Systems with Constant Mass

The feed is charged all at once to a batch reactor, and the products are removed together, the mass in the system being held constant during the reaction step. Such 

The component balance for a variable volume but otherwise ideal batch reactor can be written using moles rather than concentrations  

This is a more general version of Equation 1.25. For a first-order reaction, the number of molecules of the reactive component decreases exponentially with time. This is true whether or not the density is constant. If the density happens to be constant, the concentration of the reactive component also decreases exponentially, as in Equation 1.25. 

Most polymers have densities appreciably higher than their monomers. Consider a polymer having a density ofl040kgm that is formed from a monomer having a density of900 kg m . Suppose isothermal batch experiments require 2 h to reduce the monomer content to 20% by weight. What is the pseudo-first-order rate constant and what monomer content is predicted after 4 h  

SOLUTION Use a reactor charge of 900 kg as a basis and apply Equation 2.31 to obtain 

The feed is charged all at once to a batch reactor, and the products are removed together, with the mass in the system being held constant during the reaction step. Such reactors usually operate at nearly constant volume. The reason for this is that most batch reactors are liquid-phase reactors, and liquid densities tend to be insensitive to composition. The ideal batch reactor considered so far is perfectly mixed, isothermal, and operates at constant density. We now relax the assumption of constant density but retain the other simplifying assumptions of perfect mixing and isothermal operation. 

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All applications are for closed systems with constant mass. If a process is reversible and only p-V work is done, the first law and differentials can be expressed as follows. 

As any high school student, knows, Newton s second law of motion says that force is equal to mass times acceleration for a system with constant mass M. 

The following treatment applies to homogeneous systems with constant mass. The dissipative, time-dependent effects are caused in such homogeneous systems by disturbance of the equilibrium of the internal, molecular degrees of freedom. The... 

It is a fundamental dictum of classical thermodynamics that an isolated system, with constant mass, volume, and energy, attains equilibrium when its entropy reaches its maximum value. It is also well established that equilibrium can be operationally defined as the macroscopic state with no internal system gradients in temperature, pressure, and chemical potential. 

In geochemistry, interest is focused on open systems, in which mass is added or removed over observable time periods. A simple example of such a case is that of steady fluid flow in a system, with constant inflow of species A. Then for constant recharge of species A at concentration [AJ, (and discharge at concentration A), at rate k, with loss A in reaction with species B (recall Eq. 2.16), we have... 

Thermodynamics is concerned with energy and the way energy is transferred. It is a science of the macroscopic world but its effects are applied even at the microscopic scale. The first law introduces the basic thermodynamic concepts of work, heat and energy and can be defined as follows Energy can neither be created or destroyed in a system of constant mass, although it may be converted from one form to another. 

The above form of Newton s second law of motion applies to a system of constant mass. In fluid dynamics it is not usually convenient to work with elements of mass rather, we deal with elemental control volumes such as that shown in Fig. 5-4, where mass may flow in or out of the different sides of the... 

For chromatographic system with negligible mass transfer resistance the eddy diffusion is the dominant effect. Thereby, HETP values are constant and independent of the interstitial velocity. 

Figure 1.7 Vertical sections T(wb) and 7 (wA) through the phase prism which start at the binary water-surfactant (wb = 0) and the binary oil-surfactant (wA = 0) corner, respectively. These sections have been proven useful to study the phase behaviour of water- and oil-rich microemulsions, (a) Schematic view of the sections T wg) and T(wA) performed at a constant surfactant/fwater + surfactant) mass fraction ya and at a constant surfactant/(oil + surfactant) mass fraction 7b, respectively, (b) T(wb) section through the phase prism of the system FhO-n-octane-CioEs at ya = 0.10. Starting from the binary system with increasing mass fraction of oil wg, the oil emulsification boundary (2- 1) ascends, while the near-critical phase boundary (1 - 2) descends, (c) T(wA) section through the phase prism of the system EbO-n-octane-QoEs at 7b = 0.10. The inverse temperature behaviour is found on the oil-rich side With increasing fraction of water wA the water emulsification boundary (1 - 2) descends, whereas the near-critical phase boundary (2 —> 1) ascends.

The concentrations of reactant and products at the outlet of a packed bed reactor can be easily calculated with the mass balances for each compound supposing ideal plug flow behavior. For irreversible first-order consecutive reactions (Eq. (11.5)), the concentrations at the reactor outlet depend on the inlet concentration, Cj g, the rate constant, and the residence time, r. For reaction systems with constant fluid density, the residence time corresponds to the space-time defined as, r = V/Vg, with V the reactor volume and Vq the volumetric inlet flow. The space time... 

Eq. (5-28) is not suitable for describing spatially and temporally variable diffusion processes. Because of the principle of the conservation of mass, however, the divergence of the flux can always be set equal to the time derivative of the local concentration. This leads to Pick s second law which may be written as follows for the case of binary systems with constant diffusion coefficients ... 

Various conditions determine what states of a system are physically possible. If a uniform phase has an equation of state, property values must be consistent with this equation. The system may have certain built-in or externally-imposed conditions or constraints that keep some properties from changing with time. For instance, a closed system has constant mass a system with a rigid boundary has constant volume. We may know about other conditions that affect the properties during the time the system is under observation. 

It follows from Example 16.3 that if two systems of constant mass and volume are in equilibrium with a heat reservoir, the probability of any of their quantum states is an exponential function of its energy ... 

Fig. 1.2-2. Rates of drug dissolution. In this case, describing the system with a mass transfer coefficient k is best because it easily correlates the solution s concentration versus time. Describing the system with a diffusion coefficient D gives a similar correlation but introduces an unnecessary parameter, the film thickness 1. Describing the system with a reaction rate constant k also works, but this rate constant is a function not of chemistry but of physics.

You should be able to describe a system at equilibrium both qualitatively and quantitatively. Rigorous solutions to equilibrium problems can be developed by combining equilibrium constant expressions with appropriate mass balance and charge balance equations. Using this systematic approach, you can solve some quite complicated equilibrium problems. When a less rigorous an-... 

S] Low mass-flux with constant property system. Use with arithmetic concentration difference. 

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