E2.3 Determine an equilibrium constant by inquiry | Ontario Grade 12 Chemistry (SCH4U)

Ontario Grade 12 Chemistry

Chemical Systems and Equilibrium

SCH4U study topic E2.3

A mixture can change colour as a reaction proceeds, then appear to stop changing. The particles have not stopped reacting. At equilibrium, the forward and reverse reactions continue at equal rates, so the amounts of substances remain steady. In this lesson, you will see how an inquiry can use those steady amounts to determine an equilibrium constant. An equilibrium constant is a value calculated from equilibrium concentrations for a particular balanced reaction at a fixed temperature. It does not mean that reactant and product concentrations are equal.

What you will learn

Describe how observations can provide evidence that a reaction has reached equilibrium.
Plan an inquiry that measures equilibrium concentrations for a reversible reaction.
Use a balanced equation and equilibrium concentrations to calculate an equilibrium constant.
Identify sources of uncertainty and explain how to improve the reliability of an inquiry.

1. From observations to equilibrium

Before studying equilibrium, recall that a chemical reaction changes reactants into products. A reversible reaction can proceed in both directions. In a closed mixture, products can form from reactants while reactants also reform from products.

A visible change can help you follow a reaction. For example, a mixture may become more intensely coloured as a coloured product forms. If its colour becomes steady, that is evidence that the mixture has reached a stable state. Colour alone does not prove equilibrium, but it can be a useful measurement when the colour is linked to the amount of a substance.

At the particle level, forward and reverse reactions continue at equilibrium. The forward reaction forms products; the reverse reaction forms reactants. Their rates are equal at equilibrium. As a result, the concentrations stay constant over time, even though particles keep reacting. Constant concentrations do not mean equal concentrations.

A concentration is the amount of a dissolved substance in a given volume of solution. In this lesson, concentrations are written in moles per litre, or mol/L. A reaction mixture must be allowed to settle to equilibrium before its concentrations are used to calculate the equilibrium constant.

\text{forward rate} = \text{reverse rate}

Equilibrium is dynamic: both directions continue.
Equal forward and reverse rates lead to constant concentrations.
A steady observation is evidence to investigate, not by itself a calculation of the equilibrium constant.

2. Design an inquiry that can measure equilibrium

An inquiry needs a reaction, a way to make a mixture, and a way to measure an equilibrium amount. One suitable coloured system is the formation of the iron(III) thiocyanate ion in aqueous solution. Iron(III) ions and thiocyanate ions are nearly colourless in dilute solution, while the product gives the mixture a red colour.

The balanced reaction shows the particle ratio needed for the calculation. One iron(III) ion combines with one thiocyanate ion to form one iron(III) thiocyanate ion. The total charge is conserved: the reactant charges add to positive two, matching the product charge.

An inquiry could prepare mixtures with known starting concentrations, keep them at the same temperature, and wait until their measured colour no longer changes. A colorimeter measures how much light a solution absorbs. To use its reading as a concentration, first make reference solutions with known product concentrations and record their readings. This set of reference readings is a calibration. It lets the investigator estimate the product concentration in an unknown mixture.

For each mixture, record the initial concentrations and the equilibrium product concentration found from the calibration. Then use the balanced reaction to determine how much of each reactant was used. The one-to-one coefficients mean that the decrease in each reactant concentration equals the increase in product concentration.

Use several mixtures rather than relying on one. Repeat readings when practical, keep the temperature and measurement method consistent, and record observations and uncertainties. These practices help reveal inconsistent measurements. They do not guarantee that every reading is exact.

\mathrm{Fe^{3+}(aq) + SCN^{-}(aq) \rightleftharpoons FeSCN^{2+}(aq)}

A calibration connects an instrument reading to a concentration.
Use the balanced equation to relate changes in reactant and product concentrations.
Keep conditions consistent and collect more than one set of measurements.

3. Build the expression and calculate

For a balanced reaction, the equilibrium-constant expression compares the equilibrium product concentration with the equilibrium reactant concentrations. Each concentration is raised to the power of its coefficient in the balanced equation. In this reaction, every coefficient is one, so every concentration appears to the first power.

Use equilibrium concentrations, not initial concentrations. Initial concentrations describe the mixture before it settles. Also, do not assume that all reactants have been used up. At equilibrium, reactants and products can all remain present.

For the iron(III) thiocyanate system, divide the product concentration by the product of the two reactant concentrations. If concentrations are entered in mol/L, the calculated value has units of L/mol for this expression. Report the value with sensible significant digits, based on the precision of the measurements.

K_c = \frac{[\mathrm{FeSCN^{2+}}]}{[\mathrm{Fe^{3+}}][\mathrm{SCN^{-}}]}

Use equilibrium concentrations in the expression.
Powers in the expression come from coefficients in the balanced equation.
The calculated value applies to the reaction as written and to the temperature used.

4. Check the quality of the inquiry

A calculated equilibrium constant depends on measured concentrations. A reading taken before the mixture reaches equilibrium will not represent the equilibrium state. A poor calibration can also lead to an inaccurate product concentration and therefore an inaccurate value of the constant.

Check that every solution measurement belongs to the same reaction mixture and that the initial and equilibrium concentrations use the same units. Check the balanced equation before setting up the expression. A missing coefficient changes the powers in the expression and can change the result.

Compare values from different mixtures prepared at the same temperature. Similar values support the consistency of the method. Differences may point to measurement uncertainty, inconsistent conditions, or a mixture that was not yet at equilibrium. Do not average values without first considering whether the measurements are reliable.

The inquiry does not need to produce a particular expected value to be useful. Its purpose is to use measured equilibrium amounts and a valid reaction model to determine a value, then judge whether the evidence is consistent.

A useful result depends on equilibrium being reached and concentrations being measured well.
Check reaction stoichiometry, units, and the origin of each concentration.
Treat differences among trials as evidence to examine, not as a reason to force agreement.

Worked example

Calculate the constant from an equilibrium measurement

Practice data, provided only for this calculation and not presented as experimental results: a mixture begins with

0.00200\ \mathrm{mol/L}

of

\mathrm{Fe^{3+}}

and

0.00100\ \mathrm{mol/L}

of

\mathrm{SCN^{-}}

. It contains no

\mathrm{FeSCN^{2+}}

initially. A calibration indicates an equilibrium concentration of

0.000400\ \mathrm{mol/L}

for

\mathrm{FeSCN^{2+}}

. Calculate

K_c

.

Relate the concentration changes
The balanced reaction uses one ion of each reactant to form one product ion. Because the starting product concentration is zero, forming $0.000400\ \mathrm{mol/L}$ of product uses the same concentration of each reactant.
$\Delta[\mathrm{Fe^{3+}}] = \Delta[\mathrm{SCN^{-}}] = 0.000400\ \mathrm{mol/L}$
Find the equilibrium reactant concentrations
Subtract the amount consumed from each initial reactant concentration. Keep the units in each subtraction.
$[\mathrm{Fe^{3+}}]_{\mathrm{eq}} = 0.00200 - 0.000400 = 0.00160\ \mathrm{mol/L},\quad [\mathrm{SCN^{-}}]_{\mathrm{eq}} = 0.00100 - 0.000400 = 0.000600\ \mathrm{mol/L}$
Substitute and calculate
Use the equilibrium concentrations in the expression. The denominator has units of $(\mathrm{mol/L})^2$ , so dividing a concentration in $\mathrm{mol/L}$ gives units of $\mathrm{L/mol}$ .
$K_c = \frac{0.000400\ \mathrm{mol/L}}{(0.00160\ \mathrm{mol/L})(0.000600\ \mathrm{mol/L})} = 4.17 \times 10^2\ \mathrm{L/mol}$

Answer:

K_c = 4.17 \times 10^2\ \mathrm{L/mol}

, to three significant digits.

Check: The product concentration is smaller than either reactant concentration, as expected from the practice data. The units reduce to

\mathrm{L/mol}

, and all three measured concentrations have three significant digits.

Common mistakes and how to avoid them

Using the initial concentrations directly in the equilibrium expression.

Correction: Use the concentrations after the system has reached equilibrium. Determine them from measured equilibrium amounts and the balanced reaction.

Assuming that equilibrium means equal reactant and product concentrations.

Correction: Equilibrium means that forward and reverse reaction rates are equal and concentrations remain constant. Their values need not be equal.

Using a colour reading as though it were already a concentration.

Correction: Use a calibration made from known concentrations to connect the reading to the product concentration.

Ignoring coefficients when writing the equilibrium expression.

Correction: Balance the reaction first. Use its coefficients as powers in the equilibrium expression.

Treating one calculated value as proof that the measurement method is reliable.

Correction: Compare measurements from multiple mixtures under consistent conditions and investigate substantial differences.

Lesson summary

An inquiry determines an equilibrium constant by measuring equilibrium concentrations for a balanced reaction.
A calibrated colour measurement can estimate the concentration of a coloured product.
Use stoichiometric ratios from the balanced equation to find remaining reactant concentrations.
Substitute equilibrium concentrations into the expression and report appropriate units and significant digits.

Check your understanding

Question 1

At equilibrium, what is true of a reversible reaction?

The forward and reverse reaction rates are equal, and concentrations stay constant.
The forward reaction stops, and all reactants have been used.
Reactant and product concentrations must be equal.
The reverse reaction stops, and only products remain.

Show answer and explanation

The forward and reverse reaction rates are equal, and concentrations stay constant.

At equilibrium, both directions continue at equal rates. This keeps concentrations constant, but does not require equal concentrations.

Question 2

For

\mathrm{A(aq) + 2B(aq) \rightleftharpoons C(aq)}

, which expression uses equilibrium concentrations correctly?

$K_c = \frac{[\mathrm{C}]}{[\mathrm{A}][\mathrm{B}]^2}$
$K_c = \frac{[\mathrm{A}][\mathrm{B}]^2}{[\mathrm{C}]}$
$K_c = \frac{[\mathrm{C}]}{[\mathrm{A}]^2[\mathrm{B}]}$
$K_c = [\mathrm{A}][\mathrm{B}]^2[\mathrm{C}]$

Show answer and explanation

K_c = \frac{[\mathrm{C}]}{[\mathrm{A}][\mathrm{B}]^2}

The product concentration is in the numerator. Reactant concentrations are in the denominator, and the coefficient of

\mathrm{B}

becomes its power.

Question 3

Why prepare reference solutions when using a colorimeter to estimate a product concentration?

To connect instrument readings with known concentrations.
To make the reaction reach equilibrium instantly.
To ensure reactant and product concentrations are equal.
To replace the balanced chemical equation.

Show answer and explanation

To connect instrument readings with known concentrations.

Reference solutions provide a calibration, which relates the instrument reading to a concentration. They do not replace the reaction model or determine when equilibrium is reached.

Key terms

Reversible reaction: A reaction that can proceed from reactants to products and from products back to reactants.
Dynamic equilibrium: A state in which forward and reverse reactions continue at equal rates, so concentrations remain constant.
Equilibrium concentration: The concentration of a substance in a reaction mixture that has reached equilibrium.
Calibration: A set of measurements using known amounts to connect an instrument reading to a quantity such as concentration.
Equilibrium constant: A value calculated from equilibrium concentrations using an expression based on the balanced reaction.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 12 Chemistry (SCH4U), expectation E2.3. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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E2.3 · Determine an equilibrium constant by inquiry

Ontario Grade 12 Chemistry

SCH4U study topic E2.3

What you will learn

1. From observations to equilibrium

2. Design an inquiry that can measure equilibrium

3. Build the expression and calculate

4. Check the quality of the inquiry

Calculate the constant from an equilibrium measurement

Common mistakes and how to avoid them

Lesson summary

Check your understanding

Question 1

Question 2

Question 3

Key terms

Continue through SCH4U

About this lesson and its review