Mole number balance equation

The coefficients of a balanced equation represent numbers of moles of reactants and products. 

FIGURE 3.2 A summary of conversions between moles and grams for a chemical reaction. The numbers of moles tell how many molecules of each reactant are needed, as given by the coefficients of the balanced equation the numbers of grams tell what mass of each reactant is needed. 

According to the balanced equation, the number of moles of HC1 is the same as that of NaOH ... 

In a balanced equation, the number of moles of one substance is stoichiometrically equivalent to the number of moles of any other substance. The term stoichiometrically equivalent means that a definite amount of one substance is formed from, produces, or reacts with a definite amount of the other. These quantitative relationships are expressed as stoichiometrically equivalent molar ratios that we use as conversion factors to calculate these amounts. Table 3.3 presents the quantitative information contained in the equation for the combustion of propane, a hydrocarbon fuel used in cooking and water heating ... 

From the balanced equations, the number of moles of BaS04 equals the number of moles of Na2S04, which in turn is equal to half the number of moles of NaCI, or... 

In a balanced equation, the number preceding the formula of a gaseous substance represents the number of moles or molar volumes (22.4 L at STP) of that substance. 

If the T and P of a multiphase system are constant, then the quantities capable of change are the iadividual mole numbers of the various chemical species / ia the various phases p. In the absence of chemical reactions, which is assumed here, the may change only by iaterphase mass transfer, and not (because the system is closed) by the transfer of matter across the boundaries of the system. Hence, for phase equUibrium ia a TT-phase system, equation 212 is subject to a set of material balance constraints ... 

The general criterion of chemical reaction equiUbria is the same as that for phase equiUbria, namely that the total Gibbs energy of a closed system be a minimum at constant, uniform T and P (eq. 212). If the T and P of a siagle-phase, chemically reactive system are constant, then the quantities capable of change are the mole numbers, n. The iadependentiy variable quantities are just the r reaction coordinates, and thus the equiUbrium state is characterized by the rnecessary derivative conditions (and subject to the material balance constraints of equation 235) where j = 1,11,.. ., r ... 

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. 

Strategy (1) Start by calculating the number of moles of Fe2+. Then (2) use the coefficients of the balanced equation to find the number of moles of Mn04. Finally, (3), use molarity as a conversion factor to find the volume of KMn04 solution. 

The law of combining volumes, like so many relationships involving gases, is readily explained by the ideal gas law. At constant temperature and pressure, volume is directly proportional to number of moles (V = kin). It follows that for gaseous species involved in reactions, the volume ratio must be the same as the mole ratio given by the coefficients of the balanced equation. 

Note from the balanced equation that one mole of I2 is formed for every mole of H2. Putting it another way, as the reaction proceeds from left to right, the increase in the number of moles of I2 is the same as that for H2 ... 

Strategy First (1), write a balanced equation for the reaction, which is very similar to that for ZnS, except that Zn2+ is replaced by Bi3+. (2) Using the balanced equation, calculate the number of moles of S02. Finally (3), use the ideal gas law to calculate the volume of S02. 

STRATEGY We expect a strongly negative value because all combustions are exothermic and this oxidation is like an incomplete combustion. First, add up the individual standard enthalpies of formation of the products, multiplying each value by the appropriate number of moles from the balanced equation. Remember that the standard enthalpy of formation of an element in its most stable form is zero. Then, calculate the total standard enthalpy of formation of the reactants in the same way and use Eq. 20 to calculate the standard reaction enthalpy. 

A note on good practice The value of n depends on the balanced equation. Check to ensure that n matches the number of moles of electrons transferred in the balanced equation. 

The pragmatic consideration is that if a student were to undertake this reaction, then it would be important to react corresponding amounts of the two reactants. Amount here implies the number of moles, and the unbalanced version of the equation would imply that equal volumes of reactant solutions (if the same concentration) were needed, when actually twice as much alkali solution would be needed as acid solution because the acid is dibasic. The principled point is that the equation represents a chemical process, which is subject to the constraints of conservation rules matter (as energy) is conserved. In a chemical change, the elements present (whether as elements or in compounds), must be conserved. A balanced equation has the same elements in the quantities represented on both sides ... 

Fig. 8.10 A schematic diagram showing the relationship between mass, moles and the number of particles in a balanced equation...

C04-0147. Write the balanced equation and determine the number of moles of water produced when 2.95 mL of pyridine (C5 H5 N, p = 0.982 g/mL) reacts with excess O2 to give water, carbon dioxide, and molecular nitrogen. 

C04-0150. A former antiknock ingredient in gasoline is a colorless liquid whose formula is C5 H]2 O. Write the balanced equation, and determine the number of moles of carbon dioxide produced when 3.15 mL of the... 

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 ... 

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 ... 

The balanced equation expresses quantities in moles, but it is seldom possible to measure out quantities in moles directly. If the quantities given or required are expressed in other units, it is necessary to convert them to moles before using the factors of the balanced chemical equation. Conversion of mass to moles and vice versa was considered in Sec. 4.5. Here we will use that knowledge first to calculate the number of moles of reactant or product, and then use that value to calculate the number of moles of other reactant or product. 

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... 

How can we express the equilibrium state of such a system A direct approach would be to write each reaction that could occur among the system s species, minerals, and gases. To solve for the equilibrium state, we would determine a set of concentrations that simultaneously satisfy the mass action equation corresponding to each possible reaction. The concentrations would also have to add up, together with the mole numbers of any minerals in the system, to give the system s bulk composition. In other words, the concentrations would also need to satisfy a set of mass balance equations. 

The remaining step is to compute the system s bulk composition, if it is not fully known, according to the mass balance equations. The mole numbers Mw, Mi, and are not known when the modeler has constrained the corresponding variable nw, mt, or tig. In these cases, the mole numbers are determined directly from Equations 4.3 1.5. Where gases appear in the basis, the mole numbers Mm of gas components are similarly calculated from Equation 4.6. 

Chemical equations can be used to work out reacting masses. A balanced equation tells us the numbers of moles of each reactant that are required to produce the expected amount(s) of product in a chemical reaction. 

Attempts to define operationally the rate of reaction in terms of certain derivatives with respect to time (r) are generally unnecessarily restrictive, since they relate primarily to closed static systems, and some relate to reacting systems for which the stoichiometry must be explicitly known in the form of one chemical equation in each case. For example, a IUPAC Commission (Mils, 1988) recommends that a species-independent rate of reaction be defined by r = (l/v,V)(dn,/dO, where vt and nf are, respectively, the stoichiometric coefficient in the chemical equation corresponding to the reaction, and the number of moles of species i in volume V. However, for a flow system at steady-state, this definition is inappropriate, and a corresponding expression requires a particular application of the mass-balance equation (see Chapter 2). Similar points of view about rate have been expressed by Dixon (1970) and by Cassano (1980). 

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. 

A balanced chemical equation is a stoichiometric equation, it tells us the numbers of moles of reactants and products in a chemical reaction. A quantitative reaction is one in which the substances react completely according to the mole ratios given by the balanced equation. 

In a balanced chemical equation, the number of atoms of each element on the left-hand, or reactant, side will equal the number of atoms of eaeh element on the right-hand, or product, side. The above equation states that one mole of potassium perchlorate (KCIO 4, a reactant) will react with 4 moles of magnesium metal to produce one mole of potassinm chloride (KCl) and 4 moles of magnesinm oxide (MgO). 

---