Reacting masses and volumes

Balanced half-equations (with equal numbers of electrons) can be used to establish the mole ratio of products in electrolysis. Half equations are used to describe redox reactions. These reactions involve the transfer of electrons (Chapter 9). 

For example, if molten sodium chloride is electrolysed then the mole ratio of sodium atoms to chlorine molecules is 2 1. 

2 mol of sodium ions accept 2 mol of electrons to form 2 mol of sodium atoms  

A mole of electrons is known as a Faraday. 1 Faraday or 1 mole of electrons carries a charge of 96 500 coulombs (C). The quantity of charge carried by a single electron is known from experiments to be 1.60 x 10 C. 

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Reacting masses and volumes - mole ratios in chemical... 

First, we must identify the chemistry. This is an acid-base titration in which hydrogen phthalate anions (the acid) react with OH (the base). We use the molar equality of acid and base at the stoichiometric point together with the equations that link moles with mass and volume. 

Fig. 8.3 shows the mass and volume relationships for a fully hydrated, saturated paste of w/c ratio 0.5, calculated using the above expressions and values. Following Powers and Brownyard, the hydrated cement is treated from a purely volumetric standpoint as a composite of reacted cement, non-evaporable water and gel water. The specific volume of the non-evaporable water was assumed to be 0.73 x I0 -gel water to be 1.00 x 10 m kg several reasons for example, the pore solution is in reality not pure water, but an alkali hydroxide solution with a specific volume (for 0.3 M KOH) of... 

A 211 g sample of barium carbonate, BaC03, reacts with a solution of nitric acid to give barium nitrate, carbon dioxide and water. If the acid is present in excess, what mass and volume of dry carbon dioxide gas at STP will be produced ... 

A cylindrical system (0.02 m diameter) reacts chemically to uniformly generate 24,000 W/m throughout its volume. The chemically reacting material k of 0.5 W/m °K) is encapsulated within a second cylinder (outside radius of 0.02 m, of 4 W/m °K). If the interface temperature between the cylinders is 151°C, find the temperatures at the center of the reacting mass and the outside surface. 

The stoichiometry of a reaction can be obtained from calculations involving reacting masses, gas volumes, and volumes and concentrations of solutions. 

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). 

Consider a fixed volume V into which fuel and air are injected at a fixed total mass flow rate m and temperature T0. The fuel and air react in the volume and the injection of reactants and outflow of products (also equal to rii) are so oriented that within the volume there is instantaneous mixing of the unbumed... 

The three neutrons produced when uranium splits have the ability to split other U-235 nuclei and start a self-sustaining chain reaction. Whether a chain reaction takes place depends on the amount of fissionable material present. The more fissionable material that is present, the greater the probability that a neutron will interact with another U-235 nucleus. The reason for this involves the basic relationship between surface area and volume as mass increases. If a cube with a length of 1 unit is compared to a cube of 2 units, it is found that the surface area to volume ratio of the 1 unit cube is twice that of the 2 unit cube (Figure 17.6). This shows that volume increases at a greater rate than surface area as size increases. The probability that neutrons escape rather than react also depends on the surface area to volume ratio. The higher this ratio is the more likely neutrons escape. When a U-235 nucleus contained in a small mass of fissionable uranium is bombarded by a neutron, the... 

Model Equations to Describe Component Balances. The design of PVD reacting systems requires a set of model equations describing the component balances for the reacting species and an overall mass balance within the control volume of the surface reaction zone. Constitutive equations that describe the rate processes can then be used to obtain solutions to the model equations. Material-specific parameters may be estimated or obtained from the literature, collateral experiments, or numerical fits to experimental data. In any event, design-oriented solutions to the model equations can be obtained without recourse to equipment-specific fitting parameters. Thus translation of scale from laboratory apparatus to production-scale equipment is possible. 

Two features of this expression are important for safety purposes. First, the heat release rate of a reaction is an exponential function of temperature and second, since it is proportional to the volume, it will vary with the cube of the linear dimension of the vessel (L3) containing the reacting mass. 

The sum is calculated by taking into account every system component, that is, the reaction mass and the equipment. Hence, the heat capacity of the reactor or of the vessel-at least the parts directly in contact with the reacting system-must be considered. For a discontinuous reactor, the heat accumulation can be written with mass or volume units ... 

During boiling of a reacting mass, vapor bubbles form in the liquid phase and rise to the gas-liquid interface. During the time they travel to the surface, they occupy a certain volume in the liquid, which results in an apparent volume increase of... 

The entropy, enthalpy, and volume quantities appearing in Equations (10.1) and (10.2) are molar quantities, but care must be taken that such quantities refer to the same mass of material. This requirement is readily proved. Consider one phase, the primed phase, to contain ( ) moles of component based on a specified chemical formula, and assume that no chemical reaction takes place in this phase. Assume that the double-primed phase contains (h,)" moles of component but that a reaction, possibly polymerization or decomposition, takes place in this phase. The chemical reaction may be expressed as = i vfii = 0, where the sum is taken over all reacting species. The two Gibbs-Duhem equations may then be written as... 

The mathematical description of simultaneous heat and mass transfer and chemical reaction is based on the general conservation laws valid for the mass of each species involved in the reacting system and the enthalpy effects related to the chemical transformation. The basic equations may be derived by balancing the amount of mass or heat transported per unit of time into and out of a given differential volume element (the control volume) together with the generation or consumption of the respective quantity within the control volume over the same period of time. The sum of these terms is equivalent to the rate of accumulation within the control volume ... 

Monge m 1783 1 adopted the then new principle of measuring the volumes of the reacting gases and calculating by means of the densities of the gases from the volume ratio to the mass ratio. The value obtained for the former ratio was approximately 2 1, but his data for the relative densities of the gases were far from accurate. 

Numerous reactions are performed by feeding the reactants continuously to cylindrical tubes, either empty or packed with catalyst, with a length which is 10 to 1000 times larger than the diameter. The mixture of unconverted reactants and reaction products is continuously withdrawn at the reactor exit. Hence, constant concentration profiles of reactants and products, as well as a temperature profile are established between the inlet and the outlet of the tubular reactor, see Fig. 7.1. This requires, in contrast to the batch reactor, the application of the law of conservation of mass over an infinitesimal volume element, dV, of the reactor. In contrast to a batch reactor the existence of a temperature profile does not allow us to consider the mass balances for the reacting components and the energy balance separately. Such a separation can only be performed for isothermal tubular reactors. 

Activity, selectivity, and yield are key catalyst performance characteristics. The recommended measure of catalyst activity is turnover frequency. Turnover frequency (or rate) is defined as the number of molecules that react per active site per unit time. Activity can also be defined as (1) the reaction rate per unit mass or volume of the catalyst, (2) the space velocity at which a given conversion is achieved at a specified temperature, (3) the temperature required to achieve a given conversion level, or (4) the conversion achieved under specified reaction conditions. Alternative 2 is practical for catalyst ranking. Alternatives 3 and 4 are rather uninformative. For rapid catalyst screening the latter two criteria are acceptable, but no catalyst should be eliminated from further consideration if it is only marginally inferior based on these criteria. 

Consider an analytical method involving the titration of hydrochloric acid with anhydrous sodium carbonate to determine the concentration of the acid. The measurements made are mass (weighing out a chemical to make up a solution of known concentration) and volume (dispensing liquids with pipettes and burettes). The reaction between the two chemicals is based on amount of substance - one mole of sodium carbonate reacts with two moles of hydrochloric acid - and the mass of a mole is known (e.g. the formula weight in grams of one mole of sodium carbonate is 105.99). All the measurements are based on either length or mass and are traceable to SI units, so the method is a primary method. 

We have already considered steady-state one-dimensional diffusion in the introductory sections 1.4.1 and 1.4.2. Chemical reactions were excluded from these discussions. We now want to consider the effect of chemical reactions, firstly the reactions that occur in a catalytic reactor. These are heterogeneous reactions, which we understand to be reactions at the contact area between a reacting medium and the catalyst. It takes place at the surface, and can therefore be formulated as a boundary condition for a mass transfer problem. In contrast homogeneous reactions take place inside the medium. Inside each volume element, depending on the temperature, composition and pressure, new chemical compounds are generated from those already present. Each volume element can therefore be seen to be a source for the production of material, corresponding to a heat source in heat conduction processes. 

Our study of stochiometry has shown that substances react in definite mole and mass proportions. Using previously discussed gas laws, we can show that gases also react in simple, definite proportions by volume. For example, one volume of hydrogen always combines (reacts) with one volume of chlorine to form two volumes of hydrogen chloride, if all volumes are measured at the same temperature and pressure... 

According to the law of mass action, the rate of a chemical reaction at a given temperature, expressed as the amount reacting per unit volume per unit time, depends only on the concentrations of the various substances influencing the rate (and not, for example, on the size of the reaction vessel). The substances that influence the rate are usually one or more of the reactants, occasionally one of the products, and sometimes a catalyst that does not appear in the balanced overall chemical equation. The dependence of the rate on the concentrations can be expressed in many cases as a direct proportionality, in which the concentrations may appear to the zero, first, or second power. The power to which the concentration of a substance appears in the rate expression is called the order of the reaction with respect to that substance. Some examples follow. 

Flush The flush reaction path model is analogous to the perfectly mixed-flow reactor or the continuously stirred tank reactor in chemical engineering (Figure 2.5). Conceptually, the model tracks the chemical evolution of a solid mass through which fresh, unreacted fluid passes through incrementally. In a flush model, the initial conditions include a set of minerals and a fluid that is at equilibrium with the minerals. At each step of reaction progress, an increment of unreacted fluid is added into the system. An equal amount of water mass and the solutes it contains is displaced out of the system. Environmental applications of the flush model can be found in simulations of sequential batch tests. In the experiments, a volume of rock reacts each time with a packet of fresh, unreacted fluids. Additionally, this type of model can also be used to simulate mineral carbonation experiments. 

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