Stoichiometric coefficient number

You can calculate the equilibrium constant for a reaction, from the concentrations of reactants and products at equilibrium. In the following reaction, for example, A and B are reactants, C and D are products, and a, b, c, and d are stoichiometric coefficients (numbers showing mole multiples in a balanced equation) ... 

Find the stoichiometric coefficients (numbers that multiply entire molecular or ionic formulas in equations) that equalize the number of each type of atom on both sides of the equation. 

Exact numbers, such as the stoichiometric coefficients in a chemical formula or reaction, and unit conversion factors, have an infinite number of significant figures. A mole of CaCb, for example, contains exactly two moles of chloride and one mole of calcium. In the equality... 

One molecule (or mole) of propane reacts with five molecules (or moles) of oxygen to produce three molecules (or moles) or carbon dioxide and four molecules (or moles) of water. These numbers are called stoichiometric coefficients (v.) of the reaction and are shown below each reactant and product in the equation. In a stoichiometrically balanced equation, the total number of atoms of each constituent element in the reactants must be the same as that in the products. Thus, there are three atoms of C, eight atoms of H, and ten atoms of O on either side of the equation. This indicates that the compositions expressed in gram-atoms of elements remain unaltered during a chemical reaction. This is a consequence of the principle of conservation of mass applied to an isolated reactive system. It is also true that the combined mass of reactants is always equal to the combined mass of products in a chemical reaction, but the same is not generally valid for the total number of moles. To achieve equality on a molar basis, the sum of the stoichiometric coefficients for the reactants must equal the sum of v. for the products. Definitions of certain terms bearing relevance to reactive systems will follow next. 

Now there are four H atoms, two Na atoms, and two O atoms on each side, and the equation conforms to the law of conservation of mass. The number multiplying an entire chemical formula in a chemical equation (for example, the 2 multiplying H20) is called the stoichiometric coefficient of the substance. A coefficient of 1 (as for H2) is not written explicitly. 

In other words, the stoichiometric coefficients multiplying the chemical formulas in any balanced chemical equation tell us the relative number of moles of each substance that reacts or is produced in the reaction. 

A balanced chemical equation symbolizes both the qualitative and the quantitative changes that take place in a chemical reaction. The stoichiometric coefficients tell us the relative numbers of moles of reactants and products taking part in the reaction. 

Sometimes we need to know how much product to expect from a reaction, or how much reactant we need to make a desired amount of product. The quantitative aspect of chemical reactions is the part of chemistry called reaction stoichiometry. The key to reaction stoichiometry is the balanced chemical equation. Recall from Section H that a stoichiometric coefficient in a chemical equation tells us the relative amount (number of moles) of a substance that reacts or is produced. Thus, the stoichiometric coefficients in... 

Stoichiometric coefficients are exact numbers so they do not limit the significant figures of stoichiometric calculations (see Appendix 1C). 

A note on good practice Enthalpies of formation are expressed in kilojoules per mole and enthalpies of reaction in kilojoules for the reaction as written. Note how the stoichiometric coefficients are interpreted as numbers of moles, and that an unwritten coefficient of 1 for urea is included as 1 mol in the calculation. 

To keep the units straight, we need to use the molar convention for this calculation and to use the stoichiometric coefficients in reaction E as pure numbers. To find an expression for AGr, we substitute F q. 4 for each substance into Eq. 3a. For example, for the general reaction E,... 

We can summarize these remarks as follows for chemical equations written with the smallest whole-number stoichiometric coefficients (Fig. 9.5) ... 

The powers to which the activities are raised in the expression for an equilibrium constant must match the stoichiometric coefficients in the chemical equation, which is normally written with the smallest whole numbers for coefficients. Therefore, if we change the stoichiometric coefficients in a chemical equation (for instance, by... 

The number of electrons required to reduce a species is related to the stoichiometric coefficients in the reduction half-reaction. The same is true of oxidation. Therefore, we can set up a stoichiometric relation between the reduced or oxidized species and the amount of electrons supplied. The amount of electrons required is calculated from the current and the length of time for which the current flows. 

Stem-Gerlach experiment The demonstration of the quantization of electron spin by passing a beam of atoms through a magnetic field, stick structure See line structure. stock solution A solution stored in concentrated form, stoichiometric coefficients The numbers multiplying chemical formulas in a chemical equation. 

Stern-Gerlach experiment, 31 stibnite, 626 stiffness of bond, 92 STM, FI6, 189 Stock number, F30 stock solution, F58 stoichiometric coefficient,... 

An integer precedes the formula of each substance. These numbers are the stoichiometric coefficients. When no number appears (as for N2 in this equation), the stoichiometric coefficient is 1. 

Stoichiometric coefficients describe the relative numbers of molecules involved in the reaction. In any actual reaction, immense numbers of molecules are involved, but the relative numbers are always related through the stoichiometric coefficients. Further, these coefficients describe both the relative numbers of molecules and the relative numbers of moles involved in the reaction. For example, the Haber reaction always involves immense numbers of molecules, but the equation describing the synthesis of ammonia tells us the following ... 

The stoichiometric coefficients in a balanced chemical equation must be chosen so that the atoms of each element are conserved. Many chemical equations can be balanced by inspection. Balancing by inspection means changing stoichiometric coefficients until the number of atoms of each element is the same on each side of the arrow. Usually, we can tell what changes need to be made by looking closely at the reaction and matching the numbers of atoms of each element on both sides of the equation. Consider the following example. 

The equation is not balanced, because there are too many carbon and hydrogen atoms on the left and too many oxygen atoms on the right. We need to change the numbers of molecules by changing stoichiometric coefficients until the numbers of atoms of each element are equal. 

The limiting reactant is the one whose number of moles divided by its stoichiometric coefficient has the smallest value. 

Identify the limiting reactant by dividing the numbers of moles by the stoichiometric coefficients ... 

Our goal is to link the mass of the product with the energy released. We must determine the number of moles of ammonia and take account of the stoichiometric coefficients in the balanced equation. A flowchart summarizes the calculations ... 

Remember that the number of electrons transferred is not explicitly stated in a net redox equation. This means that any overall redox reaction must be broken down into its balanced half-reactions to determine n, the ratio between the number of electrons transferred and the stoichiometric coefficients for the chemical reagents. 

The coefficients of any balanced redox equation describe the stoichiometric ratios between chemical species, just as for other balanced chemical equations. Additionally, in redox reactions we can relate moles of chemical change to moles of electrons. Because electrons always cancel in a balanced redox equation, however, we need to look at half-reactions to determine the stoichiometric coefficients for the electrons. A balanced half-reaction provides the stoichiometric coefficients needed to compute the number of moles of electrons transferred for every mole of reagent. 

SOLUTION. Taking into account the limited number of experiments and the relatively large number of components of the reaction mixture, the maximum number of reactions is three (Nr = 3). Assuming one reaction occuiring only, the following stoichiometric coefficients were computed using Eqn. (A-3) ... 

The columns of the orthonormal matrix Vp are linear combinations of reaction invariants . In fact, the only invariants for the batch reaction being analyzed can be stoichiometric coefficients. Hence the matrix Vp may be interpreted as containing the stoichiometric information (Waller and Makila (1981)) and its rank Nr can be considered to be equal to the number of independent... 

Vj is the stoichiometric coefficient for species i in the reaction. By convention, the value of v is positive for the products and negative for the reactants. The stoichiometric coefficients relate the simplest ratio of the number of moles of reactant and product species, involved in the reaction. 

Note in Table 5.10 that many of the integrals are common to different kinetic models. This is specific to this reaction where all the stoichiometric coefficients are unity and the initial reaction mixture was equimolar. In other words, the change in the number of moles is the same for all components. Rather than determine the integrals analytically, they could have been determined numerically. Analytical integrals are simply more convenient if they can be obtained, especially if the model is to be fitted in a spreadsheet, rather than purpose-written software. The least squares fit varies the reaction rate constants to minimize the objective function ... 

Guideline 6. The great majority of known elementary steps are bimolecular, the remainder being unimolecular or termolecular. Any reaction where the stoichiometric coefficients of the reactants add up to four or more must involve a multiplicity of steps. The ammonia synthesis reaction is known to occur by a number of steps rather than as... 

The equations for effectiveness factors that we have developed in this subsection are strictly applicable only to reactions that are first-order in the fluid phase concentration of a reactant whose stoichiometric coefficient is unity. They further require that no change in the number of moles take place on reaction and that the pellet be isothermal. The following illustration indicates how this idealized cylindrical pore model is used to obtain catalyst effectiveness factors. 

Assuming that the stoichiometric coefficient of the reactant is — 1 and that there is no change in the number of moles on reaction, the material balance on the volume element at steady state can be written as ... 

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