Negligible Volume Change

In some cases the volume change may be negligible from the start to the finish of the batch. For example, one reagent may be added in a very concentrated form to a dilute solution of the second reactant in the reactor. This can lead to a situation in which the volume of added reactant is quite small compared to that of the initial volume of solution. The equations for 

We can attempt to find a complete solution for this system of equations  

What we see is that this set of seemingly naive equations is not readily soluble analytically. The combination of the second-order kinetics plus the convective flow term is enough to require the use of numerical methods. To prove this to ourselves, we can redo the problem after removing the convective flow term. That is done in the cell that follows. 

Solve ifun Inverse functions are being used by Solve, so some solutions may not be found. 

Generalstop Further output of Power infy will be suppressed during this calculation. 

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When the flux expressions are consistent, as in Eq. (5-182), the dif-fusivities in Eq. (5-181) are identical. As a result, experimental diffu-sivities are often measured under constant volume conditions but may be used for applications involving open systems. It turns out that the two versions are veiy nearly equivalent for gas-phase systems because there is negligible volume change on mixing. That is not usually true for hquids, however. 

To simulate the PECVD process, a design team creates a PDE model involving momentum and mass balances, as summarized below. It is sufficient to assume the plasma to be a continuum, with physical properties of the gas constant (independent of position and time), negligible volume change of the reacting gases, and velocity and concentration fields symmetric about the reactor centerline (azimuthal symmetry). 

Measures of the composition of solutions of a solute B (2-bromoethanol, d = 1.7629 g cm"3 at 20°C) in a solvent A (water, d = 0.9982 g cm 3 at 20°C) against the mass fraction WB XB is the mole fraction and cpB is the volume fraction (assuming negligible volume change on mixing) (left hand ordinate) and mB is the molality and CB is the molarity (right hand ordinate). 

Assume negligible volume change during the reaction so that C, = Cs( 1 Xs). 

Flow many phases exist at a triple point Describe what would happen if a small amount of heat were added under constant-volume conditions to a sample of water at the triple point. Assume a negligible volume change during fusion. 

A solution is 0.0100 M in Pb + ions. If 0.103 mol of solid Na2S04 is added to 1.00 L of this solution (with negligible volume change), what percentage of the Pb + ions remain in solution ... 

A concentrated, strong acid is added to a solid mixmre of 0.015-mol samples of Fe(OH)2 and Cu(OH)2 placed in 1.0 L of water. At what values of pH will the dissolution of each hydroxide be complete (Assume negligible volume change.)... 

L of water. At what values of pH will the dissolution of each hydroxide be complete (Assume negligible volume change.)... 

How many moles ofH30 orOH must you add to 6.5 L of HA solution to adjust its pH from 4.82 to 5.22 Assume a negligible volume change. 

The volume change in this case is on the order of 20%, which is really too large to be acceptable within the context of an analysis in which it was assumed that negligible volume change would occur. Hence we are motivated to do the analysis again without this simplifying assumption. 

X 10 mole HNO3 per liter of solution. Assume that a negligible volume change occurs as a result of the addition of HNO3 and that the system is closed. 

The saturation solubility, assuming negligible volume changes on mixing is then obtained from... 

The activity derivative can he readily evaluated from sorption vs activity measurements. The subscripts T and p, indicating which variables are held constant, will be dropped for simplicity in the subsequent equations. Equation 7 was given earlier (4) using classical diffusion analysis for systems in which there is negligible volume change of mixing. 

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