Chemical quantities mass calculations

To use the basic chemical quantity— the mole—to make calculations convenient To determine the empirical formula from percent composition or other mass-ratio data... 

The meaning of a chemical formula was discussed in Chapter 5, and we learned how to interpret formulas in terms of the numbers of atoms of each element per formula unit. In this chapter, we will learn how to calculate the number of grams of each element in any given quantity of a compound from its formula and to do other calculations involving formulas. Formula masses are presented in Section 7.1, and percent composition is considered in Section 7.2. Section 7.3 discusses the mole—the basic chemical quantity of any substance. Moles can be used to count atoms, molecules, or ions and to calculate the mass of any known number of formula units of a substance. Section 7.4 shows how to use relative mass data to determine empirical formulas, and the method is extended to molecular formulas in Section 7.5. 

Thus for a pure substance in a state such that the properties of the substance are not changing with time, a minimum description would contain statements about the chemical composition, mass, pressure, temperature, volume, and state (gas, liquid, or solid) of the substance and the magnitude and position of external force fields. Of the first group of quantities one is extraneous, since there is a thermodynamic equation relating them, and from it, in principle, any one quantity may be calculated, given the value of the others. 

Chemical stoichiometry is the area of study that considers the quantities of materials in chemical formulas and equations. Quite simply, it is chemical arithmetic. The word itself is derived from stoicheion, the Greek word for element and metron, the Greek word for measure. When based on chemical formulas, stoichiometry is used to convert between mass and moles, to calculate the number of atoms, to calculate percent composition, and to interpret the mole ratios expressed in a chemical formula. Most topics in chemical arithmetic depend on the interpretation of balanced chemical equations. Mass/mole conversions, calculation of limiting reagent and percent yield, and various relationships among reactants and products are commonly included in this topic area. 

Various operations in the field of chemical engineering and in combustion can be characterized by the simultaneous interaction of two processes, namely the transfer of heat and mass and chemical reaction. However, the determination of mean reaction rates in turbulent flows requires detailed knowledge about fluctuations of scalar quantities such as species concentrations and enthalpy. Due to the non-linear character of chemical reaction the calculation of mean reaction rates based on mean values of temperature and species concentrations is only possible in special circumstances, such as practically infinitely fast micro-mixing-rates or very small fluctuations of the scalar variable around its mean value. 

It is all very well to calculate the atomic, molecular, and formula masses of atoms, molecules, and other compounds, but since we cannot weigh an individual particle, these masses have a limited usefulness. To make measurements of mass useful, we must express chemical quantities at the macroscopic level. The bridge between the particulate and the macroscopic levels is molar mass, the mass in grams of one mole of a substance. The units of molar mass follow from its definition grams per mole (g/mol). Mathematically, the defining equation of molar mass is... 

Calculating Solution Concentration 406 Using Concentration to Calculate Mass or Volume 409 Calculating Dilution Quantities 413 Calculations Involving Solutions in Chemical Reactions 414 Calculating Molality 420 Using Molality 422... 

Chapter 9, Chemical Quantities in Reactions, describes the mole and mass relationships among the reactants and products and provides calculations of limiting reactants and percent yields. A section on Energy in Chemical Reactions completes the chapter. 

Chapter 7, Chemical Quantities and Reactions, introduces moles and molar masses of compounds, which are used in calculations to determine the mass or number of particles in a given quantity. Students leam to balance chemical equations and to recognize the types of chemical reactions combination, decomposition, single replacement, double replacement, and combustion reactions. Section 7.5 discusses Oxidation-Reduction Reactions using real-life examples, including biological reactions. Section... 

Variations in measurable properties existing in the bulk material being sampled are the underlying basis for samphng theory. For samples that correctly lead to valid analysis results (of chemical composition, ash, or moisture as examples), a fundamental theoiy of sampling is applied. The fundamental theoiy as developed by Gy (see references) employs descriptive terms reflecting material properties to calculate a minimum quantity to achieve specified sampling error. Estimates of minimum quantity assumes completely mixed material. Each quantity of equal mass withdrawn provides equivalent representation of the bulk. 

If a mass balance calculation yields the flow rate of a waste-stream, but the quantity of reported chemical in the waste-... 

The failure to identify the necessary authigenic silicate phases in sufficient quantities in marine sediments has led oceanographers to consider different approaches. The current models for seawater composition emphasize the dominant role played by the balance between the various inputs and outputs from the ocean. Mass balance calculations have become more important than solubility relationships in explaining oceanic chemistry. The difference between the equilibrium and mass balance points of view is not just a matter of mathematical and chemical formalism. In the equilibrium case, one would expect a very constant composition of the ocean and its sediments over geological time. In the other case, historical variations in the rates of input and removal should be reflected by changes in ocean composition and may be preserved in the sedimentary record. Models that emphasize the role of kinetic and material balance considerations are called kinetic models of seawater. This reasoning was pulled together by Broecker (1971) in a paper called "A kinetic model for the chemical composition of sea water."... 

During an experiment, a chemist may measure physical quantities such as mass, volume, and temperature. Usually the chemist seeks information that is related to the measured quantities but must be found by doing calculations. In later chapters we develop and use equations that relate measured physical quantities to important chemical properties. Calculations are an essential part of all of chemistry therefore, they play important roles in much of general chemistry. The physical property of density illustrates how to apply an equation to calculations. 

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 equivalent is defined in terms of a chemical reaction. It is defined in one of two different ways, depending on whether an oxidation-reduction reaction or an acid-base reaction is under discussion. For an oxidation-reduction reaction, an equivalent is the quantity of a substance that will react with or yield 1 mol of electrons. For an acid-base reaction, an equivalent is the quantity of a substance that will react with or yield 1 mol of hydrogen ions or hydroxide ions. Note that the equivalent is defined in terms of a reaction, not merely in terms of a formula. Thus, the same mass of the same compound undergoing different reactions can correspond to different numbers of equivalents. The ability to determine the number of equivalents per mole is the key to calculations in this chapter. 

Adsorption isotherms. The quantity of a chemical species i adsorbed per unit mass of a solid material contacting an aqueous solution phase is calculated with the equation (1) ... 

The mole (mol) is the amount of a substance that contains the same number of particles as atoms in exactly 12 grams of carbon-12. This number of particles (atoms or molecules or ions) per mole is called Avogadro s number and is numerically equal to 6.022 x 1023 particles. The mole is simply a term that represents a certain number of particles, like a dozen or a pair. That relates moles to the microscopic world, but what about the macroscopic world The mole also represents a certain mass of a chemical substance. That mass is the substance s atomic or molecular mass expressed in grams. In Chapter 5, the Basics chapter, we described the atomic mass of an element in terms of atomic mass units (amu). This was the mass associated with an individual atom. Then we described how one could calculate the mass of a compound by simply adding together the masses, in amu, of the individual elements in the compound. This is still the case, but at the macroscopic level the unit of grams is used to represent the quantity of a mole. Thus, the following relationships apply ... 

The first law of thermodynamics, which can be stated in various ways, enuciates the principle of the conservation of energy. In the present context, its most important application is in the calculation of the heat evolved or absorbed when a given chemical reaction takes place. Certain thermodynamic properties known as state functions are used to define equilibrium states and these properties depend only on the present state of the system and not on its history, that is the route by which it reached that state. The definition of a sufficient number of thermodynamic state functions serves to fix the state of a system for example, the state of a given mass of a pure gas is defined if the pressure and temperature are fixed. When a system undergoes some change from state 1 to state 2 in which a quantity of heat, Q, is absorbed and an amount of work, W, is done on the system, the first law may be written... 

Using the ideas of moles and masses we can use this information to calculate the quantities of the different chemicals involved. 

In practice, many of the conditions of measurement in practical chemical measurement are specified in terms of physical measurements. So, too, are many of the inputs to a given calculation. Though the establishment of traceability in these fields has been far from trivial, it is now essentially a routine matter for laboratories to obtain suitable calibrated equipment for measuring quantities such as length, volume, mass, temperature and time. The problem for most laboratories is related to their chemical reference values for amount of substance measurements. 

Toraya s WPPD approach is quite similar to the Rietveld method it requires knowledge of the chemical composition of the individual phases (mass absorption coefficients of phases of the sample), and their unit cell parameters from indexing. The benefit of this method is that it does not require the structural model required by the Rietveld method. Furthermore, if the quality of the crystallographic structure is poor and contains disordered pharmaceutical or poorly refined solvent molecules, quantification by the WPPD approach will be unbiased by an inadequate structural model, in contrast to the Rietveld method. If an appropriate internal standard of known quantity is introduced to the sample, the method can be applied to determine the amorphous phase composition as well as the crystalline components.9 The Rietveld method uses structural-based parameters such as atomic coordinates and atomic site occupancies are required for the calculation of the structure factor, in addition to the parameters refined by the WPPD method of Toraya. The additional complexity of the Rietveld method affords a greater amount of information to be extracted from the data set, due to the increased number of refinable parameters. Furthermore, the method is commonly referred to as a standardless method, since the structural model serves the role of a standard crystalline phase. It is generally best to minimize the effect of preferred orientation through sample preparation. In certain instances models of its influence on the powder pattern can be used to improve the refinement.12... 

Carrier or Tracer Addition. To quantify the purified final sample that will be measured by a radiation detection instrument (as compared to a mass spectrometer), a carrier or tracer is added to the sample. The carrier usually is the same element as the radioanalyte ( isotopic carrier ) and is standardized, typically at 5-20 mg/mL concentration. The carrier serves two purposes to provide macro quantities so that certain chemical steps (such as precipitation) may be performed on the sample, and to determine the chemical yield, usually by weight. A tracer serves only to determine the chemical yield of the process its nanogram quantities or less, comparable to the radioanalyte in the sample, prevent use as carrier. The tracer is measured by its characteristic radiation at the same time as the radioanalyte. An advantage in alpha-particle spectral analysis is that the activity of the analyte can be calculated from the activity of the tracer without knowledge of the detector counting efficiency, as discussed below. 

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