Hess's Law: The Conservation of Energy in Chemical Reactions
- Consider that you’re navigating a city’s metro system, perhaps Tokyo or London.
- To get from Station A to Station B, you have multiple route options.
- Some may involve transfers, others may be direct, but no matter which path you take, the total distance between A and B remains the same.
- This concept parallels Hess’s Law in chemistry: the enthalpy change of a reaction depends only on the starting and ending points, not the route taken.
What is Hess's Law?
Hess’s Law is an application of the law of conservation of energy, which states that energy cannot be created or destroyed: only transferred or transformed.
Hess’s Law
The total enthalpy change for a reaction is the sum of the enthalpy changes for each step of the reaction pathway.
- To illustrate, consider the oxidation of sulfur to sulfur trioxide:$$
S(s) + \dfrac{3}{2} O_2(g) \to SO_3(g) \quad \Delta H = -396 \, \text{kJ mol}^{-1}
$$ - This reaction can occur in two steps:
- Step 1: $$S(s) + O_2(g) \to SO_2(g) \quad \Delta H = -296 \, \text{kJ mol}^{-1}$$
- Step 2: $$SO_2(g) + \dfrac{1}{2} O_2(g) \to SO_3(g) \quad \Delta H = -100 \, \text{kJ mol}^{-1}$$
- Adding the enthalpy changes for these steps gives the same total enthalpy change as the overall reaction:
$$
\Delta H = (-296) + (-100) = -396 \, \text{kJ mol}^{-1}
$$
This is the essence of Hess’s Law: the sum of the enthalpy changes for individual steps equals the enthalpy change of the overall reaction.
Hess’s Law holds true because enthalpy ($H$) is a state function, meaning its value depends only on the system’s current state (reactants and products), not on the process used to reach that state.
Applying Hess's Law: Calculating Enthalpy Changes
- Hess's Law is particularly useful for calculating the enthalpy change ($\Delta H$) of reactions that are experimentally challenging to measure directly.
- By combining known enthalpy changes of related reactions, we can deduce the enthalpy change for the target reaction.
- There are two common methods for applying Hess’s Law:
- Summation of Equations Method
- Enthalpy Cycle Diagram Method
1. Summation of Equations Method
This method involves manipulating given chemical equations and their associated enthalpy changes to construct the target reaction. Key steps include:
- Reversing equations (which changes the sign of $\Delta H$).
- Scaling equations by multiplying or dividing (which scales $\Delta H$ proportionally).
Formation of Methanol
Calculate the enthalpy change for the formation of methanol ($CH_3OH$):
$$
C(s) + 2H_2(g) + \dfrac{1}{2} O_2(g) \to CH_3OH(l)
$$
Given:
- $CH_3OH(l) + \dfrac{3}{2} O_2(g) \to CO_2(g) + 2H_2O(l) \quad \Delta H = -726 \, \text{kJ mol}^{-1}$
- $C(s) + O_2(g) \to CO_2(g) \quad \Delta H = -394 \, \text{kJ mol}^{-1}$
- $H_2(g) + \dfrac{1}{2} O_2(g) \to H_2O(l) \quad \Delta H = -286 \, \text{kJ mol}^{-1}$
Solution
- Reverse Equation 1 to make $CH_3OH(l)$ a product:
$$
CO_2(g) + 2H_2O(l) \to CH_3OH(l) + \dfrac{3}{2} O_2(g) \quad \Delta H = +726 \, \text{kJ mol}^{-1}
$$ - Use Equation 2 as given:
$$
C(s) + O_2(g) \to CO_2(g) \quad \Delta H = -394 \, \text{kJ mol}^{-1}
$$ - Double Equation 3 to account for 2 moles of $H_2(g)$:
$$
2H_2(g) + O_2(g) \to 2H_2O(l) \quad \Delta H = 2(-286) = -572 \, \text{kJ mol}^{-1}
$$ - Add the modified equations:
$$
C(s) + 2H_2(g) + \dfrac{1}{2} O_2(g) \to CH_3OH(l) \quad \Delta H = (-394) + (-572) + (+726) = -240 \, \text{kJ mol}^{-1}
$$ - Result: $$
\Delta H = -240 \, \text{kJ mol}^{-1}
$$
When combining equations, ensure intermediate species (e.g., $CO_2(g)$) cancel out, leaving only the reactants and products of the target reaction.
2. Enthalpy Cycle Diagram Method
This method visualizes the problem as a cycle, where the enthalpy change of the target reaction is calculated by following an alternative pathway.
Applications of Hess's Law
Hess’s Law has wide-ranging applications in chemistry, including:
1. Using Enthalpy of Formation Data (HL only)
The standard enthalpy change of a reaction ($\Delta H_r^\circ$) can be calculated using enthalpy of formation ($\Delta H_f^\circ$) values:
$$
\Delta H_r^\circ = \sum (\Delta H_f^\circ \, \text{products}) - \sum (\Delta H_f^\circ \, \text{reactants})
$$
2. Using Enthalpy of Combustion Data
Similarly, enthalpy changes can be calculated using enthalpy of combustion ($\Delta H_c^\circ$) values:
$$
\Delta H_r^\circ = \sum (\Delta H_c^\circ \, \text{reactants}) - \sum (\Delta H_c^\circ \, \text{products})
$$
Forgetting to reverse the sign of $\Delta H$ when reversing a reaction is a common error.
Double-check that intermediate species cancel out when summing equations to ensure the final equation matches the target reaction.
- Explain why Hess’s Law works in terms of the law of conservation of energy.
- How does this principle make enthalpy calculations possible?
