D2.5 Solve reaction-energy problems with Hess’s law | Ontario Grade 12 Chemistry (SCH4U)

Ontario Grade 12 Chemistry

Energy Changes and Rates of Reaction

Use known reaction enthalpies to find the enthalpy change for a target reaction.

When a chemical reaction occurs, energy may be transferred between the reacting chemicals and their surroundings. The amount transferred depends on the starting and ending substances, not on the route taken between them. Hess’s law uses this idea to solve for an unknown reaction enthalpy from other reactions with known enthalpy changes. You will practise changing and adding equations while tracking how each change affects its enthalpy.

What you will learn

Explain Hess’s law using reaction enthalpy changes.
Adjust a chemical equation and its enthalpy change consistently.
Combine balanced equations to obtain a target reaction.
Calculate and report a reaction enthalpy change with units and an appropriate sign.

1. Review: reaction equations and enthalpy

A balanced chemical equation represents the same number of each type of atom on both sides. The coefficients show the relative amounts of substances reacting and forming. In a thermochemical equation, the enthalpy change, written as

\Delta H

, belongs to the reaction exactly as written.

Enthalpy change is measured in kilojoules for the reaction in its stated proportions. For example, if an equation produces one mole of a substance, doubling every coefficient means the equation now represents twice as much reaction. Its enthalpy change must also double. Keep physical states, such as

(s)

,

(l)

, or

(g)

, because they are part of the reaction description.

A negative

\Delta H

means energy is released to the surroundings for the reaction as written. A positive

\Delta H

means energy is absorbed from the surroundings. The sign describes the direction of the equation; it is not a label that can be ignored when combining reactions.

\Delta H_{\mathrm{reaction}}

Balance atoms before combining reaction equations.
Keep the state symbols and direction of each reaction in view.
Attach each enthalpy change to its equation.

2. Hess’s law: why reaction equations can be added

Imagine comparing two ways of getting from the same starting substances to the same final substances. The total energy change is the same, even if the route uses different intermediate steps. An intermediate is a substance made in one step and used up in another. When the steps are added, an intermediate that appears on both sides cancels.

At the particle level, the initial and final substances determine the overall energy change. Breaking the route into steps does not change those endpoints. Hess’s law applies this idea to reaction equations: if several balanced reactions add to the target reaction, their enthalpy changes add to give the target enthalpy change.

To use the law, compare the given equations with the target. Reverse any equation whose substances are on the wrong sides. Reversing an equation changes the sign of its

\Delta H

. Multiply an equation by a number if its coefficients need scaling; multiply its

\Delta H

by the same number. Then add the adjusted equations and cancel substances found on both sides.

A substance cancels only when its formula and state match on both sides. Check that the remaining equation is exactly the target, including states and coefficients. Finally, add the adjusted enthalpy values with their signs and include the unit kJ.

\Delta H_{\mathrm{target}}=\sum_i \Delta H_i

Reverse a reaction: change the sign of $\Delta H$ .
Scale a reaction: scale $\Delta H$ by the same factor.
Add equations and cancel matching substances on opposite sides.
The enthalpy changes add using their positive and negative signs.

3. A reliable problem-solving routine

First, write the target equation clearly. Identify which substances must be reactants and which must be products. This prevents accidentally solving for the reverse reaction.

Next, choose the given equations that contain the target substances. Adjust each equation so the target substances appear on the correct sides and in the required amounts. Record each change to the enthalpy beside that equation. For example, reversing and then doubling a reaction means its enthalpy is first sign-reversed and then doubled.

Add the adjusted equations. Cancel substances that occur on both sides in the same state. If a substance does not cancel, or if the final equation differs from the target, revisit the equation choices or adjustments. Do not change coefficients simply to make the energy numbers convenient.

Add the adjusted enthalpy values. Keep signs during the calculation, and round the final result to a sensible precision based on the supplied data. Report the sign, value, and unit, and state that it applies to the target equation as written.

\Delta H_{\mathrm{adjusted}}=n\Delta H_{\mathrm{original}}

Use the target equation as the guide for every adjustment.
Show enough working to make reversals, scaling, and cancellation visible.
Check the final equation before calculating the final enthalpy.

4. Reading the result and checking your work

The sign of the result should match the direction of the target equation. If the target is reversed, its enthalpy change has the opposite sign. This follows from the same reversal rule used for each supplied equation.

A useful final check is to inspect three things: the target equation is balanced, the remaining reactants and products match it, and all enthalpy changes were adjusted along with their equations. A calculation can add numbers correctly and still be wrong if an equation was reversed or scaled without changing its enthalpy.

Use the enthalpy values given in the problem. Hess’s law does not require you to measure a reaction or assume an unprovided value. It provides a way to combine known reaction-energy information into the value for a specified overall reaction.

A negative result indicates energy release for the target reaction as written.
A positive result indicates energy absorption for the target reaction as written.
The overall reaction and the enthalpy calculation must describe the same direction and scale.

Worked example

Find the enthalpy change for carbon monoxide formation

Use the following reactions to find

\Delta H

for

\mathrm{C(s)+\frac{1}{2}O_2(g)\rightarrow CO(g)}

:

\mathrm{C(s)+O_2(g)\rightarrow CO_2(g)}

,

\Delta H=-393.5\ \mathrm{kJ}

; and

\mathrm{CO(g)+\frac{1}{2}O_2(g)\rightarrow CO_2(g)}

,

\Delta H=-283.0\ \mathrm{kJ}

.

Match the target
The target has carbon and oxygen as reactants and carbon monoxide as the product. The first given reaction already places carbon on the reactant side, but the second places carbon monoxide on the reactant side. Reverse the second equation so carbon monoxide is produced.
$\mathrm{CO_2(g)\rightarrow CO(g)+\frac{1}{2}O_2(g)}$
Reverse the enthalpy
Reversing a reaction reverses its energy change. The second reaction’s value changes from negative to positive. The first reaction remains unchanged.
$\Delta H_2=+283.0\ \mathrm{kJ}$
Add and cancel
Add the first equation to the reversed second equation. Carbon dioxide appears on both sides in the same state, so it cancels. The remaining equation is the target, including its coefficients.
$\mathrm{C(s)+O_2(g)+CO_2(g)\rightarrow CO_2(g)+CO(g)+\frac{1}{2}O_2(g)}$
Calculate the target value
Add the enthalpy changes with their signs. The result is negative, so the target reaction releases energy as written. The given values are stated to one decimal place, so report the result to one decimal place.
$\Delta H=-393.5\ \mathrm{kJ}+283.0\ \mathrm{kJ}=-110.5\ \mathrm{kJ}$

Answer:

\Delta H=-110.5\ \mathrm{kJ}

for

\mathrm{C(s)+\frac{1}{2}O_2(g)\rightarrow CO(g)}

.

Check: After cancelling

\mathrm{CO_2(g)}

and one-half mole of

\mathrm{O_2(g)}

, the equation is balanced and matches the target. The negative sign indicates energy release in the target direction.

Common mistakes and how to avoid them

Reversing an equation but keeping its original enthalpy sign.

Correction: Change the sign whenever the reaction direction is reversed.

Multiplying the coefficients but leaving the enthalpy unchanged.

Correction: Multiply the enthalpy by the same factor as every coefficient.

Cancelling substances that have different states.

Correction: Cancel only matching formulas in the same state on opposite sides.

Adding enthalpy magnitudes without their signs.

Correction: Keep positive and negative signs through the full sum.

Lesson summary

Hess’s law says that enthalpy changes add when balanced reactions add to the target reaction.
Reverse an equation and reverse its enthalpy sign.
Scale an equation and scale its enthalpy by the same factor.
Cancel matching substances, verify the target equation, and report the signed result in kJ.

Check your understanding

Question 1

A reaction has

\Delta H=-120\ \mathrm{kJ}

. What is

\Delta H

when the reaction is reversed?

$+120\ \mathrm{kJ}$
$-120\ \mathrm{kJ}$
$+60\ \mathrm{kJ}$
correctIndex

Show answer and explanation

+120\ \mathrm{kJ}

Reversing the equation changes the sign but not the magnitude, so the reversed reaction has

\Delta H=+120\ \mathrm{kJ}

.

Question 2

A reaction is multiplied by

3

. Its original enthalpy change is

+25\ \mathrm{kJ}

. What is the enthalpy change for the multiplied equation?

$+75\ \mathrm{kJ}$
$+25\ \mathrm{kJ}$
$-75\ \mathrm{kJ}$
correctIndex

Show answer and explanation

+75\ \mathrm{kJ}

Scaling the whole equation by

3

also scales its enthalpy change:

3\times(+25\ \mathrm{kJ})=+75\ \mathrm{kJ}

.

Question 3

When can a substance be cancelled while adding reaction equations?

When the same formula and state appear on opposite sides.
Whenever the same element appears in two equations.
Whenever a substance appears as a product in one equation.
correctIndex

Show answer and explanation

When the same formula and state appear on opposite sides.

Cancellation is valid for the same substance, including its state, on opposite sides of the summed equation.

Key terms

Enthalpy change: The energy change associated with a reaction as written, represented by $\Delta H$ .
Intermediate: A substance produced in one reaction step and used up in another, so it can cancel when the steps are added.
Hess’s law: The rule that the enthalpy change for an overall reaction equals the sum of the enthalpy changes for reaction steps that add to it.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 12 Chemistry (SCH4U), expectation D2.5. 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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D2.5 · Solve reaction-energy problems with Hess’s law

Ontario Grade 12 Chemistry

Use known reaction enthalpies to find the enthalpy change for a target reaction.

What you will learn

1. Review: reaction equations and enthalpy

2. Hess’s law: why reaction equations can be added

3. A reliable problem-solving routine

4. Reading the result and checking your work

Find the enthalpy change for carbon monoxide formation

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