Lecture 4: 1st Law: Chemical Reactions



Lecture 4: 1st Law: Chemical Reactions

Review:

• State variables during p-V work (mechanical work) and heat

• State Variable during a phase transitions

• Application of 1st Law for chemical reactions

Today:

• Application to biochemical reactions

o Example: Biochemical oxidation of Sucrose

o Example: Biochemical oxidation of Glycine

• Begin discussion of 2nd Law of thermodynamics

o Carnot cycle

Changes involved in chemical reactions

Consider a general reaction

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o Heat effects depend on whether the reaction takes place under conditions of PV work or not. If only work involved is PV type, then ΔE=qV, ΔH=qP= ΔE+Δ(PV). In general for gaseous reactant we assume ideal gas law so: ΔH=ΔE+Δ(PV) becomes ΔH= ΔE+Δ(nRT)

o If the reaction takes place with accompanying rise in temperature or evolution of heat (q negative) then the reaction is called as exothermic. Similarly, if the reaction results in flow of heat from surrounding into system (q positive) then the reaction is called as endothermic.

o Ħ is the standard heat of formation at 25ºC. Tables of heat of formation are in appendix A5-A7. Generally these heats are determined using Bomb calorimetry.

Temperature dependence of ΔH of a reaction

[pic]Note this form is exactly same as we found for ΔH for the phase change. However the meaning of specific heat change is different.

[pic]

Using these equation we can calculate the heat of reaction at different temperature. Next we consider few examples of how we can use these equations.

Oxidation of Sucrose.

Consider oxidation of sucrose by oxygen given by following:

[pic]

Average person needs about 8000kJ-10000kJ per day for sustenance. This corresponds about 450-600 gms of sugar if all the energy is derived from sugar. Note the magnitude of nutritional Calorie is different from thermal calories!

What is important to note is that the energy released, as calculated, is the same whether it involves chemical or biochemical oxidation mediated by series of enzymatic processes. This is because H is a state variable depending only on the initial and final states.

In above case, we used the heat of formation of solid sugar. In biochemical reactions we are interested in the heat of formation for the solvated sugar molecule. To realize the corresponding H, one needs to measure the heat of solution.

Biochemical Oxidation of Glycine.

Chemical oxidation

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However, we know from biochemistry the reaction product is Urea. So let us calculate the heat of hydrolysis of urea to yield CO2 and NH3:

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Subtracting the two equations and the corresponding ΔH’s and rearranging we obtain:

[pic]Thus, using a combination of two chemical reactions we have estimated a heat of biochemical reaction. However, we can still fine-tune the above reaction by taking into account the heat of solution for both urea and glycine as follows.

[pic]

Now subtracting twice the hydration of glycine reaction and adding solvation reaction of urea we can show:

[pic]

Second Law of Thermodynamics

Introduces a concept of entropy, a new state variable. It is perhaps the most widely term common language. It indicates an extent of disorder. It was developed during the studies of steam engines. Heated steam (“ideal gas”) does mechanical work of moving piston but it also looses some of the heat to surrounding environment wasting “useful” energy. Issue is what is the theoretically maximum efficiency of the process.

To understand Carnot’s construction, we have to understand adiabatic paths. Adiabatic path is the one where the state of the system changes without loss of heat to surrounding. According to 1st law ΔE=q+W, for adiabatic process q=0. For small change in volume there will be work and the change in the temperature of the system is given by:

[pic]

Note for adiabatic path pVγ is the equation of state.

Carnot Cycle

Carnot cycle considers following cyclic path for a reversible engine.

Isothermal expansion

Adiabatic Adiabatic

Compression expansion

Isothermal Compression

Calculation of q and W for the Carnot Cycle.

o Path I. Isothermal reversible expansion of gas at T1. Since this increases the final volume of the gas the work is negative. In isothermal reversible expansion the net change in the internal energy is zero.

[pic]

o Adiabatic reversible Expansion

[pic]

o Isothermal reversible compression.

[pic]

o Adiabatic reversible compression

[pic]

Thus total heat absorbed and work done is:

[pic]

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Ideal Gas

T1,P1,V1

Gas at P2,V2,T1

Gas

P3,V3,T2

Gas at

P4,V4,T2

P

V

Adiabatic path

Isothermal Path

I

2

3

4

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