IB Chemistry Topic R1.2.4 Hess's Law with Combustion and Formation Data Revision Notes (HL)

IB Chemistry Topic R1.2.4 Hess's Law with Combustion and Formation Data Revision Notes (HL) | RevisionDojo

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Applying Hess’s Law with Combustion Data

Hess’s law can be used to calculate the enthalpy change of a reaction ($ \Delta H_r^\circ $) from combustion data using the formula: $$
\Delta H_r^\circ = \sum \Delta H_c^\circ (\text{reactants}) - \sum \Delta H_c^\circ (\text{products})
$$
This equation works because enthalpy is a state function, so the overall enthalpy change of a reaction is independent of the route and can be found using a combustion cycle.

Example question

Let’s calculate the enthalpy change for the reaction:

$$
\text{C}_2\text{H}_4(g) + H_2(g) \to \text{C}_2\text{H}_6(g)
$$

Using the following combustion data:

$ \Delta H_c^\circ (\text{C}_2\text{H}_4) = -1411 \, \text{kJ mol}^{-1} $
$ \Delta H_c^\circ (\text{C}_2\text{H}_6) = -1560 \, \text{kJ mol}^{-1} $
$ \Delta H_c^\circ (\text{H}_2) = -286 \, \text{kJ mol}^{-1} $

Solution

Write the combustion equation for each species:
- $ \text{C}_2\text{H}_4(g) + 3\text{O}_2(g) \to 2\text{CO}_2(g) + 2\text{H}_2\text{O}(l) $
- $ \text{C}_2\text{H}_6(g) + \frac{7}{2}\text{O}_2(g) \to 2\text{CO}_2(g) + 3\text{H}_2\text{O}(l) $
- $ \text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \to \text{H}_2\text{O}(l) $
Apply the formula:
$$
\Delta H_r^\circ = \Delta H_c^\circ (\text{C}_2\text{H}_4) + \Delta H_c^\circ (\text{H}_2) - \Delta H_c^\circ (\text{C}_2\text{H}_6)
$$
Substitute the values:
$$
\Delta H_r^\circ = (-1411) + (-286) - (-1560)
$$
Simplify:
$$
\Delta H_r^\circ = -1411 - 286 + 1560 = -137 \, \text{kJ mol}^{-1}
$$
Thus, the enthalpy change for the reaction is $ \Delta H_r^\circ = -137 \, \text{kJ mol}^{-1} $.

Common Mistake

Be careful with the signs!
Subtracting a negative value is equivalent to adding it.

Applying Hess’s Law with Formation Data

Hess’s law can also be applied to formation data using the formula: $$
\Delta H_r^\circ = \sum \Delta H_f^\circ (\text{products}) - \sum \Delta H_f^\circ (\text{reactants})
$$
This approach is particularly useful when combustion data is unavailable.

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Applying Hess’s Law with Combustion Data

Hess’s law can be used to calculate the enthalpy change of a reaction ($ \Delta H_r^\circ $) from combustion data using the formula: $$
\Delta H_r^\circ = \sum \Delta H_c^\circ (\text{reactants}) - \sum \Delta H_c^\circ (\text{products})
$$
This equation works because enthalpy is a state function, so the overall enthalpy change of a reaction is independent of the route and can be found using a combustion cycle.

Example question

Let’s calculate the enthalpy change for the reaction:

$$
\text{C}_2\text{H}_4(g) + H_2(g) \to \text{C}_2\text{H}_6(g)
$$

Using the following combustion data:

$ \Delta H_c^\circ (\text{C}_2\text{H}_4) = -1411 \, \text{kJ mol}^{-1} $
$ \Delta H_c^\circ (\text{C}_2\text{H}_6) = -1560 \, \text{kJ mol}^{-1} $
$ \Delta H_c^\circ (\text{H}_2) = -286 \, \text{kJ mol}^{-1} $

Solution

Write the combustion equation for each species:
- $ \text{C}_2\text{H}_4(g) + 3\text{O}_2(g) \to 2\text{CO}_2(g) + 2\text{H}_2\text{O}(l) $
- $ \text{C}_2\text{H}_6(g) + \frac{7}{2}\text{O}_2(g) \to 2\text{CO}_2(g) + 3\text{H}_2\text{O}(l) $
- $ \text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \to \text{H}_2\text{O}(l) $
Apply the formula:
$$
\Delta H_r^\circ = \Delta H_c^\circ (\text{C}_2\text{H}_4) + \Delta H_c^\circ (\text{H}_2) - \Delta H_c^\circ (\text{C}_2\text{H}_6)
$$
Substitute the values:
$$
\Delta H_r^\circ = (-1411) + (-286) - (-1560)
$$
Simplify:
$$
\Delta H_r^\circ = -1411 - 286 + 1560 = -137 \, \text{kJ mol}^{-1}
$$
Thus, the enthalpy change for the reaction is $ \Delta H_r^\circ = -137 \, \text{kJ mol}^{-1} $.

Common Mistake

Be careful with the signs!
Subtracting a negative value is equivalent to adding it.

Applying Hess’s Law with Formation Data

Hess’s law can also be applied to formation data using the formula: $$
\Delta H_r^\circ = \sum \Delta H_f^\circ (\text{products}) - \sum \Delta H_f^\circ (\text{reactants})
$$
This approach is particularly useful when combustion data is unavailable.

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Structure 1. Models of the particulate nature of matter5 subtopics

Structure 2. Models of bonding and structure4 subtopics

Structure 3. Classification of matter2 subtopics

Reactivity 1. What drives chemical reactions?4 subtopics

Reactivity 2. How much, how fast and how far?3 subtopics

Reactivity 3. What are the mechanisms of chemical change?4 subtopics

IB Chemistry R1.2.4 Hess's Law with Combustion and Formation Data Notes

Structure 1. Models of the particulate nature of matter5 subtopics

Structure 2. Models of bonding and structure4 subtopics

Structure 3. Classification of matter2 subtopics

Reactivity 1. What drives chemical reactions?4 subtopics

Reactivity 2. How much, how fast and how far?3 subtopics

Reactivity 3. What are the mechanisms of chemical change?4 subtopics

Applying Hess’s Law with Combustion Data

Applying Hess’s Law with Formation Data

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Applying Hess’s Law with Combustion Data

Applying Hess’s Law with Formation Data

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