Mass molar

6 Define molar mass or interpret statements in which the term molar mass is used. 

7 Calculate the molar mass of any substance whose chemical formula is given (or known). 

The molar mass Per relationship yields a defining equation that is a conversion factor for dimensional analysis calculations. See Section 3.3. 

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 

The definitions of atomic mass, the mole, and molar mass are all directly or indirectly related to carbon-12. This leads to two important facts  

The values for the average masses of the atoms of the elements are listed inside the front cover of this book. 

Problem Solving Does the Answer Make Sense  

When you finish a problem, always think about the reasonableness of your answers. In Example 8.4, 5.68 mg of silicon is clearly much less than 1 mol of silicon (which has a mass of 28.09 g), so the final answer of 

22 X 10 ° atoms (compared to 6.022 x 10 atoms in a mole) at least lies in the right direction. That is, 1.22 x 10 ° atoms is a smaller number than 

022 X 10. Also, always include the units as you perform calculations and make sure the correct units are obtained at the end. Paying careful attention to units and making this type of general check can help you detect errors such as an inverted conversion factor or a number that was incorrectly entered into your calculator. 

To understand the definition of molar mass. To learn to convert between moles and mass of a given sample of a chemical compound. 

Note that when we say 1 mole of methane, we mean 1 mole of methane molecules. 

A chemical compound is, fundamentally, a collection of atoms. For example, methane (the major component of natural gas) consists of molecules each containing one carbon atom and four hydrogen atoms (CH4). How can we calculate the mass of 1 mole of methane That is, what is the mass of 6.022 X 10 CH4 molecules Because each CH4 molecule contains one carbon atom and four hydrogen atoms, 1 mole of CH4 molecules consists of 

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Various numbers of methane molecules showing their constituent atoms. 

IV is used to calculate average molar mass using the Mark-Houwink-Sakurada relationship, equation 6, 

During SEC, polymer molecules in solution are separated according to hydrodynamic volume on a column packed with an inert porous material such as a highly cross-linked polymer or silica. Separation occurs because large molecules are unable to penetrate aU of the pores in the packing. Successively smaller molecules spend more time in the packing material and elute later. 

This process, often called conventional calibration, has several limitations. Separation is based on size, not molar mass, so results are relative to the calibration standards. The chemical types of standards are limited and may not be available for copolymers. The range of molar masses is also limited and calculation of higher molar mass samples may rely upon extrapolated parts of the calibration curve. High molar mass polymers such as flocculants may block column frits and pores of the packing, and the relatively high pressure may degrade the polymer by shearing. 

Polyelectrolytes often interact with the column packing in aqueous systems, and it is necessary to use simple electrolytes and buffers to prevent or at least subdue unfavourable interactions that would otherwise lead to non-size exclusion behaviour. If the polymer contains hydrophobic groups, perhaps in a copolymer, addition of a less polar solvent such as methanol or acetonitrile maybe necessary for successful elution. 

The limitations of conventional calibration techniques are addressed by multiple detector techniques. On-line viscometers [10] and light scattering detectors [11, 12] enable more information to be elucidated from a chromatographic run. 

For simplicity, we use whole numbers for the molar masses of hydrogen and oxygen here. In general, you should use molar masses with at least as many significant figures as the actual data involved in the problem you are working. 

Because balanced chemical equations are always expressed in terms of numbers of particles, it will be convenient to have some easy way to determine the number of particles in a given sample of some substance. But there is no simple laboratory instrument that can measure the number of moles in a sample directly. Instead, we usually determine the number of moles indirectly from the mass of a sample. 

The link between the mass of a sample and the number of moles present is the molar mass of the substance in question. To determine the molar mass of a compound, we can exploit the idea of conservation of mass. Consider one mole of water as an example. We know that one mole of the compound must contain Avo-gadro s number of H2O molecules. Furthermore, we know that each of those molecules must contain one O atom and two H atoms. Avogadro s number of oxygen atoms is one mole, and we know from the periodic table that one mole of O atoms has a mass of 16.0 g. Because each molecule contains two hydrogen atoms, the entire one mole sample will contain two moles of H atoms. Again consulting the periodic table, we see that a mole of H atoms has a mass of 1.0 g, so two moles must have a mass of 2.0 g. The masses of the O and H atoms must be the same as the mass of the mole of H2O, so we can simply add them to get 18.0 g as the mass of one mole of H2O. In other words, the molar mass of H2O is 18.0 g/mol. We can do the same thing for any compound the sum of the molar masses of all of the atoms is the molar mass of the compound. In Example Problem 3.5, we determine the molar mass of several explosive compounds. 

Determine the molar mass of each of the following compounds, all of which have been used as explosives (a) lead azide, PbN, (b) nitroglycerin, C3H5N5O9, (c) mercury fulminate, Hg(ONC)2 

We must determine the mass contributed by each element and then add them up to calculate the molar mass. When parentheses appear in the formula, each atom inside the parentheses must be multiplied by its own subscript and by the subscript appearing after the right-hand parenthesis. 

Solution Since we are given a mass of isopentyl acetate and want the number of molecules, we must first compute the molar mass. 

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 mass in grams of one mole of a substance is the molar mass. 

The relationship above gives a way of converting from grams to moles to particles, and vice versa. If you have any one of the three quantities, you can calculate the other two. This becomes extremely useful in working with chemical equations, as we will see later, because the coefficients in the balanced chemical equation are not only the number of individual atoms or molecules at the microscopic level, but also the number of moles at the macroscopic level. 

In this case, the term 12.01 limits the number of significant figures. 

A substance s molar mass Is the mass in grams of 1 mole of the substance. 

Because 16.04 g represents the mass of 1 mole of methane molecules, it makes sense to call it the molar mass for methane. Thus the molar mass of a substance is the mass in grams ofl mole of the compound. Traditionally, the term molecular weight has been used for this quantity. However, we will use molar mass exclusively in this text. The molar mass of a known substance is obtained by summing the masses of the component atoms as we did for methane. 

Methane is a molecular compound—its components are molecules. Many substances are ionic—they contain simple ions or polyatomic ions. Examples are NaCl (contains Na+ and Q ) and CaCOs (contains and COs ). Because ionic compounds do not 

Calculate each of the following in 2.00 mol of H3PO4 a. moles of H b. moles of O 

A single atom or molecule is much too small to weigh, even on the most accurate balance. In fact, it takes a huge number of atoms or molecules to make enough of a substance for you to see. An amount of water that contains Avogadro s number of water molecules is only a few sips. However, in the laboratory, we can use a balance to weigh out Avogadro s number of particles for 1 mol of substance. 

For any element, the quantity called molar mass is the quantity in grams that equals the atomic mass of that element. We are counting 6.022 X 10 atoms of an element when we weigh out the number of grams equal to its molar mass. For example, carbon has an atomic mass of 12.01 on the periodic table. This means 1 mol of carbon atoms has a mass of 12.01 g. Then to obtain 1 mol of carbon atoms, we would need to weigh out 12.01 g of carbon. Thus, the molar mass of carbon is found by looking at its atomic mass on the periodic table. 

Given the chemical formula of a substance, calculate its molar mass. 

To determine the molar mass of a compound, multiply the molar mass of each element by its subscript in the formula and add the results as shown in Sample Problem 7.3. In this text, we round the molar mass of an element to the hundredths place 0.01) place or use at least four significant figures for calculations. 

Short-chain branched Long-chain branched Ladder 

Other properties such as fracture toughness and Young s modulus show a similar molar mass dependence, with constant values approached in the high molar mass region. Polymer properties are often obtained in the molar mass range from 10000 to 30000 g mol L Rheological properties such as melt 

All these averages are equal only for a perfectly monodisperse polymer. In all other cases, the averages are different M M M. The viscosity 

Let us now show that the mass average is always greater than the number average  

Equality occurs only when a sample is truly monodisperse, i.e. when all molecules are of the same molar mass. It can be shown that the breadth of the 

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Gray G W 1990 Low-molar-mass thermotropio liquid orystals Phil. Trans. R. Soc. A 330 73... 

As can be seen from equation 8.14, we may improve a method s sensitivity in two ways. The most obvious way is to increase the ratio of the precipitate s molar mass to that of the analyte. In other words, it is desirable to form a precipitate with as large a formula weight as possible. A less obvious way to improve the calibration sensitivity is indicated by the term of 1/2 in equation 8.14, which accounts for the stoichiometry between the analyte and precipitate. Sensitivity also may be improved by forming precipitates containing fewer units of the analyte. 

The product s molar mass, coupled with the temperature range, suggests that this represents the loss of H2O. The residue is CaC204. 

Be careful to use the necessary number of significant figures for the molar masses.) For... 

The wide variety of ketomethylene and amino ketone monomers that could be synthesized, and the abiUty of the quinoline-forming reaction to generate high molar mass polymers under relatively mild conditions, allow the synthesis of a series of polyquinolines with a wide stmctural variety. Thus polyquinolines with a range of chain stiffness from a semirigid chain to rod-like macromolecules have been synthesized. Polyquinolines are most often prepared by solution polymerization of bis(i9-amino aryl ketone) and bis (ketomethylene) monomers, where R = H or C H, in y -cresol with di-y -cresyl phosphate at 135—140°C for a period of 24—48 h (92). 

The next approach to incorporate the 12F-diol into a polyurethane matrix was reaction of the y -12F-diol with aUphatic diacid chlorides (where a = 3 or 4) to give low molar mass polyesters (141) ... 

Polarity Parameter. Despite their appareat simplicity, these parameters, ( ), show a good correlatioa with plasticizer activity for nonpolymeric plasticizers (10). The parameter is defiaed 2ls (j) = [M A j Po)]/1000 where M = molar mass of plasticizer, = number of carboa atoms ia the plasticizer excluding aromatic and carboxyHc acid carbon atoms, and Pg — number of polar (eg, carbonyl) groups present. The 1000 factor is used to produce values of convenient magnitude. Polarity parameters provide useful predictions of the activity of monomeric plasticizers, but are not able to compare activity of plasticizers from different families. 

The Flory-Huggins Interaction Parameter. These ideas, based on a study of polymer miscibility, have been appHed to plasticizers according to the foUowiag equation ia which is the molar volume of the plasticizer, obtaiaed from molar mass figures and density values at T, and represents the iateraction parameter (11). 

Mechanistic studies on the formation of PPS from polymerization of copper(I) 4-bromobenzenethiolate in quinoline under inert atmosphere at 200°C have been pubUshed (91). PPS synthesized by this synthetic procedure is characterized by high molar mass at low conversions and esr signals consistent with a single-electron-transfer mechanism, the Sj l-type mechanism described earlier (22). 

Chemical Grafting. Polymer chains which are soluble in the suspending Hquid may be grafted to the particle surface to provide steric stabilization. The most common technique is the reaction of an organic silyl chloride or an organic titanate with surface hydroxyl groups in a nonaqueous solvent. For typical interparticle potentials and a particle diameter of 10 p.m, steric stabilization can be provided by a soluble polymer layer having a thickness of - 10 nm. This can be provided by a polymer tail with a molar mass of 10 kg/mol (25) (see Dispersants). 

Third, picking the point on the cui ve of retention versus molar mass where 90 percent falls is inexacl . The retention cui ve usually bends in a way that makes picking the 90 percent point somewhat arbitraiy. 

The UF-resin itself is formed in the acid condensation step, where the same high molar ratio as in the alkaline methylolation step is used (F/U = 1.8 to 2.5) the methylolureas, urea and the residual free formaldehyde react to form linear and partly branched molecules with medium and even higher molar masses, forming polydispersed UF-resins composed of oligomers and polymers of different molar m.asses. Molar ratios lower than approx. 1.7-1.8 during this acid condensation step might cause resin precipitation. 

Molecules with higher molar masses, which are resin molecules in the closer sense of the word. 

The condensation reaction and the increase of the molar mass can also be monitored by GPC [25], With longer duration of the acid condensation step, oligomers of higher molar masses are progressively formed. 

PMDI is produced on an industrial scale by the phosgenation of diamin-odiphenylmethane. Structure and molar mass of PMDI depend on the number of aromatic rings in the molecule. For PMDI the distribution of the three monomeric isomers has a great influence on the quality, because the reactivities of the various isomers (4,4 -, 2,4 - and 2,2 -MDI) differ significantly. The greater the portion of the 2,2 - and 2,4 -isomers, the lower is the reactivity. This can lead to different bonding strengths as well as to residual isomers in the produced wood-based panels. 

PMDI also contains isocyanates with higher molar masses (triisocyanates, tetraisocyanates, polyisocyanates), whereby the structure and the molar mass depend on the number of phenyl groups. This distribution influences, to a great extent, the reactivity, but also the usual properties like viscosity, flowing and wetting behavior as well as the penetration into the wood surface. 

Polymer. The polymer determines the properties of the hot melt variations are possible in molar mass distribution and in the chemical composition (copolymers). The polymer is the main component and backbone of hot-melt adhesive blend it gives strength, cohesion and mechanical properties (filmability, flexibility). The most common polymers in the woodworking area are EVA and APAO. 

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