5: State Functions

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A state function is one that depends only on the present state of the system, not on the path the system took to reach that state. A state function depends only on the initial and final states. So, “delta” for a particular transformation, is always the same if that transformation is a state function, is always the same.

Let’s suppose that you are travelling from St. Cloud, MN to Denver. The altitude in St. Cloud is about 1020 feet and that of Denver (“the mile high city”) is 5280.

Altitude is like a state function because change in altitude for the trip is always + 4240 feet. It doesn’t matter whether you drive or fly to Denver, or whether you go by way of Milwaukee or Kansas City-the change in altitude is the same. Then, when you return, you lose 4240 feet.

Gasoline consumption, on the other hand, would not be a state function. Even though the initial and final states are the same, the amount of gas it takes to get there would depend on the route. And, you don’t get the gas back on the return trip!

Determine whether the following “travel functions” are state functions:
1. Latitude
2. Longitude
3. Tire tread wear
4. Cost
5. Amount of food consumed

Hess’s Law

Enthalpy, entropy and free energy are all state functions.

Hess’s Law states that if a reaction can be carried out in one step or a series of steps, the sum of the changes of the individual steps will be the same as if it had been carried out in one step.

If a series of equations add up to one of interest, the sum of the individual reactions will equal the Δ H for the overall reactions.

We have actually already used Hess’s Law when we talked about coupled reactions in biochemistry. (In this specific case an endergonic reaction and a (more) exergonic reaction add together to produce a net reaction that is overall exergonic.

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Write out the net reaction.
Calculate the ΔG for the net reaction.

Practice Problems

Calculate ΔH for CO + NO -> CO2 + 0.5 N₂

CO + 0.5 O₂ -> CO₂ΔH= -283kJ

N₂ + O₂ -> 2NO ΔH= 181kJ
Calculate ΔH for the formation of ClF₃ from ClF and F₂.

2ClF + O₂ -> Cl₂O +OF₂ΔH= 167.5kJ

2F₂ + O₂ -> 2OF₂ ΔH= -43.5kJ

2ClF₃ + 2O₂ -> Cl₂O + 3OF₂ ΔH= 394.1kJ
Calculate ΔH for the reaction of H₂ + Cl₂ -> 2HCl

N₂ +3H₂ -> 2NH₃ ΔH= -91.8kJ

N₂ + 4H₂ + Cl₂ -> 2NH₄Cl ΔH= -628.8kJ

NH₃ + HCl -> NH₄Cl ΔH= -176.2 kJ