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The first law thermodynamics

Enthalpy and thermochemistry

We here introduce and define the enthalpy state function. If a new function is defined as a linear combination of state functions, it can be shown that the new function is also a state function. Defining the enthalpy of a system as H = U + PV means that H is a state function, since each of its components are also state functions. Defining the enthalpy is useful because of the relationship ΔH = qP .
That is, the enthalpy change of the system as a result of a process carried at constant pressure is equal to the amount of heat q transferred - denoted as qP - and we can readily measure enthalpy changes for chemical reactions in solution under atomospheric pressure. We also see that for processess accompanied by small changes in volume, ΔH and ΔU are approximately equal . Generally speaking, differences between ΔH and ΔU are not significant unless gases are produced or consumed.  
There are a number of important properties of state functions that we will use enthalpy to illustrate. There are equivalent ways in which the state function properties can be stated. Path-independence, thermodynamic cycles, and Hess' law are all direct consequences or applications of state functions

Enthalpy is a state function: Path independence

Path-independence means that no matter what path (sequence of changes in chemical compostion and other state variables) a system takes in going from state 1 to state 2, the change in value of the state function is the same. Another way of saying this is that the value of a state function is determined solely by its current state, not by its "history" (exactly how it got to that state). The figure below, which represents enthalpy changes along a vertical axis, illustrates the idea of path independence for the example of the formation of diatomic hydrogen. If we include oxygen in our system, we can imagine the same process occurring in the presence of oxygen. As long as oxygen remains unchanged, the enthalpy change for the reaction converting H atoms to H2 molecules remains the same, – 435 kJ/mol (the downward red arrow in the figure). However, given the presence of oxygen in the system, we can also imagine an alternate path - path 2 - connecting the two states (the three consecutive blue arrows - steps a, b,and c). The sum of the enthalpies for the three steps is – 435 kJ/mol, thus ΔH is the same for two different paths connecting the same two states. This is actually just another way of saying enthalpy is a state function.
   
 

Enthalpy is a state function: Thermodynamic cycles

Since enthalpy is a state function, we can rely on the fact that there is no net change in its value for a cyclic process. In a cyclic process, the path followed is such that the initial and final states are the same. Thus, ΔH = 0 for a thermodynamic cycle. As an example of how this can be applied, consider the two reactions that produce hydrogen and oxygen gas shown in part (a) of the figure below, which show examples of enthalpy diagrams. Given the values of ΔH° as shown, the ΔH° of a third reaction can be computed, since we can construct a thermodynamic cycle from the three reactions. The cycle begins and ends with 2 mol water and 1 mol oxygen at standard state, as shown in part (b) of the figure. That the value of ΔH° for the reaction in which hydrogen peroxide is converted into water and oxygen can be directly calculated is illustrated in the enthalpy diagram.
  The figure at left illustrates the same idea in a slightly different way. Since enthalpy is a state function, ΔH is the same for two different paths that amount to the same net reaction. If we do not know or cannot directly measure the ΔH for path (1), we could calculate it if is known for both path (2) and path (3). We thus calculate for the reaction using the numbers for a different path. The path (2) plus (3) plus the reverse of (1) is a thermodynamic cycle.  

Standard state enthalpies, enthalpy of formation, and Hess' law

Consult Chemistry: Structure and Dynamics, 2nd ed., by Spencer, Bodner, and Pickard. There are texts in the Student Lounge (1st flr., Hughes).
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