Hess's Law in Photosynthesis and Respiration
HSC Chemistry Syllabus
- Apply Hess’s Law to simple energy cycles and solve problems to quantify enthalpy changes within reactions, including but not limited to:
– Enthalpy changes involved in photosynthesis
– Enthalpy changes involved in respiration
Hess's Law in Photosynthesis & Respiration
This video explains how to use Hess's Law to determine overall enthalpy change of two complex processes: photosynthesis and respiration.
Hess's Law Reviewed
Hess's Law states that the total enthalpy change of a reaction is independent of the pathway taken, provided the initial and final conditions remain the same. This principle is based on the law of conservation of energy, which ensures that energy cannot be created or destroyed but can only be transferred or transformed.
Mathematically, Hess’s Law can be written as:
$$\Delta H_{\text{total}} = \Delta H_1 + \Delta H_2 + ...$$
This means that if a chemical reaction can be expressed as the sum of multiple reactions, the total enthalpy change for the reaction is the sum of the enthalpy changes of those individual reactions.
Hess’s Law is particularly useful in determining enthalpy changes for reactions that are difficult to measure directly, such as photosynthesis and respiration.
Enthalpy Changes in Photosynthesis
Photosynthesis is the process in which plants and certain other organisms convert carbon dioxide and water into glucose and oxygen using sunlight energy. Glucose is an energy-rich organic compound that can be broken down to produce energy for plant cells to use.
Photosynthesis is a complex process that consists of multiple chemical reactions.
The overall reaction is represented by the chemical equation:
$$6CO_2(g) + 6H_2O(l) \rightarrow C_6H_{12}O_6(s) + 6O_2(g)$$
This is an endothermic reaction because it requires an input of energy (sunlight). However, measuring this enthalpy change directly is challenging. Instead, Hess’s Law allows us to determine indirectly using known enthalpy changes of combustion reactions.
Step 1: Write the formation reactions of glucose and reactants
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Formation of CO₂:
$$C(s) + O_2(g) \rightarrow CO_2(g) \hspace{2cm} \Delta H_1 = -394 \text{ kJ/mol}$$
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Formation of H₂O:
$$H_2(g) + \frac{1}{2} O_2(g) \rightarrow H_2O(l) \hspace{2cm} \Delta H_2 = -285 \text{ kJ/mol}$$
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Formation of glucose:
$$6C(s) + 6H_2(g) + 3O_2(g) \rightarrow C_6H_{12}O_6(s) \hspace{2cm} \Delta H_3 = -1271 \text{ kJ/mol}$$
Note that the enthalpy change of formation of oxygen gas is zero because it is already in the standard state of oxygen.
Step 2: Reverse the formation equations for carbon dioxide and water
Since carbon dioxide and water are reactants of photosynthesis, they need to be broken down instead of formed. Therefore, the associated change in enthalpy would need to be reversed.
The stepwise reaction pathway of photosynthesis can be visualised using the following diagram. The break-down of carbon dioxide and water produces carbon, oxygen and hydrogen in their standard states as shown at the top of the diagram. These elements then react (bonds are formed) to form the products of photosynthesis: glucose and oxygen gas.
The relative enthalpy change of each reaction or step can be better visualised by the following diagram. The overall enthalpy change of photosynthesis can be determined by finding the difference in enthalpy between the starting condition i.e. water and final condition i.e. glucose and oxygen (represented by the black arrow). This is an application of Hess's law as the enthalpy change is the same regardless of the pathway (whether it's stepwise or directly from reactants to products).
Thus, the enthalpy change for photosynthesis is given by:
$$\Delta H = +394 \times 6 + 285 \times 6 - 1271 = +2803 \text{ kJ/mol}$$
Keep in mind that the molar enthalpy change of formation of carbon dioxide and water each needs to be reversed and multiplied by six to account for the stoichiometric ratio of photosynthesis.
Enthalpy Changes in Respiration
Overall, cellular respiration is the reverse of photosynthesis. Inside the mitochondria of cells of organisms break down glucose in the presence of oxygen to release energy, producing carbon dioxide and water:
This is an exothermic reaction because energy is released.
Since respiration is simply the reverse of photosynthesis, the enthalpy change is the negative of the enthalpy change for photosynthesis:
$$C_6H_{12}O_6(s) + 6O_2(g) \rightarrow 6CO_2(g) + 6H_2O(l) \hspace{2cm} \Delta H = -2803 \text{ kJ/mol}$$
The enthalpy change involved in each stepwise step of respiration can be visualised by the following diagram. First, glucose and oxygen are broken down into their constituent elements in standard states. This is followed by formation of carbon dioxide and water from these elements.
By Hess's law, the overall enthalpy change of respiration can be determined by considering the change in enthalpy directly between the starting reactants (glucose and oxygen) and final products (carbon dioxide and water).
$$\Delta H = +1271 - 394 \times 6 - 285 \times 6 = -2803 \text{ kJ/mol}$$
This confirms that respiration releases 2803 kJ per mole of glucose, which cells use for energy.