Chemistry » Chemical Equilibrium » The Equilibrium Constant

# Calculating Equilibrium Constant

## Calculating the equilibrium constant

When calculations involving the equilibrium constant are done, the following tips may help:

1. Always read the question carefully to be sure that you understand what you have been asked to calculate.

2. If the equilibrium constant is involved, make sure that the concentrations you use are the concentrations at equilibrium, and not the concentrations or quantities that are present at some other time in the reaction.

3. When you are doing more complicated calculations, it helps to draw up a RICE table (shown in next lesson). This is gone into in more detail later in this section.

Remember that the general form of the expression for $$\text{K}_{\text{c}}$$ of a reaction at chemical equilibrium (a$$\color{orange}{\text{A}}$$ + b$$\color{orange}{\text{B}}$$ $$\leftrightharpoons$$ c$$\color{purple}{\text{C}}$$ + d$$\color{purple}{\text{D}}$$) is:

$\text{K}_{\text{c}} = \dfrac{{[\color{purple}{\text{C}}\text]}^{c}{[\color{purple}{\text{D}}\text]}^{d}}{{[\color{orange}{\text{A}}\text]}^{a}{[\color{orange}{\text{B}}\text]}^{b}}$

## Example: Writing Expressions for $$\text{K}_{c}$$

### Question

For the reaction:

$$9\text{X}(\text{g}) + \text{Y}_{3}(\text{g})$$ $$\rightleftharpoons$$ $$3\text{X}_{3}\text{Y}(\text{g})$$

Write an expression for the equilibrium constant $${\text{K}}_{\text{c}}$$.

### Step 1: Write the general expression for $${\text{K}}_{\text{c}}$$

$\text{K}_{\text{c}}=\dfrac{\text{[C]}^{c}{\text{[D]}}^{d}}{\text{[A]}^{a}{\text{[B]}}^{b}}$

### Step 2: Determine the reactants and the products of the reaction

X(g) and $$\text{Y}_{3}(\text{g})$$ are both reactants. They are gases and will be included in the expression.

$$\text{X}_{3}\text{Y}(\text{g})$$ is a product. It is a gas and will be included in the expression.

### Step 3: Write the general expression for $$\text{K}_{\text{c}}$$ for this reaction

$\text{K}_{\text{c}}=\dfrac{\text{[X}_{3}{\text{Y]}}^{z}}{\text{[X]}^{x}{\text{[Y}}_{3}{\text{]}}^{y}}$

### Step 4: What are the coefficients in the balanced equation?

The compound $$\text{X}$$ has a coefficient of 9. The compound $$\text{Y}_{3}$$ has a coefficient of 1. The compound $$\text{X}_{3}\text{Y}$$ has a coefficient of 3.

### Step 5: Write the expression for $$\text{K}_{\text{c}}$$ for this reaction

$\text{K}_{\text{c}}=\dfrac{\text{[X}_{3}{\text{Y]}}^{3}}{\text{[X]}^{9}{\text{[Y}}_{3}{\text{]}}^{1}}$

## Example: Calculating Reagent Concentration

### Question

For the reaction:

$$\text{S}(\text{s}) + \text{O}_{2}(\text{g})$$ $$\leftrightharpoons$$ $$\text{SO}_{2}(\text{g})$$

1. Write an expression for the equilibrium constant.

2. Calculate the equilibrium concentration of $$\text{O}_{2}$$ if:

$$\text{K}_{\text{c}}$$ = 6 and $$[\text{SO}_{2}]$$ = $$\text{3}$$ $$\text{mol.dm^{-3}}$$ at equilibrium.

### Step 1: Determine which compounds will be part of the $$\text{K}_{\text{c}}$$ expression

$$\color{red}{\text{S(s)}}$$ + $$\text{O}_{2}(\text{g})$$ $$\leftrightharpoons$$ $$\text{SO}_{2}(\text{g})$$

$$\text{O}_{2}$$ and $$\text{SO}_{2}$$ are gases and so will be part of the expression for $$\text{K}_{\text{c}}$$. S is solid and so will not be part of the expression for $$\text{K}_{\text{c}}$$.

### Step 2: Write the expression for $$\text{K}_{\text{c}}$$

$\text{K}_{\text{c}}=\frac{{\text{[SO}}_{2}\text{]}}{{\text{[O}}_{2}\text{]}}$

### Step 3: Re-arrange the expression so that oxygen is on its own on one side of the expression

$\text{[O}_{2}\text{]}=\frac{{\text{[SO}}_{2}\text{]}}{\text{K}_{\text{c}}}$

### Step 4: Fill in the values you know and calculate $$[\text{O}_{2}]$$

${\text{[O}}_{2}\text{]}=\frac{\text{3}\text{ mol.dm^{-3}}}{6} = \text{0.5}\text{ mol.dm^{-3}}$

## Example: Calculating $$\text{K}_{c}$$

### Question

For the reaction:

$$\text{SO}_{2}(\text{g}) + \text{NO}_{2}(\text{g})$$ $$\rightleftharpoons$$ $$\text{NO}(\text{g}) + \text{SO}_{3}(\text{g})$$

The concentrations of the compounds used are:

$$[\text{SO}_{2}]$$ = $$\text{0.2}$$ $$\text{mol.dm^{-3}}$$, $$[\text{NO}_{2}]$$ = $$\text{0.1}$$ $$\text{mol.dm^{-3}}$$, $$[\text{NO}]$$ = $$\text{0.4}$$ $$\text{mol.dm^{-3}}$$ and

$$[\text{SO}_{3}]$$ = $$\text{0.2}$$ $$\text{mol.dm^{-3}}$$

Calculate the value of $$\text{K}_{\text{c}}$$.

### Step 1: Write the general expression for $$\text{K}_{\text{c}}$$

$\text{K}_{\text{c}}=\dfrac{\text{[C]}^{c}{\text{[D]}}^{d}}{\text{[A]}^{a}{\text{[B]}}^{b}}$

### Step 2: Determine the reactants and the products of the reaction

$$\text{SO}_{2}(\text{g})$$ and $$\text{NO}_{2}(\text{g})$$ are both reactants. They are gases and will be included in the expression.

$$\text{NO}(\text{g})$$ and $$\text{SO}_{3}(\text{g})$$ are both products. They are gases and will be included in the expression.

### Step 3: Write the expression for $$\text{K}_{\text{c}}$$ for this reaction

All four compounds have a coefficient of 1.

$\text{K}_{\text{c}}=\frac{{\text{[NO]}}^{1}{\text{[SO}}_{3}\text{]}^{1}}{{\text{[SO}}_{2}{\text{]}}^{1}{\text{[NO}}_{2}\text{]}^{1}}$

### Step 4: Fill in the values you know for this expression and calculate $$\text{K}_{\text{c}}$$

$\text{K}_{\text{c}}=\dfrac{\text{(}\text{0.4}\text{)(}\text{0.2}\text{)}}{\text{(}\text{0.2}\text{)(}\text{0.1}\text{)}}= \text{4}$

#### Tip:

You do not need to fill in the coefficients in a $$\text{K}_{\text{c}}$$ calculation when they are $$\text{1}$$. They are shown here so that you do not forget where the coefficients are reflected in the equation.