Calculating with $K_c$ and $K_p$

10 minAS Level7.1.7

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

By the end of this lesson

By the end you can calculate $K_c$ from equilibrium amounts in a known volume, calculate $K_p$ from mole fractions and a total pressure, and decide which routine a question is asking for.

The two routines

Every calculation in this topic follows one of two paths.

For $K_c$ : amounts → concentrations (divide by volume) → substitute → answer.

For $K_p$ : amounts → mole fractions (divide by total moles) → partial pressures (multiply by total pressure) → substitute → answer.

In both cases the substitution step is identical; only the preparation differs.

Three checks before you substitute

Most lost marks in these calculations are not chemistry errors. They are these three:

Is the equation balanced? Every coefficient becomes a power, so an unbalanced equation poisons the whole calculation.
Are these equilibrium amounts? The expression only accepts what is present at equilibrium, never what you started with.
Have you converted units? A volume in $\text{cm}^3$ must be divided by 1000 to give $\text{dm}^3$ ; a total pressure in $\text{kPa}$ must be used consistently.

Worked example: Worked example: $K_c$ from equilibrium concentrations

Hydrogen and iodine are mixed in a $1.00\ \text{dm}^3$ flask at $700\ \text{K}$ :

$\text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2\text{HI}(g)$

Initially there is $1.00\ \text{mol}$ of each reactant. At equilibrium the flask contains $1.80\ \text{mol}$ of $\text{HI}$ . Calculate $K_c$ .

Have a go first?

Worked example: Worked example: $K_c$ when the volume is not 1

Nitrogen dioxide is sealed in a $2.00\ \text{dm}^3$ vessel and equilibrates:

$2\text{NO}_2(g) \rightleftharpoons \text{N}_2\text{O}_4(g)$

Initially there is $2.00\ \text{mol}$ of $\text{NO}_2$ . At equilibrium $0.60\ \text{mol}$ of $\text{NO}_2$ remains. Calculate $K_c$ .

Have a go first?

Worked example: Worked example: $K_p$ from mole fractions

At equilibrium a mixture of $\text{SO}_2$ , $\text{O}_2$ and $\text{SO}_3$ has mole fractions $0.20$ , $0.40$ and $0.40$ respectively. The total pressure is $2.0\ \text{atm}$ . Calculate $K_p$ for

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

Have a go first?

Reading a question for the right routine

Look at what the question supplies before deciding which constant it wants.

Given	Use
amounts and a volume	$K_c$
concentrations directly	$K_c$
partial pressures	$K_p$
mole fractions and total pressure	$K_p$
amounts and total pressure, no volume	$K_p$

If a volume is given but the question asks for $K_p$ , the volume is a distraction — mole fractions do not need it.

Common mistakes

Moles can be substituted directly into a $K_c$ expression.

$K_c$ requires concentrations, so divide amounts by the volume in $\text{dm}^3$ first.

In the exam

Write the expression before substituting; method marks are awarded for it.
Divide by the volume in $\text{dm}^3$ (not $\text{cm}^3$ ) for $K_c$ , and show the division.
Round only at the end, and give the same number of significant figures as the least precise datum.
For $K_p$ , show the mole fraction calculation and the multiplication by total pressure separately.
State the units of $K_p$ ; do not invent units for $K_c$ .

Checking the idea

Multiple choiceQuestion 1 · Apply

Answer the 3 questions above to continue.