Molar Mass and Calculations

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. In the laboratory, we can use a balance to weigh out Avogadro s number of particles or 1 mole of a 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 6.02 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 mole of carbon atoms has a mass of 12.01 g. Then to obtain 1 mole of carbon atoms, we would weigh out 12.01 g of carbon. The molar mass of carbon is found by looking at its atomic mass on the periodic table. 

The molar mass of an element is useful to convert moles of an element to grams, or grams to moles. For example, 1 mole of sulfur has a mass of 32.07 g. We can express the molar mass of sulfur as an equahty 

From this equality, two conversion factors can be written as 32.07 g S, 1 mole S 

To calculate the molar mass for a compound, we multiply the molar mass of each element by its subscript in the formula, and add the results as shown in Sample Problem 7.3. 

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Polarity varies widely from one polymer to the next. PDMS has a dielectric constant of only 2.8 [13], meaning that its polarity is close to that of toluene. Solid PEG has a Kamlett-Taft k (polarity/polarizability) value of 0.86 and an Ej(30) value of 45.7 [19], The r(30) value implies a polarity comparable to MeCN or DMSO while the n value is surprisingly high for an entirely saturated structure. Ohno and Kawanabe showed that the Ej(30) of a polyether increases with molar mass and calculated that the E-j-(30) values of PEG and PPG with infinite chain lengths would be 46.6 and 38.5 kcal mol [20]. Thus PPG is significantly less polar, matching the polarity of butyl acetate. 

Molecular Formulas, Molar Masses, and Calculated Room Temperature Densities (with Standard Error and % Standard Error) of Cellulose-Mimicking Oligomers with Increasing Degree of Polymerization... 

Step polymerisation Monomer concentration drops rapidly to zero early in the reaction. Polymer molar mass rises steadily during reaction. Long reaction times increase molar mass and are essential to obtain very high molar masses. At all stages of the reaction every possible molecular species from dimers to polymers of large degrees of polymerisation are present in a calculable distribution. 

Example illustrates the use of isotopic molar masses and natural abundances to calculate the molar mass of elemental iron. 

As emphasized in Section 2-, many of the calculations in chemistry involve converting back and forth among the mass of a substance, the number of moles, and the number of atoms and/or molecules. These calculations are all centered on the mole. The connections shown in Figure apply to chemical compounds as well as to atoms of pure elements. Molar mass and Avogadro s number provide links between mass of a sample, the number of moles, and the number of molecules. 

The chemicai formuia identifies the ions that are present in the finai soiution. The formula also tells us how many moles of each ion are present in one moie of the sait. Use mass, molar mass, and volume to calculate molarity. 

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... 

The overall molarity of NaOH can be calculated from mass, molar mass, and volume ... 

In semi-dilute solutions, the Rouse theory fails to predict the relaxation time behaviour of the polymeric fluids. This fact is shown in Fig. 11 where the reduced viscosity is plotted against the product (y-AR). For correctly calculated values of A0 a satisfactory standardisation should be obtained independently of the molar mass and concentration of the sample. 

The 2D experiment yielded separation with respect to functionality and molar mass, and FTD and MMD could be determined quantitatively. For calculating FTD, the relative concentration of each functionality fraction must be determined. These concentrations are equivalent to the volume of each peak in the contour plot. With the... 

This equation is the one most often used to calculate the cohesion energy of a liquid. From the molar mass and density of the liquid, the molar volume can be determined, and by means of Eq. (6.36) the value of S can be determined. The importance of the solubility parameter for interpreting several types of interactions will now be illustrated. 

There are a variety of ways to do the calculations. Most of these, however, involve the calculation of the number of moles (n) from the ideal gas equation n = PV/RT. The mass of the vapor sample is calculated from the difference between measurements 1 and 2. The temperature (measurement 3) is converted to kelvin. The pressure (measurement 4) is converted to atmospheres. Measurement 5 is converted to liters. Inserting the various numbers into the ideal gas equation allows you to calculate the number of moles. The molar mass is calculated by dividing the mass of the sample by the moles. 

Calculate the moles of each reactant from the masses and molar masses. Then calculate the yield based on the limiting reagent. The mass of the product, determined at the end of the synthesis, divided by the mass calculated from the limiting reagent times 100%, gives the percent yield. There are numerous possible analysis calculations. 

Volume of the unit cell (VcM). This may be calculated from the unit cell constants by using the following formulae. From this the density (/>) of the compound may be obtained p = Mcc /FccM, where MceH is the mass of the matter in the unit cell, that is the sum of the masses of all the atoms contained. The mass of an individual atom is calculated in grams by the ratio of the atomic molar mass and the Avogadro number. 

Calculate the molar volumes of Aroclor 1242 and Fyrquel from the corresponding average molar masses and densities ... 

To calculate the molality of a solution prepared by dissolving 10.5 g of sodium chloride in 250 g of water, we convert the mass of sodium chloride to moles of NaCl (by dividing the mass by the molar mass) and divide it by the mass of water in kilograms ... 

STRATEGY The molality is the number of moles of solute per kilogram of solvent. Therefore, consider a solution made with exactly 1 kg of solvent and work out the mass of solute present from the number of moles and the molar mass. Then calculate the mass percentage of solute by dividing the mass of solute by the total mass of the solution and multiply by 100%. 

Molar masses, and therefore molecular masses, can also be calculated using the ideal gas law. Imagine, for instance, that an unknown gas bubbling up in a swamp is collected, placed in a sample bulb, and found to have a density of 0.714 g/L at STP. What is the molecular mass of the gas ... 

Knowing both the mass and the number of moles of insulin, we can calculate the molar mass and hence the molecular mass ... 

Fig. 18. Molar mass distributions calculated from PCS and TDFRS measurements with different exposure times. Superimposed is the molar mass distribution obtained from size exclusion chromatography. From Ref. [37]...

The relative molar masses of the gaseous components and the associated uncertainty in the relative molar masses are calculated from tables of atomic weights. The relative molar mass and uncertainties are combined with the gas purity and weighing uncertainty using the Gravcalc software. 

You can use what you now know about the mole to carry out calculations involving molar mass and the Avogadro constant. One mole of any compound or element contains 6.02 x 1023 particles. The compound or element has a mass, in grams, that is determined from the periodic table. 

Design an investigation to collect the gas given off by a certain mass of Rotela water plants. Find the mass and volume of the gas. Use this data to calculate the molar mass and molar volume of the gas. (Note This experiment will take several days to do correctly. If possible, do multiple trials.)... 

Q O Carry out your procedure. Use the volume and the mass of the gas, along with the temperature of the water and pressure of the room, to calculate the average molar mass and the molar volume of the gas. 

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