Isotherm constants

The exposure interval for the bed, T, is inversely proportional to the kiln rotation rate. Hence, equation 21 shows that the time constant for desorption is directly proportional to the bed depth and inversely proportional to the square root of the kiln rotation rate. However, the overriding factor affecting is the isotherm constant iC which in general decreases exponentially with increasing temperature as in equation 4. 

Isothermal—constant temperature Isometric—constant volume Isobaric—constant pressure Isentropic—constant entropy Isenthalpic—constant enthalpy... 

Programmed Temperature Injectors The programmed temperature injector is held near the boiling point of the solvent after injection of the sample, it is temperature programmed rapidly until it reaches the desired maximum temperature, which is normally higher than that of an isothermal (constant temperature) injector. As the sample components vaporize, they are transferred onto the head of the GC column. This technique is a varia-... 

This is shown graphically by the (Vm, p, T) surface given in Figure 1.3. The three variables p, Vm, and T exist together only on this surface. Cutting through the surface with isothermal (constant T) planes generates hyperbolic curves... 

The Isothermal Process In an isothermal (constant temperature) expansion, heat is added to balance the work removed, so that the temperature of the system does not change. The amount of work can be calculated from the line... 

This reaction can be elementary if = 1 or 2. More generally, it is complex. Noninteger values for n are often found when fitting rate data empirically, sometimes for sound kinetic reasons, as will be seen in Section 2.5.3. For an isothermal, constant-volume batch reactor. 

All the results obtained for isothermal, constant-density batch reactors apply to isothermal, constant-density (and constant cross-section) piston flow reactors. Just replace t with z/u, and evaluate the outlet concentration at z = L. Equivalently, leave the result in the time domain and evaluate the outlet composition t = L/u. For example, the solution for component B in the competitive reaction sequence of... 

Example 7.5 Suppose the consecutive reactions 2A B C are elementary. Determine the rate constants from the following experimental data obtained with an isothermal, constant-volume batch reactor ... 

Equilibrium Compositions for Single Reactions. We turn now to the problem of calculating the equilibrium composition for a single, homogeneous reaction. The most direct way of estimating equilibrium compositions is by simulating the reaction. Set the desired initial conditions and simulate an isothermal, constant-pressure, batch reaction. If the simulation is accurate, a real reaction could follow the same trajectory of composition versus time to approach equilibrium, but an accurate simulation is unnecessary. The solution can use the method of false transients. The rate equation must have a functional form consistent with the functional form of K,i,ermo> e.g., Equation (7.38). The time scale is unimportant and even the functional forms for the forward and reverse reactions have some latitude, as will be illustrated in the following example. 

Example 14.1 Consider a first-order reaction occurring in a CSTR where the inlet concentration of reactant has been held constant at uq for f < 0. At time f = 0, the inlet concentration is changed to Up Find the outlet response for t > 0 assuming isothermal, constant-volume, constant-density operation. 

Example 14.3 The initial portion of a reactor startup is usually fed-batch. Determine the fed-batch startup transient for an isothermal, constant-density... 

Example 14.5 A CSTR is operating at steady state with a first-order reaction. It is desired to shut it down. Suppose this is done by setting = 0 while maintaining Qout = Q until the reactor is empty. Assume isothermal, constant-density operation with first-order reaction. 

Example 14.6 Explore the consequences of the following shutdown strategy for an isothermal, constant-density CSTR that has been operating at steady state. At time zero, the discharge flow rate is increased by a factor of 1 -b 5. Simultaneously, the inlet flow rate is made proportional to the fluid volume in the vessel. When does the vessel empty and what happens to the composition of the discharge stream during the shutdown interval ... 

Determine the fractional Ailing rate QflulQ that will All an isothermal, constant-density, stirred tank reactor while simultaneously achieving the steady-state conversion corresponding to flow rate Q. Assume a second-order reaction with aj kt = 1 and t = 5 h at the intended steady state. 

The complex chemical reaction, shown below, is carried out in an isothermal, constant-volume, batch reactor. All the reactions follow simple first-order kinetic rate relationships, in which the rate of reaction is directly proportional to concentration (Fig. 1.3). 

It is convenient to approach the concept of reaction rate by considering a closed, isothermal, constant pressure homogeneous system of uniform composition in which a single chemical reaction is taking place. In such a system the rate of the chemical reaction (r) is defined as ... 

Equations 3.1.47 and 3.1.50 express the relation between system concentrations and the fraction conversion for variable-volume systems that satisfy the linearity assumption of equation 3.1.40. This assumption is a reasonably unre-strictive one that is valid for all practical purposes in isothermal constant pressure systems in... 

Physical Methods that have been Used to Monitor Reaction Kinetics. In this section some physical property measurements of general utility are discussed. One of the oldest and most useful techniques used in kinetics studies involves the measurement of the total pressure in an isothermal constant volume reactor. This technique is primarily used to follow the course of homogeneous gas phase reactions that involve a change in the total number of gaseous molecules present in the reaction vessel (e.g., the hydrogenation of propylene). 

The reaction takes place in the gas phase in an isothermal constant volume reactor. Determine the order of the reaction and the reaction rate constant. The order may be assumed to be an integer. 

We will consider gases under two possible conditions isothermal and isentropic (or adiabatic). The isothermal (constant temperature) condition may be approximated, for example, in a long pipeline in which the residence time of the gas is long enough that there is plenty of time to reach thermal equilibrium with the surroundings. Under these conditions, for an ideal gas,... 

We do this for isothermal constant-density conditions first in a BR or PFR, and then in a CSTR. The reaction conditions are normalized by means of a dimensionless reaction number MAn defined by... 

For an nth-order isothermal, constant-density reaction in a BR or PFR (n 1), equa-... 

Table 18.1 Comparison of PFR and CSTR for series-reaction network A -4 B -+ C (isothermal, constant-density system K = kz/ki)...

Using an initial anthracene concentration of 0.025 mol L-1, determine the product distribution in an isothermal, constant-volume batch reactor, when the concentration of ANT is at a... 

A number of attempts have been made to modify the IAS model (Eqs. 22-29) to improve its accuracy and reduce computational efforts. Using the IAS model, DiGiano et al. [80] derived a Simplified Competitive Equilibrium Adsorption Model (SCAM). This model, which is based on the Freundlich isotherm, assumes the single-solute isotherms of all the components are equal and it utilizes average isotherm constants when this assumption is not valid. The IAS model equations have been reduced to a single expression ... 

Let us try to describe some of these phenomena quantitatively. For simphe-ity, we will assume isothermal, constant-holdup, constant-pressure, and constant density conditions and a perfectly mixed liquid phase. The gas feed bubbles are assumed to be pure component A, which gives a constant equihhrium concentration of A at the gas-liquid interface of CX (which would change if pressure and temperature were not constant). The total mass-transfer area of the bubbles is Aj j- and could depend on the gas feed rate f constant-mass-transfer coefficient (with units of length per time) is used to give the flux of A into the liquid through the liquid film as a flinction of the driving force. 

The new Liquid Lightning reactor is a single, isothermal, constant-holdup CSTR in which the concentration of ethanol, C, is controlled by manual changes in the feed concentration, Cq. Ethanol undergoes an irreversible first-order reaction at a specific reaction rate k = 0.25/day. The volume of the reactor is 100 barrels, and the throughput is 25 barrels/day. 

This kind of reactor can be used for isothermal constant pressure operations, of reactions having a single stoichiometry. For such systems the volume is linearly related to the conversion, or... 

Figure E4.6.1. Illustration of isotherms (constant temperature lines) below a thermal power plant discharging to a river.

Langmuir adsorption isotherm constants for several compounds on several adsorbents/water systems at ambient temperature are presented in Table 1.23, Appendix I. 

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