6.9.B.1 Energy Conservation and Enthalpy Sum in Reaction Sequences:

1. First Law of Thermodynamics:

Mathematically, this is usually expressed as:

ΔU=Q−W

Where:
– ( Delta U ) is the system’s change in internal energy,
– ( Q ) is the heat put into the system, and
– (W) is the work done by the system on the surroundings.

Therefore, if the system receives heat (Q > 0) or performs work (W > 0), it will influence the internal energy of the system (Delta U).

It’s a basic principle of thermodynamics and aids in comprehending processes such as heating, cooling, and mechanical work!

2. Enthalpy (H):

 Enthalpy (H) is a convenient thermodynamic property, particularly when working with heat exchange under constant pressure. It is defined as:

H = U + PV

Where:
– (H) is the enthalpy,
– (U) is the internal energy,
– (P) is the pressure, and
– (V) is the volume.

The change in enthalpy, (Delta H), is especially useful because, at constant pressure, it is exactly equal to the heat (Q) absorbed or evolved by the system:

ΔH=Qp​

Where:
– (Qp) is the heat transferred at constant pressure.

This makes enthalpy particularly valuable in processes such as chemical reactions or phase changes (e.g., boiling, melting) since the heat transfer can be linked to the change in enthalpy.

For example, if you heat something at constant pressure, the change in enthalpy informs you of how much energy has been absorbed or emitted.

3. Reaction Sequences and Hess’s Law:

The total enthalpy change of a reaction is the sum of the enthalpy changes of the individual steps, irrespective of the path followed.

Mathematically, it can be represented as:   ΔHtotal ​= ∑ΔHsteps​

– ΔHtotal is the overall enthalpy change of the reaction,
– ΔHsteps​  are the enthalpies of the individual steps.

This follows the idea that enthalpy is a state function, so it doesn’t matter what path was taken to reach a given state; it will only depend on the initial state and the final state.

 How It Works:
If you have a multi-step complex reaction, and you know each step’s enthalpy changes, you can use Hess’s Law to compute the net enthalpy change of the reaction. Even when the reaction cannot be measured, you can employ Hess’s Law by decomposing it into some simple reactions, which are simpler to investigate.
Take the synthesis of carbon dioxide from carbon and oxygen as an example. The reaction can occur in more than one step. For instance:

1. Step 1: Graphite reacts with oxygen to produce carbon monoxide (CO).
C(s)+O2​(g)→CO(g)  ΔH1​

2. Step 2: Carbon monoxide reacts with oxygen to give carbon dioxide (CO₂).
CO(g) + O2(g) → CO2(g)  ΔH2

According to Hess’s Law, you can add these two reactions together to produce the overall reaction:
C(s) + O2(g) → CO2(g)

And the net enthalpy change for this reaction would be the sum of the separate enthalpy changes:
ΔHtotal = ΔH1 + ΔH2

This principle enables us to determine enthalpy changes for hard-to-measure reactions by simply using known enthalpy changes for similar reactions. It’s building a road from known steps!

4. Energy Transfer in Reactions:

Energy transfer in chemical reactions occurs through a change of potential energy between reactants and products. This causes heat to be released or to be absorbed:

– Exothermic reaction: Products have lower potential energy than reactants, and heat is emitted to the surroundings.
– Endothermic reactions: Products have more potential energy than reactants, with heat being taken in from the surroundings.

Activation energy has to be supplied to initiate the reaction. Energy diagrams illustrate such changes, showing heat given out (exothermic) or taken in (endothermic).