Mole balances unsteady-state

An unsteady state mole balance yields — = -Vdot... 

In general, for unsteady state, the component mass or mole balance for each process unit may be stated as... 

After substituting Equations 3.1.2 and 3.1.3 into Equation 3.1.1, the oxygen mole balance reduces to Equation 3.1.4 in Table 3.1.1. Because Equation 3.1.4 is an unsteady-state, first-order differential equation, we need an initial condition to calculate the constant of integration. Initially, the tank contains air, which has an oxygen concentration of approximately 21 % by volume. We could also write the mole balance for nitrogen, but in this case it is more convenient to write the total mole balance, which results in Equation 3.1.5. Once we write Equations 3.1.4 to 3.1.6, the nitrogen mole balance is not an independent equation. Equation 3.1.7 states that the molar flow rate is equal to the product of the molar density and the volmnetric flow rate. 

The unsteady-state energy balance for an open system that has n species, each entering and leaving the system at its respective molar flow rates Fi (moles of i per time) and with its respective energy (joules per mole of i), is... 

In this chapter, we have already discussed the unsteady operation of one type of reactor, the batch reactor. In this section, w C discuss two other aspects of unsteady operation startup of a CSTR and seniibatch reactors. First, the startup of a CSTR is examined to determine the time necessary to reach steady-state operation [see Figure 4-14(a)], and then semibaich reactors are discussed, in each of these cases, we are interested in predicting the concentration and conversion as a function of lime. Closed-form analytical solutions to the differential equations arising from the mole balance of the.se reaction types can be obtained only for zero- and first-order reactions. ODE solvers must be used for other reaction orders. 

Apply the unsteady-state mole and energy balances to this system. Consider the upper steady state. Use the values you obtained in pan (b) as your initial values to plot C and T versus time up to 6 hours and then to plot versus T. What did you find Do you want to change any of your answers to pan (b) ... 

P4-29. Apply the unsteady state mole balances to three CSTRs in series. Use POLYMATH to solve three coupled ODEs. 

The coefficient of dNi/dt in the summation of (6-4) is defined as the partial molar internal energy of species i, because differentiation with respect to mole numbers of component i is performed at constant T, p and mole numbers of all other species in the mixture. The unsteady-state mass balance for species i in a batch reactor,... 

Total number of moles of species A that has been transported across the gas-liquid interface, based on an unsteady-state macroscopic mass balance... 

Time-Averaged Properties. The unsteady-state macroscopic mass balance for mobile component A is applied to the quiescent liquid, where the rate of interphase mass transfer via equation (11-205) is interpreted as an input term due to diffusion across the gas-liquid interface. There are no output terms, sources, sinks, or contributions from convective mass transfer in the macroscopic mass balance. Hence, the accumulation rate process is balanced by the rate of interphase mass transfer across time-varying surface S t), where both terms have dimensions of moles per time ... 

Before we go into the details of reactors, let us first write down the general mole balance under unsteady-state conditions around an arbitrary control volume shown in Figure 1.2 ... 

Solution to Example 6.2. This program calculates and plots % the concentration profiles of a gas A diffusing in liquid B % by solving the unsteady-state mole balance equation using % the function PARABOLICID.M. 

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