Hess' law says route doesn't affect ΔH

Hess' law states that the overall standard enthalpy change (ΔH^⦵) of a reaction is the same, regardless of whether the reaction takes place in one step or several steps.

This allows you to break a reaction into component steps and add up their enthalpy changes to find the total ΔH^⦵ for the overall reaction.

Worked example 1 - Calculating ΔH⦵ using enthalpy of reaction data

Calculate ΔH^⦵_r for the reaction: 2C_(s) + 2H_2(g) + O_2(g) ➔ CH₃COOH_(l) using the following equations:

Step 1: Draw an enthalpy cycle diagram

Step 2: Apply Hess' law

ΔH_{(route 1)} = ΔH_{(route 2)}

Step 3: Substitution and correct evaluation

$\mathrm{\Delta }{H}_{\text{(route 1)}}=(-394\times 2)+(-286\times 2)-(-875)=-788-572+875=-485{\text{ kJ mol}}^{-1}$.

Standard enthalpy change of formation

The standard enthalpy change of formation (ΔH^⦵_f) is the enthalpy change when one mole of a compound forms from elements under standard conditions. ΔH^⦵_f values can be positive or negative.

For example, the equation representing the standard enthalpy change of formation of carbon dioxide (CO₂) is:

C_(s) + O_2(g) ➔ CO_2(g) ΔH^⦵_f = $-$394 kJ mol^-1.

Using enthalpies of formation

Standard enthalpies of formation (ΔH^⦵_f) can be used with Hess' law to determine unknown ΔH^⦵ values.

• ΔH^⦵_f values are known for many compounds.
• ΔH^⦵_f for elements in their standard states is defined as 0 kJ mol^−1^.

To calculate the standard enthalpy change of a reaction (ΔH^⦵_r), use the equation:

ΔH^⦵_r = ΣΔH^⦵_f(products) - ΣΔH^⦵_f(reactants)

where Σ = sum of

Worked example 2 - CalculatingΔH⦵ using enthalpy of formation data

Calculate ΔH^⦵_r for the reaction:

SO_2(g) + 2H₂S_(g) ➔ 3S_(s) + 2H₂O_(l)

Given:

ΔH^⦵_f(SO_2(g) = $-$297 kJ mol^-1

ΔH^⦵_f(H₂S_(g)) = $-$20.2 kJ mol^-1

ΔH^⦵_f(H₂O_(l)_) = $-$286 kJ mol^-1^

This diagram shows the reaction pathway from reactants to products. We can use Hess' law and known enthalpy values to calculate ΔH^⦵ for this reaction.

Step 1: Equation

ΔH^⦵_r = ΣΔH^⦵_f(products) $-$ ΣΔH^⦵_f(reactants)

Step 2: Substitution and correct evaluation

ΔH^⦵_f(products) = 3(0) + 2($-$286) = $-$572 kJ mol^-1^

ΔH^⦵_f(reactants) = -297 + 2($-$20.2) = $-$337.4 kJ mol^-1^

Step 3: Determine the overall ΔH^⦵

ΔH^⦵ = -572 + 337.4 = $-$234.6 kJ mol^-1^

Therefore, the ΔH^⦵ for the reaction is $-$235 kJ mol^-1^

Using enthalpies of combustion

In a similar way, standard enthalpies of combustion can be used to find unknown ΔH^⦵_r values for reactions.

To calculate the standard enthalpy change of a reaction (ΔH^⦵_r), use the equation:

ΔH^⦵_r = ΣΔH^⦵_c(reactants) $-$ ΣΔH^⦵_c(products)

where Σ = sum of

Worked example 3 - Calculating ΔH⦵ using enthalpy of combustion data

Calculate ΔH^⦵_r for the reaction:

C₂H₅OH_(l) + 3O_2(g) ➔ 2CO_2(g) + 3H₂O_(l)

Given:

ΔH^⦵_c(C_2_H_5_OH) = $-$1,367 kJ mol^−1^

ΔH^⦵_c(C) = $-$394 kJ mol^−1^

ΔH^⦵_c(H_2_) = $-$286 kJ mol^−1^

This diagram shows the reaction pathway from reactants to products. We can use Hess' law and known enthalpy values to calculate ΔH^⦵ for this reaction.

Step 1: Equation

ΔH^⦵_r = ΣΔH^⦵_c(reactants) $-$ ΣΔH^⦵_c(products)

Step 2: Substitution and correct evaluation

ΔH^⦵_c(reactants) = 2(-394) + 3(-286) = $-$1,646 kJ mol^-1^

ΔH^⦵_c(products) = $-$1,367 kJ mol^-1^

Step 3: Determine the overall ΔH^⦵

ΔH^⦵ = -1,646 $-$ ($-$1,367) = $-$279 kJ mol^-1^

Therefore, the ΔH^⦵ for the formation of ethanol is $-$279 kJ mol^-1^.