Relating masses of reactants and products

The concept of molar mass makes it easy to determine the number of particles in a sample of a substance by simply measuring the mass of the sample. The concept is also useful in relating masses of reactants and products in chemical reactions. 

To learn to relate masses of reactant and products in a chemical reaction... 

Balanced chemical equations make it possible to relate masses of reactants and products, Scales are devices commonly used to measure mass. 

Suppose you wanted to produce 500 g of methanol. How many grams of CO2 gas and H2 gas would you need How many grams of water would be produced as a by-product Those are questions about the masses of reactants and products. But the balanced chemical equation shows that three molecules of hydrogen gas react with one molecule of carbon dioxide gas. The equation relates molecules, not masses, of reactants and products. 

You see from the preceding discussion that a balanced chemical equation relates the amounts of snbstances in a reaction. The coefficients in the equation can be given a molar interpretation, and using this interpretation you can, for example, calculate the moles of product obtained from any given moles of reactant. Also, yon can extend this type of calcnlation to answer questions about masses of reactants and products. 

In Chapter 13, you learned how to use moles and molar mass along with a balanced chemical equation to calculate the masses of reactants and products in a chemical reaction. Now that you know how to relate volumes, masses, and moles for a gas, you can do stoichiometric calculations for reactions involving gases. 

Under natural conditions the rates of dissolution of most minerals are too slow to depend on mass transfer of the reactants or products in the aqueous phase. This restricts the case to one either of weathering reactions where the rate-controlling mechanism is the mass transfer of reactants and products in the soHd phase, or of reactions controlled by a surface process and the related detachment process of reactants. 

Figure 5. Relation between mass weighted coordinates of reactants and products in Type I reactions.

Numeroxis 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 The mixture of unconverted reactants and reaction products is continuously withdrawn at the reactor exit.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. 8.10). This requires, in contrast to the batch reactor, the application of the law of conservation of mass over an infinitesimal volume element, d V, or mass element, dW, of the reactor. For a tubular reactor with a fixed catalytic bed, it is more convenient to relate the production rates to the catalyst mass, rather than to the reactor volume. 

Example 4-12 demonstrates how the weight in grams of reactants and products in a chemical reaction are related. As shown in Figure 4-2, a calculation of this type is a three-step process involving (1) transformation of the known mass of a substance in grams to a corresponding number of moles, (2) multiplication by a factor that accounts for the stoichiometry, and (3) reconversion of the data in moles back to the metric units called for in the answer. 

The rate expressions derived above describe the dependence of die reaction rate expressions on kinetic parameters related to the chemical reactions. These rate expressions are commonly called the intrinsic rate expressions of the chemical reactions. However, as discussed in Chapter 1, in many instances, the local species concentrations depend also on the rate that the species are transported in the reaction medium. Hence, the actual reaction rates are affected by the transport rates of reactants and products. This is manifested in two general cases (i) gas-solid heterogeneous reactions, where species diffusion through the pore plays an important role, and (ii) gas-hquid reactions, where interfacial species mass-transfer rate as wen as solubility and diffusion play an important role. Considering the effect of transport phenomena on the global rates of the chemical reactions represents a very difficult task in the design of many chemical reactors. These topics are beyond the scope of this text, but the reader should remember to take them into consideration. 

A balanced equation contains a wealth of quantitative information relating individual chemical entities, amounts of chemical entities, and masses of substances. It is essential for all calculations involving amounts of reactants and products if you know the number of moles of one substance, the balanced equation tells you the number of moles of all the others in the reaction. 

To verify that mass is conserved, first convert moles of reactant and product to mass by multiplying by a conversion factor-the molar mass-that relates grams to moles. 

The successive carboxylation and decarboxylation reactions are both close to equilibrium (they have low values of their standard free energies) as a result, the conversion of pyruvate to phosphoenolpyruvate is also close to equilibrium (AG° = 2.1 kj mol = 0.5 kcalmoh ). A small in crease in the level of oxaloacetate can drive the equilibrium to the right, and a small increase in the level of phosphoenolpyruvate can drive it to the left. A concept well known in general chemistry, the law of mass action, relates the concentrations of reactants and products in a system at equilibrium. Changing the concentration of reactants or products causes a shift to reestablish equilibrium. A reaction proceeds to the right on addition of reactants and to the left on addition of products. 

The most important characteristic of this problem is that the Hougen-Watson kinetic model contains molar densities of more than one reactive species. A similar problem arises if 5 mPappl Hw = 2CaCb because it is necessary to relate the molar densities of reactants A and B via stoichiometry and the mass balance with diffusion and chemical reaction. When adsorption terms appear in the denominator of the rate law, one must use stoichiometry and the mass balance to relate molar densities of reactants and products to the molar density of key reactant A. The actual form of the Hougen-Watson model depends on details of the Langmuir-Hinshelwood-type mechanism and the rate-limiting step. For example, consider the following mechanism ... 

Briefly, the flow-through reactor has the advantages of essentially no external or internal mass transfer limitations, no substrate holdup, and no channeling all of which contribute to a more efficient utilization of immobilized enzyme. The substrate must contact all reactive sites while passing through the pores therefore eliminating dispersion or diffusion related problems. One can perform sequential reactions, since there is no holdup of reactants and products from one reaction step to the next. 

Chemical formulas and chemical equations both have a quantitative significance in that the subscripts in formulas and the coefficients in equations represent precise quantities. The formula H2O indicates that a molecule of this substance (water) contains exactly two atoms of hydrogen and one atom of oxygen. Similarly, the coefficients in a balanced chemical equation indicate the relative quantities of reactants and products. But how do we relate the numbers of atoms or molecules to the amounts we measure in the laboratory Although we cannot directly count atoms or molecules, we can indirectly determine their numbers if we know their masses. Therefore, before we can pursue the quantitative aspects of chemical formulas and equations, we must examine the masses of atoms and molecules. 

The molecular partition functions, Q, can be related to molecular properties of reactants and products. The partition function expresses the probability of encountering a molecule, so that the ratio of partition functions for the products versus the reactants of a chemical reaction expresses the relative probability of encountering products versus reactants and, therefore, the equilibrium constant. The partition function can be written as a product of independent factors at the level of various approximations, each of which is related to the molecular mass, the principal moments of inertia, the normal vibration frequency, and the electronic energy levels, respectively. When the ratio of isotopic partition function is calculated, the electronic part of the partition function cancels, at the level of the Born-Oppenheimer approximation, an approximation stating that the motion of nuclei in ordinary molecular vibrations is slow relative to the motions of electrons. 

In electrode reactions, the reactant has to find the electrode surface where electrons are taken or released, and therefore the mass transport of reactants and products becomes very important in the description of electrode reactions where we will be interested in current-time and current-potential relations. The master equation for mass transport to an electrode surface is the Nernst-Planck equation ... 

In Chapter 0, we used relationships between amounts (in moles) and masses (in grams) of reactants and products to solve stoichiometry problems. When the reactants and/or products are gases, we can also use the ideal gas equation to relate the number of moles n to the volume V or pressure P to solve such problems. Examples 5.7 and 5.8 show how the ideal gas equation is used in such calculations. 

Equation (15.2) is the mathematical form of the law of mass action. It relates the concentrations of reactants and products at equilibrium in terms of a qrrantity called the equilibrium constant The equilibritun constant is defined by a quotient. The ntunera-tor is obtained by mrrltiplying together the eqtrilibrium concentrations of the products, each raised to a power equal to its stoichiometric coefficient in the balanced equation. The same procedrrre is applied to the equilibrium concentrations of reactants to obtain the denominator. This formulation is based on purely empirical evidence, such as the study of reactions like NO2-N2O4. 

Reaction heat and temperature difference between gas stream and catalyst leads to the heat transfer processes between gas and solid. The mass and heat transfer coefficients depend on Reynold and Prandtl numbers of fluid flow, i.e., state and physical properties of fluid flow. Mass and heat transfer processes in solid cataljret and catal3dic reaction process on internal surface of catalysts take place simultaneously, which relate to the diffusion coefficients of reactants and products as well as the heat conductivity coefficient of catalysts. Therefore, the overall rate of a catal3dic reaction depends not only on the rate of chemical reaction, but also on several physical processes such as flowing state, mass and heat transfer. The kinetics involving physical process effect is usually called as apparent or macrokinetics, while that having no physical processes is called intrinsic or microkinetics. 

If one works with data collected in the kinetic regime, i.e., free from mass transfer limitations, then steps 1 and 5 are very rapid on a relative scale and can be ignored. Thus the challenge is to acquire data in the kinetic regime and then describe the surface reaction at a microscopic level by a series of elementary steps which are used to derive a rate expression relating the unknown concentrations of surface intermediates to observable macroscopic concentrations of reactants (and products, if necessary). 

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