Balancing equations atoms

Relationship between formulas, mass, moles and gas volumes Balanced equations Atomic structure. 

The analysis of steady-state and transient reactor behavior requires the calculation of reaction rates of neutrons with various materials. If the number density of neutrons at a point is n and their characteristic speed is v, a flux effective area of a nucleus as a cross section O, and a target atom number density N, a macroscopic cross section E = Na can be defined, and the reaction rate per unit volume is R = 0S. This relation may be appHed to the processes of neutron scattering, absorption, and fission in balance equations lea ding to predictions of or to the determination of flux distribution. The consumption of nuclear fuels is governed by time-dependent differential equations analogous to those of Bateman for radioactive decay chains. The rate of change in number of atoms N owing to absorption is as follows ... 

Formulate the constraining material-balance equations, based on conservation of the total number of atoms of each element in a system comprised of w elements. Let subscript k identify a particular atom, and define Ai as the total number of atomic masses of the /cth element in the feed. Further, let a be the number of atoms of the /cth element present in each molecule of chemical species i. The material balance for element k is then... 

General Material Balances. According to the law of conservation of mass, the total mass of an isolated system is invariant, even in the presence of chemical reactions. Thus, an overall material balance refers to a mass balance performed on the entire material (or contents) of the system. Instead, if a mass balance is made on any component (chemical compound or atomic species) involved in the process, it is termed a component (or species) material balance. The general mass balance equation has the following form, and it can be applied on any material in any process. 

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. 

Chemical reactions are represented by chemical equations, which identify reactants and products. Formulas of reactants appear on the left side of the equation those of products are written on the right In a balanced chemical equation, there are the same number of atoms of a given element on both sides. The same situation holds for a chemical reaction that you carry out in the laboratory atoms are conserved. For that reason, any calculation involving a reaction must be based on the balanced equation for that reaction. 

H.3 The first box below represents the reactants for a chemical reaction and the second box the products that form if all the reactant molecules shown react. Using the key below write a balanced equation for the reaction. Assume that if two atoms... 

Aniline, C6H5NH2(1), is a derivative of benzene in which a hydrogen atom has been replaced by an NH2 group, (a) Write the balanced equation for the combustion of aniline, (b) What is the mass of each product when 0.1754 g of aniline is burned in excess oxygen (c) If the bomb calorimeter in which this reaction was carried out had a volume of 355 mL, what minimum pressure of oxygen at 23°C must have been used to ensure complete combustion Assume that the volume of the aniline is negligible. 

When balancing redox equations, we consider the gain of electrons (reduction) separately from the loss of electrons (oxidation), express each of these processes as a halfreaction, and then balance both atoms and charge in each of the two half-reactions. When we combine the halfreactions, the number of electrons released in the oxidation must equal the number used in the reduction. 

Using models in learning about ehemieal equations has proved a successful tool, espeeially by students with diffieulties in eoneept understanding. By eounting the number of atoms in partiele representations they better understood the meaning of a balanced equation. Some students still have problems with balaneing chemical equations when models are not avail-... 

Balanced equation An equation using formulae where the number of atoms of each element involved in the reaction is the same on each side of the arrow. 

There are a number of past and present commercial routes to phenol using benzene as a feed stock. Outline two such processes, writing balanced equations for the reactions involved. Compare the two routes in terms of atom economy. 

Review a recent synthetic reaction you have carried out in the laboratory. Write a balanced equation for the reaction(s) and calculate the atom economy. From your experimental results calculate the Yield, E-factor and Effective Mass Yield (ignoring any water used). Identify ways in which this reaction could be made greener. 

C20-0083. Write a balanced equation for the reaction catalyzed by the enzyme superoxide dlsmutase. Make a sketch of the coordination environment around the two metal atoms. 

This assumption is the basis of the Bohr model for the hydrogen-like atom. When solved for m, this balancing equation is... 

Figure 9. A schematic and ideal model showing how the residence time of the magma in a steady-state reservoir of constant mass M, replenished with an influx O of magma and thoroughly mixed, can be calculated from disequilibrium data, in the simplifying case where crystal fractionation is neglected (Pyle 1992). The mass balance equation describing the evolution through time of the concentration [N2] (number of atoms of the daughter nuclide per unit mass of magma) in the reservoir is ...

A chemical equation describes a chemical reaction in many ways as an empirical formula describes a chemical compound. The equation describes not only which substances react, but the relative number of moles of each undergoing reaction and the relative number of moles of each product formed. Note especially that it is the mole ratios in which the substances react, not how much is present, that the equation describes. In order to show the quantitative relationships, the equation must be balanced. That is, it must have the same number of atoms of each element used up and produced (except for special equations that describe nuclear reactions). The law of conservation of mass is thus obeyed, and also the "law of conservation of atoms. Coefficients are used before the formulas for elements and compounds to tell how many formula units of that substance are involved in the reaction. A coefficient does not imply any chemical bonding between units of the substance it is placed before. The number of atoms involved in each formula unit is multiplied by the coefficient to get the total number of atoms of each element involved. Later, when equations with individual ions are written (Chap. 9), the net charge on each side of the equation, as well as the numbers of atoms of each element, must be the same to have a balanced equation. The absence of a coefficient in a balanced equation implies a coefficient of 1. 

The equation states that elementary sodium reacts with elementary chlorine to produce sodium chloride, table salt. (The fact that chlorine is one of the seven elements that occur in diatomic molecules when not combined with other elements is indicated.) The numbers before the Na and NaCI are coefficients, stating how many formula units of these substances are involved. If there is no coefficient in a balanced equation, a coefficient of 1 is implied, and so the absence of a coefficient before the Cl2 implies one Cl2 molecule. The equation thus states that when the two reagents react, they do so in a ratio of two atoms of sodium to one molecule of chlorine, to form two formula units of sodium chloride. In addition, it states that when the two reagents react, they do so in a ratio of 2 mol of sodium to 1 mol of chlorine molecules, to form 2 mol of sodium chloride. The ratios of moles of each reactant and product to every other reactant or product are implied ... 

A thermal decomposition reaction is a reaction that is activated by heat or high temperatures and that generates simpler (i.e., containing fewer atoms and thus characterized by lower molecular weights) substances from a single complex substance. The overall balanced equation for the thermal decomposition of sodium bicarbonate reveals the simpler substances produced ... 

If no KIE is present, the contribution of the derivative atom to the measured 8 value of the derivatised compound can be calculated using a simple mass balance equation (14.2), where n is number of moles of the isotope of interest, F is the fractional abundance of the isotope of interest, c refers to the compound of interest, d refers to the derivative group and... 

Next, balance oxygen atoms with water molecules in each half-equation ... 

Step 1 Begin balancing equations by trying suitable coefficients that will give the same number of atoms of each element on both sides of the equation. Remember to change coefficients, not subscripts. 

This is a critical chapter in your study of chemistry. Our goal is to help you master the mole concept. You will learn about balancing equations and the mole/mass relationships (stoichiometry) inherent in these balanced equations. You will learn, given amounts of reactants, how to determine which one limits the amount of product formed. You will also learn how to determine the empirical and molecular formulas of compounds. All of these will depend on the mole concept. Make sure that you can use your calculator correctly. If you are unsure about setting up problems, refer back to Chapter 1 of this book and go through Section 1-4, on using the Unit Conversion Method. Review how to find atomic masses on the periodic table. Practice, Practice, Practice. 

The Law of Conservation of Mass states that the total mass remains unchanged. This means that the total mass of the atoms of each element represented in the reactants must appear as products. In order to indicate this, we must balance the reaction. When balancing chemical equations, it is important to realize that you cannot change the formulas of the reactants and products the only things you may change are the coefficients in front of the reactants and products. The coefficients indicate how many of each chemical species react or form. A balanced equation has the same number of each type of atom present on both sides of the equation and the coefficients are present in the lowest whole number ratio. For example, iron metal reacts with oxygen gas to form rust, iron(III) oxide. We may represent this reaction by the following balanced equation ... 

This equation tells us that 4 iron atoms react with 3 oxygen molecules to form 2 rust compounds. Note that the number of iron atoms and oxygen atoms are the same on both sides of the equation (2 x Fe203 = 4 Fe and 6 O). Let s see how we went about arriving at the balanced equation for the rusting of iron. 

This balanced equation can be read as 4 iron atoms react with 3 oxygen molecules to produce 2 iron(III) oxide units. However, the coefficients can stand not only for the number of atoms or molecules (microscopic level) but they can also stand for the number of moles of reactants or products. So the equation can also be read as 4 mol of iron react with 3 mol of oxygen to produce 2 mol ofiron(III) oxide. In addition, if we know the number of moles, the number of grams or molecules may be calculated. This is stoichiometry, the calculation of the amount (mass, moles, particles) of one substance in the chemical equation from another. The coefficients in the balanced chemical equation define the mathematical relationship between the reactants and products and allow the conversion from moles of one chemical species in the reaction to another. 

Equation (1.11) is now examined closely. If the s (products) total a number / , one needs (// + 1) equations to solve for the // n s and A. The energy equation is available as one equation. Furthermore, one has a mass balance equation for each atom in the system. If there are a atoms, then (/t - a) additional equations are required to solve the problem. These (// a) equations come from the equilibrium equations, which are basically nonlinear. For the C—H—O—N system one must simultaneously solve live linear equations and (/t - 4) nonlinear equations in which one of the unknowns, T2, is not even present explicitly. Rather, it is present in terms of the enthalpies of the products. This set of equations is a difficult one to solve and can be done only with modem computational codes. 

If you look again at each half-reaction above, you will notice that the atoms and the charges are balanced. Like other types of balanced equations, half-reactions are balanced using the smallest possible whole-number coefficients. In the following equation, the atoms and charges are balanced, but the coefficients can all be divided by 2 to give the usual form of the half-reaction. 

As each reaction equation is entered, several checks are performed to catch errors in formulation or typing the correct number of tabs, equals, balanced quotes or parentheses, and conformance to the syntax rules which allows the equation to be separated into reactants and products, and these in turn to be decomposed into atoms. Each time a new chemical species is encountered it is reported to the user, who can determine whether a valid name has been entered. The equation is checked for balances in atomic elements and charges, and discrepancies listed for corrective action. Species names may be either formulas or text in the latter case the balance checking feature must be turned off to avoid false errors. 

Only six oxygen molecules are required to oxidize one glucose molecule, due to the presence of six "internal" oxygen atoms in glucose. There are 18 oxygen atoms on both sides of the balanced equation. 

Our discussion of balancing chemical equations has focused on accounting for atoms and molecules in both reactants and products. Although a balanced equation tells us how many atoms of an element it may take to form so many molecules, it is impractical to speak in these terms for common applications. For example, if we want to know how much carbon dioxide is produced when some vinegar is added to bak-... 

Because the balanced equation involves two magnesium and oxygen atoms, the previous equations are more appropriately written as... 

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