Equations balancing

When we write down a chemical reaction in the form of an equation, we have to balance the equation to ensure that we don t make mass appear or disappear. That is to say, the number of atoms of any particular element that are present at the beginning of the reaction, on the left-hand side or LHS of the arrow, is equal to the number on the right-hand side (RHS). Looking at a simple equation such as the combustion or burning of hydrogen  

The molecule of water always contains 1 oxygen atom, and the molecule of oxygen always contains 2 atoms of oxygen. The above equation has thus managed to lose an atom of oxygen in going from the LHS to the RHS. The law of conservation of mass does not allow this In order to correct this we must double up the number of molecules of water  

This now gives 2 atoms of oxygen on both sides of the equation. But, now there are 4 atoms of hydrogen on the RHS of the equation and only 2 on the left. To even this out, double up the number of hydrogen 

Left-hand side (LHS) Right-hand side (RHS) 

After balancing, the number of atoms on the LHS should be the same as the number on the RHS. 

Most moiecuiar bonds are covaient. However, in soiids there are four bonding entities or mechanisms ionic, covaient, metaiiic, and van der Waais. 

Formulas for hydrocarbon compounds may be expressed with a type of shorthand notation. For example, propane has a shorthand formula CH3-CH2-CH3 that is more accurately called a condensed structural formula. When using the shorthand formula, it is important to remember that the real compound and the three carbons are not in a straight line rather, they are connected at a 110-degree angle. 

Being able to balance a simple equation is an important part of working in the chemical industry. The raw materials that go into the development of new products on a commercial scale are very expensive. Balancing equations allows a technician to accurately determine the amount of reactants needed or products to be made. 

An unbalanced chemical equation will not yield the correct quantities. The law of conservation of matter is satisfied only when an equation is balanced. The total amount of reactants must equal the total amount of products in other words, what goes in must come out. Correct proportions are involved at every step of a chemical process. 

When looking at a chemical equation, the number immediately to the left of the chemical determines the molecules or mole units. For example, 2H2O indicates that there are two water molecules. Another common equation found in the chemical processing industry is 

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The equilibrium ratios are not fixed in a separation calculation and, even for an isothermal system, they are functions of the phase compositions. Further, the enthalpy balance. Equation (7-3), must be simultaneously satisfied and, unless specified, the flash temperature simultaneously determined. 

DGA Partial derivative of the enthalpy balance equation (7-14) with respect to the vapor-feed ratio. 

Reservoir engineers describe the relationship between the volume of fluids produced, the compressibility of the fluids and the reservoir pressure using material balance techniques. This approach treats the reservoir system like a tank, filled with oil, water, gas, and reservoir rock in the appropriate volumes, but without regard to the distribution of the fluids (i.e. the detailed movement of fluids inside the system). Material balance uses the PVT properties of the fluids described in Section 5.2.6, and accounts for the variations of fluid properties with pressure. The technique is firstly useful in predicting how reservoir pressure will respond to production. Secondly, material balance can be used to reduce uncertainty in volumetries by measuring reservoir pressure and cumulative production during the producing phase of the field life. An example of the simplest material balance equation for an oil reservoir above the bubble point will be shown In the next section. 

The material balance equation relating produced volume of oil (Np stb) to the pressure drop in the reservoir (AP) is given by ... 

Solution of the material balance equations gives the pressure and... 

Knowing the solution of the material balance equations It is easy to calcu>... 

The differential material balances contain a large number of physical parameters describing the structure of the porous medium, the physical properties of the gaseous mixture diffusing through it, the kinetics of the chemical reaction and the composition and pressure of the reactant mixture outside the pellet. In such circumstances it Is always valuable to assemble the physical parameters into a smaller number of Independent dimensionless groups, and this Is best done by writing the balance equations themselves in dimensionless form. The relevant equations are (11.20), (11.21), (11.22), (11.23), (11.16) and the expression (11.27) for the effectiveness factor. 

For ease of exposition, let us limit attention to. two independent reactions--the generalization to more reactions is straightforward. Then the material balance equations take the form... 

In order to Introduce thermal effects into the theory, the material balance equations developed in this chapter must be supplemented by a further equation representing the condition of enthalpy balance. This matches the extra dependent variable, namely temperature. Care must also be taken to account properly for the temperature dependence of certain parameters In... 

As In the case of the material balance equations, the enthalpy balance can be written in dimensionless form, and this introduces new dimensionless parameters in addition to those listed in Table 11.1. We shall defer consideration of these until Chapter 12, where we shall construct the unsteady state enthalpy and material balances, and reduce them to dimensionless form. 

In section 11.4 Che steady state material balance equations were cast in dimensionless form, therary itancifying a set of independent dimensionless groups which determine ice steady state behavior of the pellet. The same procedure can be applied to the dynamical equations and we will illustrate it by considering the case t f the reaction A - nB at the limit of bulk diffusion control and high permeability, as described by equations (12.29)-(12.31). 

Derivation of the working equations of upwinded schemes for heat transport in a polymeric flow is similar to the previously described weighted residual Petrov-Galerkm finite element method. In this section a basic outline of this derivation is given using a steady-state heat balance equation as an example. 

NOTE Alternately, you may want to try using a Tin/HC system which will give an equivalent yield in a much shorter time with the disadvantage that Tin is a much more expensive metal. The balanced equation for the reduction follows ... 

Besides equilibrium constant equations, two other types of equations are used in the systematic approach to solving equilibrium problems. The first of these is a mass balance equation, which is simply a statement of the conservation of matter. In a solution of a monoprotic weak acid, for example, the combined concentrations of the conjugate weak acid, HA, and the conjugate weak base, A , must equal the weak acid s initial concentration, Cha- ... 

The second type of equation is a charge balance equation. A charge balance equation is a statement of solution electroneutrality. 

Note that the concentration of Ca + is multiplied by 2, and that the concentrations of H3O+ and OH are also included. Charge balance equations must be written carefully since every ion in solution must be included. This presents a problem when the concentration of one ion in solution is held constant by a reagent of unspecified composition. For example, in many situations pH is held constant using a buffer. If the composition of the buffer is not specified, then a charge balance equation cannot be written. 

Write a mass balance and charge balance equations for a 0.10 M solution of NaHC03. 

Counting unknowns, we find four ([HE], [E-], [H3O4], and [OH-]). To solve this problem, therefore, we need to write two additional equations involving these unknowns. These equations are a mass balance equation... 

How does the result of this calculation change if we require our assumptions to have an error of less than 1%. In this case we can no longer assume that [HF] >> [F ]. Solving the mass balance equation (6.37) for [HF]... 

From the ladder diagram it appears that we may safely assume that the concentrations of H2L+ and L are significantly smaller than that for HL, allowing us to simplify the mass balance equation to... 

Substituting these equations, along with the equation for into the charge balance equation gives us... 

Note that in writing this mass balance equation, the concentration of Ag(NH3)2i" must be multiplied by 2 since two moles of NH3 occurs per mole of Ag(NH3)2i". The second additional equation is a mass balance on iodide and silver. Since Agl is the only source of N and Ag+, every iodide in solution must have an associated silver ion thus... 

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