad p_{\text{H}_2} = 6.0\ \text{atm} \qquad p_{\text{NH}_3} = 4.0\ \text{atm}$

Write the $K_p$ expression, state its units, and calculate $K_p$ to 2 significant figures.

Have a go first?

Worked example: Worked example: a heterogeneous gas equilibrium

Carbon dioxide reacts with carbon at high temperature:

$\text{CO}_2(g) + \text{C}(s) \rightleftharpoons 2\text{CO}(g)$

At equilibrium $p_{\text{CO}_2} = 0.20\ \text{atm}$ and $p_{\text{CO}} = 0.60\ \text{atm}$ . Write the $K_p$ expression and calculate $K_p$ .

Have a go first?

Which constant should you use?

Use whichever constant matches the data you are given. Moles and volumes point to $K_c$ ; partial pressures or a total pressure with mole fractions point to $K_p$ .

You do not need to convert between them: the relationship between $K_p$ and $K_c$ is outside the 9701 syllabus.

Common mistakes

$K_p$ uses the total pressure of the mixture.

It uses the partial pressure of each gas, raised to its own coefficient. The total pressure only enters through mole fractions.

$K_p$ is always unitless because constants are just numbers.

In the exam

Use $p$ with a subscript for each gas, and never square brackets in a $K_p$ expression.
Give units unless the powers cancel; examiners often award a separate mark for them.
Substitute into the expression before doing any arithmetic, so the working is visible.
Check the equation is balanced first — a wrong coefficient gives a wrong power and a wrong unit.
Leave out any species marked $(s)$ or $(l)$ .

Checking the idea

Multiple choiceQuestion 1 · Apply

Answer the 3 questions above to continue.