Molar mass finding

Given molar mass, find the mass in grams of each of the following substances ... 

To convert the mass of each element into the amount in moles, you must multiply by the proper conversion factor, which is the reciprocal of the molar mass. Find molar mass by using the periodic table. 

Figure 15.6 indicates that this is a relatively noninteractive column. PMMA is eluted in toluene, yet the calibration dependences surprisingly diverge in the area of high molar masses. It has the opposite tendency to that observed for various polymers with PS/DVB columns by Dawkins (5,20) and also contradicts the finding for columns No. 5 and 6. 

Notice that the formula of a substance must be known to find its molar mass. It would be ambiguous, to say the least, to refer to the molar mass of hydrogen. One mole of hydrogen atoms, represented by the symbol H, weighs 1.008 g the molar mass of H is 1.008 g/mol. One mole of hydrogen molecules, represented by the formula H weighs 2.016 g the molar mass of H2 is 2.016 g/mol. 

Strategy Find the molar mass of CgH T and use it to convert moles to grams in (a), grams to moles in (b), and (with Avogadro s number) grams to molecules in (c). 

As you will see shortly, the formula of a compound can be used to determine the mass percents of the elements present. Conversely, if the percentages of the elements are known, the simplest formula can be determined. Knowing the molar mass of a molecular compound, it is possible to go one step further and find the molecular formula. In this section we will consider how these three types of calculations are carried out. 

Strategy Calculate the molar mass corresponding to the simplest formula, CH20. Then find the multiple by dividing the actual molar mass, 60 g/mol, by the molar mass of CH20. 

The escape velocity required for gas molecules to overcome the earths gravity and go off to outer space is 1.12 X 103m/s at 15°C Calculate die molar mass of a species with that velocity. Would you expect to find He and H2 molecules in the earth s atmosphere How about argon atoms ... 

Strategy In (a), find the repeating unit from which the polymer chain is constructed. In (b), divide the molar mass of the polymer by that of the monomer. 

How can we determine the amount of substance present if we can t count the atoms directly We can find the amount if we know the mass of the sample and the molar mass, M, the mass per mole of particles ... 

It follows that n — m M. That is, to find the number of moles, n, we divide the total mass, m, of the sample by the molar mass. 

SOLUTION To find the mass of KMn04, mKMnU, that corresponds to 0.10 mol KMn04, we note that, because the molar mass of the compound is 158.04 g-mol 1,... 

To find the molecular formula of a compound, we need one more piece of information—its molar mass. Then all we have to do is to calculate how many empirical formula units are needed to account for the molar mass. One of the best ways of determining the molar mass of an organic compound is by mass spectrometry. We saw this technique applied to atoms in Section B. It can be applied to molecules, too and, although there are important changes of detail, the technique is essentially the same. 

To find the number of C3H4C>3 formula units needed to account for the observed molar mass of vitamin C, we divide the molar mass of the compound by the molar mass of the empirical formula unit ... 

Use their molar masses to find the amounts (in moles) of each gas present. 

We have seen that effusion reveals that the average speed of molecules in a gas is inversely proportional to the square root of their molar mass. In effusion experiments at different temperatures, we find that the rate of effusion increases as the temperature is raised. Specifically, for a given gas, the rate of effusion increases as the square root of the temperature ... 

A finely powdered solid sample of an osmium oxide (which melts at 40. °C and boils at 130.°C) with a mass of 1.509 g is placed into a cylinder with a movable piston that can expand against the atmospheric pressure of 745 Torr. Assume that the amount of residual air initially present in the cylinder is negligible. When the sample is heated to 200.°C, it is completely vaporized and the volume of the cylinder expands by 235 mL. What is the molar mass of the oxide Assuming that the oxide is OsOv, find the value of x. 

All noble gases except helium crystallize with ccp structures at very low temperatures. Find an equation relating the atomic radius to the density of a ccp solid of given molar mass and apply it to deduce the atomic radius of each of the following noble gases, given the density of each (in g-cm ) Ne, 1.20 Ar, 1.40 Kr, 2.16 Xe, 2.83 Rn, 4.4 (estimated). 

Use the molar mass of butane, 58.12 g-mol, to find the mass of product. 

Find the amount of each species from the molar masses of solute and solvent. 

Use the molar mass of atomic sulfur to find the value of x in the molecular formula Sv. 

J 10 Use osmometry to find the molar mass of a solute (Toolbox 8.2 and Example 8.10). 

As for conventional linear polymers, gel permeation chromatography (GPC) can be used to find information on the composition of dendrimers, including their polydispersities. Obtaining standards of known relative molar mass and polydispersity is a problem with dendrimers, so the approach that has been taken most often is to use polystyrene standards, as described in Chapter 6. 

If the molar mass of the compound is not known, the best we can do is to find the simplest formula that agrees with the elemental analysis. This simplest formula, or empirical formula, contains the smallest set of whole-number subscripts that match the elemental analysis. The empirical formula of caffeine is C4 H5 N2 O. 

First, follow the four-step process for finding the empirical formula. Then compare the empirical formula with the molar mass information to find the true formula. 

A petroleum chemist isolated a component of gasoline and found its molar mass to be 114 g/mol. When a 1.55-g sample of this compound was burned in excess oxygen, 2.21 g of H2 O and 4.80 g of CO2 were produced. Find the empirical and molecular formulas of the compound. 

The flowchart in Figure 3-15 outlines the process. From masses of products, determine masses of elements. Then convert masses of elements to moles of elements. From moles of the elements, find the empirical formula. Finally, use information about the molar mass to obtain the molecular formula. 

Does it bother you to find that neither the chemical formula nor the molar mass is needed for these calculations Remember that not all data are necessarily required for any particular calculation. Because average kinetic energy depends on temperature but not on molar mass, we do not need mass information to do this problem. 

The ideal gas equation can be combined with the mole-mass relation to find the molar mass of an unknown gas PV = nRT (ideal gas equation) and n — (mole-mass relation) if we know the pressure, volume, and temperature of a gas sample, we can use this information to calculate how many moles are... 

We can use the ideal gas equation to calculate the molar mass. Then we can use the molar mass to identify the correct molecular formula among a group of possible candidates, knowing that the products must contain the same elements as the reactants. The problem involves a chemical reaction, so we must make a connection between the gas measurements and the chemistry that takes place. Because the reactants and one product are known, we can write a partial equation that describes the chemical reaction CaC2(. ) +H2 0(/) Gas -I- OH" ((2 q) In any chemical reaction, atoms must be conserved, so the gas molecules can contain only H, O, C, and/or Ca atoms. To determine the chemical formula of the gas, we must find the combination of these elements that gives the observed molar mass. 

A temperature of 350 K is 77 °C, a reasonable result. Notice that the molar mass and the gas constant appear in both calculations, so we can find the temperature requirement by... 

Our task is to estimate the volume occupied by one atom of lithium. As usual, the mole is a convenient place to begin the calculations. Visualize a piece of lithium containing one mole of atoms. The molar mass, taken from the periodic table, tells us the number of grams of Li in one mole. The density equation can be used to convert from mass to volume. Once we have the volume of one mole of lithium, we divide by the number of atoms per mole to find the volume of a single atom. 

Viscoelastic properties have been discussed in relation to molar mass, concentration, solvent quality and shear rate. Considering the molecular models presented here, it is possible to describe the flow characteristics of dilute and semi-dilute solutions, as well as in simple shear flow, independent of the molar mass, concentration and thermodynamic quality of the solvent. The derivations can be extended to finite shear, i.e. it is possible to evaluate T) as a function of the shear rate. Furthermore it is now possible to approximate the critical conditions (critical shear rate, critical rate of elongation) at which the onset of mechanical degradation occurs. With these findings it is therefore possible to tune the flow features of a polymeric solution so that it exhibits the desired behaviour under the respective deposit conditions. 

A major challenge in using interactive chromatography for polyamides is to find a suitable mobile phase (Mengerink et al., 2001, 2002 Weidner et al., 2004). Polyamides form semicrystalline morphologies that limit the solubility in organic solvents. Besides hot phenol, formic acid, and trifluoroethanol (TFE) (Mori and Barth, 1999), 1,1,1,3,3,3-hexafluoroisopropanol (HFIP) represents a suitable solvent for polyamides (Chen et al., 2002). These solvents are mainly used to analyze the molar mass distribution of polyamides by SEC. 

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