Conversion factors chemical equations

The system of atomic units was developed to simplify mathematical equations by setting many fundamental constants equal to 1. This is a means for theorists to save on pencil lead and thus possible errors. It also reduces the amount of computer time necessary to perform chemical computations, which can be considerable. The third advantage is that any changes in the measured values of physical constants do not affect the theoretical results. Some theorists work entirely in atomic units, but many researchers convert the theoretical results into more familiar unit systems. Table 2.1 gives some conversion factors for atomic units. 

The dimensions of permeabiUty become clear after rearranging equation 1 to solve for P. The permeabiUty must have dimensions of quantity of permeant (either mass or molar) times thickness ia the numerator with area times a time iaterval times pressure ia the denomiaator. Table 1 contains conversion factors for several common unit sets with the permeant quantity ia molar units. The unit nmol/(m-s-GPa) is used hereia for the permeabiUty of small molecules because this unit is SI, which is preferred ia current technical encyclopedias, and it is only a factor of 2, different from the commercial permeabihty unit, (cc(STP)-mil)/(100 in. datm). The molar character is useful for oxygen permeation, which could ultimately involve a chemical reaction, or carbon dioxide permeation, which is often related to the pressure in a beverage botde. 

This rule allows you to find AH corresponding to any desired amount of reactant or product. To do this, you follow the conversion-factor approach used in Chapter 3 with ordinary chemical equations. Consider, for example,... 

A chemical equation tells us the relations between the amounts (in moles) of each reactant and product. By using the molar masses as conversion factors, we can express these relations in terms of masses. 

C03-0042. Diagram the process for converting from the mass of a compound of a known chemical formula to the number of atoms of one of its constituent elements. Include all necessary equations and conversion factors. 

Fig. 8-1 The conversion of moles of one reagent to moles of another, using a ratio of the coefficients of the balanced chemical equation as a factor label...

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. 

The pivotal conversion is from one substance to another, in moles with the balanced chemical equation providing the conversion factor. 

The conversion factor is obtained from the balanced chemical equation. 

The balanced chemical equation provides a conversion factor between the two compounds. 

QA First, determine the mass of iron that has reacted as Fe2+ with the titrant. The balanced chemical equation provides the essential conversion factor. 

The balanced chemical equation for a reaction is used to set up the conversion factor from one substance to another and that conversion factor, the mole ratio for the reaction, is applied to the moles given to calculate the moles required. 

Stoichiometry is the series of calculations on the basis of formulas and chemical equations and will be covered in Chapter 4. The use of conversion factors is common even when the relative proportions are not fixed by a chemical formula. Consider a silver alloy used for jewelry production. (Alloys are mixtures of metals and, as mixtures, may be produced in differing ratios of the metals.) A particular alloy contains 86 percent silver. Factors based on this composition, such as... 

We will specifically consider water relations, solute transport, photosynthesis, transpiration, respiration, and environmental interactions. A physiologist endeavors to understand such topics in physical and chemical terms accurate models can then be constructed and responses to the internal and the external environment can be predicted. Elementary chemistry, physics, and mathematics are used to develop concepts that are key to understanding biology—the intent is to provide a rigorous development, not a compendium of facts. References provide further details, although in some cases the enunciated principles carry the reader to the forefront of current research. Calculations are used to indicate the physiological consequences of the various equations, and problems at the end of chapters provide further such exercises. Solutions to all of the problems are provided, and the appendixes have a large list of values for constants and conversion factors at various temperatures. 

Consider the reaction of phosphorus with chlorine as shown in the previous equation. Of course, the chemist is not required to place exactly 2 mol of P and 3 mol of CI2 in a reaction flask. The equation gives the reacting ratio. Ratios of coefficients from balanced chemical equations can be used as conversion factors for solving problems. 

The coefficients in a balanced chemical equation show the relative numbers of moles of the substances in the reaction. As a result, you can use the coefficients in conversion factors called mole ratios. Mole ratios bridge the gap and can convert from moles of one substance to moles of another, as shown in Skills Toolkit 1. 

Does the chemical equation tell you anything about the masses of the reactants and products Not directly. But as you learned in Chapter 11, the mass of any substance can be determined by multiplying the number of moles of the substance by the conversion factor that relates mass and number of moles, which is the molar mass. Thus, the mass of the reactants can be calculated in this way. 

Mole ratios You have seen that the coefficients in a chemical equation indicate the relationships among moles of reactants and products. For example, return to the reaction between iron and oxygen described in Table 12-1. The equation indicates that four moles of iron react with three moles of oxygen. It also indicates that four moles of iron react to produce two moles of iron(III) oxide. How many moles of oxygen react to produce two moles of iron(III) oxide You can use the relationships between coefficients to write conversion factors called mole ratios. A mole ratio is a ratio between the numbers of moles of any two substances in a balanced chemical equation. As another example, consider the reaction shown in Figure 12-2. Aluminum reacts with bromine to form aluminum bromide. Aluminum bromide is used as a catalyst to speed up a variety of chemical reactions. 

To solve the problem, you need to know how the unknown moles of hydrogen are related to the known moles of potassium. In Section 12.1 you learned to use the balanced chemical equation to write mole ratios that describe mole relationships. Mole ratios are used as conversion factors to convert a known number of moles of one substance to moles of another substance in the same chemical reaction. What mole ratio could be used to convert moles of potassium to moles of hydrogen In the correct mole ratio, the moles of unknown (H2) should be the numerator and the moles of known (K) should be the denominator. The correct mole ratio is... 

Determine the moles of the unknown substance from the moles of the given substance. Use the appropriate mole ratio from the balanced chemical equation as the conversion factor. 

Multiply by chemical conversion factor from balanced equation... 

The coefficients in a balanced chemical equation give chemical conversion factors between the amounts of substances consumed in or produced by a chemical reaction. If 6.16 mol butane reacts according to the preceding equation, the amounts of O2 consumed and CO2 generated are... 

Most chemical reactions that occur on the earth s surface, whether in living organisms or among inorganic substances, take place in aqueous solution. Chemical reactions carried out between substances in solution obey the requirements of stoichiometry discussed in Chapter 2, in the sense that the conservation laws embodied in balanced chemical equations are always in force. But here we must apply these requirements in a slightly different way. Instead of a conversion between masses and number of moles, using the molar mass as a conversion factor, the conversion is now between solution volumes and number of moles, with the concentration as the conversion factor. 

The balanced chemical equation states that 1 mol of K2Ct207 reacts to give 2 mol of Cr and 3 mol of CI2. Using these two chemical conversion factors gives... 

The balanced chemical equation is the source of conversion factors relating moles of one substance to moles of another substance. 

This section is designed to fill the gap between the familiar formulas presented above and the assumptions and definitions of terms and physical constants needed to apply them. Values for all physical constants and needed conversion factors are provided, and dimensional analyses are included to show how the final results and their units are obtained. This close focus on the details and units of the equations themselves is followed by worked examples from the chemical literature. The goal is to provide nearly everything the interested reader may need to evaluate his or her own data, with reasonable confidence that he or she is doing so correctly. 

In these calculations, we will be generating conversion factors from the coefficients in the balanced chemical equation. 

As part of our calculation, we convert from moles of one substance (P4O10) to moles of another (H2O), so we need a conversion factor that relates the numbers of particles of these substances. The coefficients in the balanced chemical equation provide us with information that we can use to build this conversion factor. They tell us that six molecules of H2O are needed to react with one molecule of P4O10 in order to produce four molecules of phosphoric acid ... 

Example 10.1 shows how the coefficients in a balanced chemical equation provide a number of conversion factors that allow us to convert from moles of any reactant or product to moles of any other reactant or product. 

To see how molarity can be used in equation stoichiometry problems, let s take a look at the thought process for calculating the number of milliliters of 1.00 M AgN03 necessary to precipitate the phosphate from 25.00 mL of0.500 M Na3P04. The problem asks us to convert from amount of one substance in a chemical reaction to amount of another substance in the reaction, so we know it is an equation stoichiometry problem. The core of our setup will be the conversion factor for changing moles of sodium phosphate to moles of silver nitrate. To construct it, we need to know the molar ratio of AgN03 to Na3P04, which comes from the balanced equation for the reaction. 

Given a balanced chemical equation (or enough information to write one), construct conversion factors that relate moles of any two reactants or products in the reaction. 

Learning Goal Performing Calculations based on a chemical equation requires a facility for relating the number of atoms of an element to a corresponding number of moles of that element and ultimately to their mass in grams. Such calculations involve the use of conversion factors. This type of calculation was first described in Chapter 1. Some examples follow. 

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