Standard Enthalpy Change for a Reaction

We have just seen that the standard enthalpy of formation corresponds to the formation of a compound from its constituent elements in their standard states  

We can use these two concepts—the decomposition of a compound into its elements and the formation of a compound from its elements—to calculate the enthalpy change of any reaction by mentally taking the reactants through two steps. In the first step we decompose the reactants into their constituent elements in their standard states in the second step v form the products from the constituent elements in their standard states. 

We can demonstrate this procedure by calculating the standard enthalpy change (A//°xn) for the combustion of methane  

The second step, the formation of the products from their constituent elements, has two parts (a) the formation of 1 mol CO2 and (b) the formation of 2 mol H2O. Since part (b) forms 2 mol H2O, we multiply the AHf for that step by 2. 

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As we mentioned, it is necessary to have information about the standard enthalpy change for a reaction as well as the standard entropies of the reactants and products to calculate the change in Gibbs function. At some temperature T, A// j can be obtained from Af/Z of each of the substances involved in the transformation. Data on the standard enthalpies of formation are tabulated in either of two ways. One method is to list Af/Z at some convenient temperature, such as 25°C, or at a series of temperatures. Tables 4.2 through 4.5 contain values of AfZ/ at 298.15 K. Values at temperatures not listed are calculated with the aid of heat capacity equations, whose coefficients are given in Table 4.8. 

Just as the standard enthalpy change for a reaction can be calculated from the standard free enthalpies of formation of the reactants and products, the standard free energy... 

The change in the equilibrium constant with tenperature is determined by the standard enthalpy change for a reaction using the van t Hoff equation (Equation 10.16). 

Plan We can use standard enthalpies of formation to calculate AH for the reaction. We can then use Le ChateUer s principle to determine what effect temperature will have on the equilibrium constant. Recall that the standard enthalpy change for a reaction is given by the sum of the standard molar enthalpies of formation of the products, each multipUed by its coefficient in the balanced chemical equation, less the same quantities for the reactants. At 25 C, AHj for NH3( ) is —46.19 kj/mol. The AHJ values for H2(g) and N2(g) are zero by definition, because the enthalpies of formation of the elements in their normal states at 25 C are defined as zero (S tion 5.7). Because 2 mol of NH3 is formed, the total enthalpy change is... 

Now let us see how to use standard enthalpies of formation (listed in Table 6.2) to find the standard enthalpy change for a reaction. We will first look at this problem from... 

In practice, what you do is measure certain heats of reaction and use them to tabulate enthalpies of formation, AH°f. The standard enthalpy change for a reaction is... 

In Chapter 6, we learned how to calculate standard changes in enthalpy (AH°xJ for chemical reactions. We now turn to calculating standard changes in entropy for chemical reactions. Recall from Section 6.9 that the standard enthalpy change for a reaction (AH°x ) is the change in enthalpy for a process in which all reactants and products are in their standard states. Recall also the definition of the standard state ... 

To determine the standard enthalpy change for a reaction, we add the standard enthalpies of formation for all the products then we subtract the sum of the standard enthalpies of the reactants. The standard enthalpy change for reaction (6) is therefore given by the following equation ... 

Both the integrated and differential forms show that a plot of log K against 1/T should yield a straight line with a slope equal to -AH0/2.303 R. Thus, a measured value of AH0 can be employed to calculate the equilibrium constant at temperatures other than that for which it is given. Conversely, it is possible to use measurements of the equilibrium constant at a number of temperatures to evaluate the standard enthalpy change for the reaction. 

The standard enthalpy change for this reaction at 200 °C is —126 kJ/mole for the reaction as written. Each CSTR has a volume of 0.2 m3. The feed rate is 66 cm3/sec. The following data on average heat capacities are available. 

A/Tf, the standard molar enthalpy of formation of a substance, is the enthalpy change for a reaction in which 1 mole of the substance in a specific state is formed from its elements in their standard states. 

Now let us consider how the standard enthalpies of formation can be used to calculate the standard enthalpy change for a chemical reaction. First, we calculate the total standard enthalpy of formation of all the products. We then calculate the total standard enthalpy of formation of all the reactants. The difference between the two totals is the... 

The most stable state of nitrogen in acidic solution is the ammonium ion, NH4(aq), which is isoelectronic with CH4 and H30+. It is a tetrahedral ion with strong N-H bonds. The mean N-H bond enthalpy in NH4(aq) is 506 kJ mol 1 (that of the O-H bonds in H30 + is 539 kJ mol" ). The enthalpy of hydration of the ammonium ion is — 345 kJ mol V This value placed into the Born equation (3.32) gives an estimate of the radius of the ammonium ion of 135 pm, a value insignificantly different from its thermochemical radius of 136 pm. The value is comparable to that estimated for the smaller H30+ ion (99 pm) from its more negative enthalpy of hydration (— 420 kJ mol -see Section 2.6.1). The proton affinity of the ammonia molecule is of interest in a comparison of its properties with those of the water molecule. The proton affinity is defined as the standard enthalpy change for the reaction ... 

There has been a tendency to view the lanthanide elements as having nearly identical chemistry In recent times this view has been criticized.75 Standard enthalpy changes for three reactions are plotted in Figure 14.17. How do you account for the dramatic differences shown in plots (a) and (b)7 Can you provide an explanation for the bumps" at Eu and Yb in plot (c) ... 

When we say, for example, that CI2 has a bond dissociation energy D = 243 kj/mol, we mean that the standard enthalpy change for the reaction 02(g) — 2 Cl(g) is AH° = 243 kj. Bond dissociation energies are always positive because energy must always be put into a bond to break it. 

The standard free energy for this reaction, AG°, is a measure of the gas-phase acidity of BH (AG°cid) or the gas-phase basicity of B (AG +). The standard enthalpy change for this reaction, AH°, is known as the proton affinity (PA) of the base B (a neutral or anionic species, depending on whether v = 1 or v = 0, respectively). The significance of these values lies in the fact that they are intrinsic in nature, as they are free of solvation contributions6 from both neutral and charged species in a bulk condensed phase. 

This table also gives the standard enthalpy change for the reaction, Af/°. With the help of the values, the equilibrium constant valid for a temperature other than 25°C can be calculated on the basis of the thermodynamic relation... 

Determine the enthalpy change for a reaction using standard enthalpies of formation data. 

One such important measurable quantity is the enthalpy change when a bond is broken in the gas phase, called the bond enthalpy. This is invariably positive because heat must be added to a collection of stable molecules to break their bonds. For example, the bond enthalpy of a C—H bond in methane is 438 kj mol , measured as the standard enthalpy change for the reaction... 

A system with an equilibrium constant of 5 x 10 Lmol at 25°C is subjected to a temperature jump of 5°C. Calculate the new equilibrium constant given that the standard enthalpy change for the reaction is lOkJmol. ... 

When a change occurs with the evolution of heat to the surroundings at constant pressure it is referred as exothermic and the enthalpy of the system decreases AH is negative). If the change takes in heat from the surroundings it is endothermic AH is positive). Many reactions have been studied and the value of the enthalpy of reaction determined accurately. Tables of standard molar enthalpies of formation A H at 25 °C are to be found in several sources and the standard enthalpy change for another reaction may be calculated from them using Hess s Law. This... 

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