Molar reaction heat capacity

ILLUSTRATIVE EXAMPLE 12.8 A 2 1 molar mixture of ethylene oxide (A) and water was fed to a 10 liter adiabatic tank flow reactor. The flow rate of the solution was 1000 L/h. The initial concentration of ethylene oxide was measured to be 38.3 gmol/L. The temperature at the reactor outlet was found to be 375°F. The heat of reaction, activation energy, average heat capacity and reaction velocity constant for this system are known ... 

STRATEGY The heat released by the reaction at constant pressure is calculated from the temperature change multiplied by the heat capacity of the calorimeter. Use the molar mass of one species to convert the heat released into the reaction enthalpy corresponding to the thermochemical equation as written. If the temperature rises, the... 

The temperature variation of the standard reaction enthalpy is given by Kirchhoff s law, Eq. 23, in terms of the difference in molar heat capacities at constant pressure between the products and the reactants. 

Hydrochloric acid oxidizes zinc metal in a reaction that produces hydrogen gas and chloride ions. A piece of zinc metal of mass 8.5 g is dropped into an apparatus containing 800.0 mL of 0.500 M HCl(aq). If the initial temperature of the hydrochloric acid solution is 25°C, what is the final temperature of this solution Assume that the density and molar heat capacity of the hydrochloric acid solution are the same as those of water and that all the heat is used to raise the temperature of the solution. 

Use the estimates of molar constant-volume heat capacities given in the text (as multiples of R) to estimate the change in reaction enthalpy of N2(g) + 3 H,(g) —> 2 NH.(g) when the temperature is increased from 300. K to 500. K. Ignore the vibrational contributions to heat capacity. Is the reaction more or less exothermic at the higher temperature ... 

The kinetic equilibrium constant is estimated from the thermodynamic equilibrium constant using Equation (7.36). The reaction rate is calculated and compositions are marched ahead by one time step. The energy balance is then used to march enthalpy ahead by one step. The energy balance in Chapter 5 used a mass basis for heat capacities and enthalpies. A molar basis is more suitable for the current problem. The molar counterpart of Equation (5.18) is... 

In the model equations, A represents the cross sectional area of reactor, a is the mole fraction of combustor fuel gas, C is the molar concentration of component gas, Cp the heat capacity of insulation and F is the molar flow rate of feed. The AH denotes the heat of reaction, L is the reactor length, P is the reactor pressure, R is the gas constant, T represents the temperature of gas, U is the overall heat transfer coefficient, v represents velocity of gas, W is the reactor width, and z denotes the reactor distance from the inlet. The Greek letters, e is the void fraction of catalyst bed, p the molar density of gas, and rj is the stoichiometric coefficient of reaction. The subscript, c, cat, r, b and a represent the combustor, catalyst, reformer, the insulation, and ambient, respectively. The obtained PDE model is solved using Finite Difference Method (FDM). 

C06-0139. Suppose 100.0 mL of 1.00 M HCl and 100.0 mL of 1.00 M NaOH, both initially at 25.0 °C, are mixed in a Thermos flask. When the reaction is complete, the temperature is 31.8 °C. Assuming that the solutions have the same heat capacity as pure water, compute the heat released. Use this value to evaluate the molar heat of the neutralization reaction H3 O (a q) + 0H ((3 q) 2H2 0(/)... 

Figure 6.4a shows the behavior of an endothermic reaction as a plot of equilibrium conversion against temperature. The plot can be obtained from values of AG° over a range of temperatures and the equilibrium conversion calculated as illustrated in Examples 6.1 and 6.2. If it is assumed that the reactor is operated adiabatically, a heat balance can be carried out to show the change in temperature with reaction conversion. If the mean molar heat capacity of the reactants and products are assumed constant, then for a given starting temperature for the reaction Ttn, the temperature of the reaction mixture will be proportional to the reactor conversion X for adiabatic operation, Figure 6.4a. As the conversion increases, the temperature decreases because of the reaction endotherm. If the reaction could proceed as far as equilibrium, then it would reach the equilibrium temperature TE. Figure 6.4b shows how equilibrium conversion can be increased by dividing the reaction into stages and reheating the reactants...

Equation 12.3-16 is valid whether heat is transferred to or from the system, and whether the reaction is exothermic or endothermic. Note that each term on the left side of equation 12.3-16 may be an input or an output. Furthermore, CP is the molar heat capacity of the system, and is given by equation 12.3-13 as such, it may depend on both T and composition (through /A). The right side of equation 12.3-16 may also be expressed on a specific-mass basis (12.3-11). This does not affect the consistency of the units of the terms in the energy balance, which are usually J s-1. 

The temperature dependence of reaction enthalpies can be determined from the heat capacity of the reactants and products. When a substance is heated from T to T2 at a particular pressurep, assuming no phase transition is taking place, its molar enthalpy change from AHm (T]) to AHm (T2) is... 

We ignited a 1.5886 g sample of glucose (C6H1206) in a bomb calorimeter. The temperature increased by 3.682°C. The heat capacity of the calorimeter was 3.562 kJ/°C, and the calorimeter contained 1.000 kg of water. Find the molar heat of reaction (J/mol of glucose) for the reaction ... 

Information on partial molar heat capacities [1,18] is indeed very scarce, hindering the calculation of the temperature correction terms for reactions in solution. In most practical situations, we can only hope that these temperature corrections are similar to those derived for the standard state reactions. Fortunately, due to the upper limits set by the normal boiling temperatures of the solvents, the temperatures of reactions in solution are not substantially different from 298.15 K, so large ArCp(T - 298.15) corrections are uncommon. 

As shown by Helgeson et al. (1978), satisfactory estimates of standard state molar entropy for crystalline solids can be obtained through reversible exchange reactions involving the compound of interest and an isostructural solid (as for heat capacity, but with a volume correction). Consider the generalized exchange reaction... 

If the heat capacity functions of the various terms in the reaction are known and their molar enthalpy, molar entropy, and molar volume at the 2) and i). of reference (and their isobaric thermal expansion and isothermal compressibility) are also all known, it is possible to calculate AG%x at the various T and P conditions of interest, applying to each term in the reaction the procedures outlined in section 2.10, and thus defining the equilibrium constant (and hence the activity product of terms in reactions cf eq. 5.272 and 5.273) or the locus of the P-T points of univariant equilibrium (eq. 5.274). If the thermodynamic data are fragmentary or incomplete—as, for instance, when thermal expansion and compressibility data are missing (which is often the case)—we may assume, as a first approximation, that the molar volume of the reaction is independent of the P and T intensive variables. Adopting as standard state for all terms the state of pure component at the P and T of interest and applying... 

Table 2.3 lists the molar internal enthalpies of black powder reaction products such as CO2 where Cp values are the molar heat capacities of the products at constant pressure. Using these, it is possible to estimate the heat of reaction at a particular temperature by assuming two temperature values and summing up the internal enthalpies for the reaction products multiplied by their corresponding number of moles as in Table 2.4. 

For reaction (83), at a conversion the mean molar heat capacity is... 

This approximation is good enough to allow extrapolations of equilibrium constants over modest temperature ranges for many commonly encountered reactions. The reason is that the molar heat capacities C°P of the reactants and the products tend to cancel, giving a standard heat capacity change of reaction ACp which is often negligible ... 

STRATEGY To use Kirchhoff s law, we need to know the molar heat capacities of the reactants and products these can be found in Appendix 2A. Combine them in the same way that enthalpies of formation would be combined to calculate a reaction enthalpy and then substitute in Eq. 32. Note that the temperatures must be expressed in kelvins. 

Cpm - is the standard heat capacity of species j at constant pressure, and Ns is the number of species in the chemical reaction. Note that the standard molar heat capacities of the elements cancel in the summation. Equation 10.4-2 was given earlier as equation 3.2-19, and it was used to show that the pK of acetic acid goes through a maximum not far from room temperature. Equation 10.4-3 was given earlier as equation 3.2-16. 

Calorimetric measurements yield enthalpy changes directly, and they also yield information on heat capacities, as indicated by equation 10.4-1. Heat capacity calorimeters can be used to determine Cj , directly. It is almost impossible to determine ArCp° from measurements of apparent equilibrium constants of biochemical reactions because the second derivative of In K is required. Data on heat capacities of species in dilute aqueous solutions is quite limited, although the NBS Tables give this information for most of their entries. Goldberg and Tewari (1989) have summarized some of the literature on molar heat capacities of species of biochemical interest in their survey on carbohydrates and their monophosphates. Table 10.1 give some standard molar heat capacities at 298.15 K and their uncertainties. The changes in heat capacities in some chemical reactions are given in Table 10.2. 

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