Mole-mass calculations

The approach followed in Chapter 3 to calculate mole-mass relations in reactions is readily applied to solution reactions represented by net ionic equations. 

In a mass-to-mass calculation, convert the given mass into amount in moles,... 

Mass-mole-number calculations often involve atoms yvithin a compound as well as the compound itself. The chemical formula provides the link between moles of a compound and the number of moles of the compound s individual elements ... 

As with all calculations of chemical amounts, we must work with moles. Because grams are asked for, we must do a mole-mass conversion this requires the molar mass of the substance, which in turn requires that we know the chemical formula. 

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... 

Because we know we are dealing with a buffer solution made from a specific conjugate acid-base pair, we can work directly with the buffer equation. We need to calculate the ratio of concentrations of conjugate base and acid that will produce a buffer solution of the desired pH. Then we use mole-mass-volume relationships to translate the ratio into actual quantities. 

Step 2 Find the limiting reactant by first converting the reactant masses to moles, then calculate the required molar ratio of one reactant to another and comparing the required ratio to the available ratio. If the available molar ratio is greater than the required molar ratio for a reactant, then it will be in excess and the other reactant is the limiting reactant. 

This is a critical chapter in your study of chemistry. Our goal is to help you master the mole concept. You will learn about balancing equations and the mole/mass relationships (stoichiometry) inherent in these balanced equations. You will learn, given amounts of reactants, how to determine which one limits the amount of product formed. You will also learn how to determine the empirical and molecular formulas of compounds. All of these will depend on the mole concept. Make sure that you can use your calculator correctly. If you are unsure about setting up problems, refer back to Chapter 1 of this book and go through Section 1-4, on using the Unit Conversion Method. Review how to find atomic masses on the periodic table. Practice, Practice, Practice. 

Using the molar mass, calculate the moles of all weighed samples. The moles of substances are converted to molarities by dividing by the volume (in liters) of the solution. Molarities may also be determined from pipet or buret readings using the dilution equation. (If a buret is used, one of the volumes is calculated from the difference between the initial and final readings.) The dilution equation may be needed to calculate the concentration of each reactant immediately after all the solutions are mixed. 

The enthalpy change is calculated by dividing the calculated energy by the moles, mass, or some other designated quantity. 

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. 

Using Numbers Use the mass of gas and the number of moles to calculate the molar mass of the gas. 

The molar masses of elements are determined by using mass spectrometry to measure the masses of the individual isotopes and their abundances. The mass per mole of atoms is the mass of an individual atom multiplied by the Avogadro constant (the number of atoms per mole). However, there is a complication. Most elements occur in nature as a mixture of isotopes we saw in Section B, for instance, that neon occurs as three isotopes, each with a different mass. In chemistry, we almost always deal with natural samples of elements, which have the natural abundance of isotopes. So, we need the average molar mass, the molar mass calculated by taking into account the masses of the isotopes and their relative abundances in typical samples. All molar masses quoted in this text refer to these average values. Their values are given in Appendix 2D. They are also included in the periodic table inside the front cover and in the alphabetical list of elements inside the back cover. 

In a mass-to-mass calculation, convert the given mass to moles, apply the mole-to-mole conversion factor to obtain the moles required, and finally convert moles required to mass. 

Carry out mole-to-mole, mass-to-mole, and mass-to-mass calculations for any two species involved in a chemical reaction, Example L.l. 

The theoretical yield of a reaction is the maximum amount (moles, mass, or volume) of product that can be obtained from a given amount of reactant. The amounts of products calculated from a given mass of reactant in Section L were all theoretical yields. 

Because one mole of any substance is a specific number of molecules (1 mol things = 6.02 x 1023 things from Chapter 2), the relative numbers of moles undergoing reaction are the same as the relative numbers of molecules. Because of the relationship of molecules to moles, the equation above can be interpreted in terms of masses calculated directly from the Periodic Table (H = 1,0 = 16, N = 24, all in g/mol). 

The acid mine water is defined as SOLUTION 0 and the water in the carbonate channel as SOLUTION 1. Within the key word KINETICS 1-10 the calculation tolerance as well as the initial and the total mole mass of calcite can be defined. Obligatory are only the parameter 50 and 0.6. These are needed by the BASIC program, which must be implemented within the key word RATES. Here, we use the BASIC program listed at the end of the database PHREEQC.dat. If the database PHREEQC.dat is used (which is not free of troubles, since there are, e g., no data for uranium) or if the paragraph is copied into another database, it is not necessary to define a RATES block in the input file. PHREEQC uses automatically the RATES block from the database. Yet, if any other kinetic rates are to be used, the BASIC program must be copied into the input file under RATES. In any case, the KINETICS block is required. 

From pure reagent Select the desired concentration and volume determine the required of moles, then calculate the mass (using the molar mass). 

Understand how to use the mole to calculate the number of liters a gas will occupy, the number of molecules present, the mass of a sample, and the number of moles of another substance in a reaction. 

Use the value of Avogadro s number, the mass of one C atom (exactly 12 amu), and the definition of a mole to calculate the number of atomic mass units per gram. 

In Section 10.1, we learned to calculate the number of moles of any substances involved in a chemical reaction from the number of moles of any other substance. We can solve problems that include mass calculations by simply changing the masses to moles or the moles to masses, as discussed in Chapter 7. In Figure 10.2, these conversions have been added to those shown in Figure 10.1. 

If the quantity of any substance is given in terms of mass instead of in moles, the mass must be changed to moles before calculating the number of moles of another substance in the reaction. If the mass of a substance is required as an answer to a problem, its number of moles must be converted to a mass. (Conversions between mass and moles are presented in Chapter 7.) (Section 10.2) If some other measure of the quantity of a substance is given or required (for example, the number of molecules of a substance), an appropriate conversion factor is needed to convert to or from moles (Section 10.3). 

Now that you have learned about and practiced conversions between mass, moles, and representative particles, you can see that the mole is at the center of these calculations. Mass must always be converted to moles before being converted to atoms, and atoms must similarly be converted to moles before calculating their mass. Figure 11-5 shows the steps to follow as you work with these conversions. 

The specified unit of the given substance determines at what point you will start your calculations. If the amount of the given substance is in moles, step 2 is omitted and step 3, mole-to-mole conversion, becomes the starting point for the calculations. However, if mass is the starting unit, calculations begin with step 2. The end point of the calculation depends upon the specified unit of the unknown substance. If the answer is to be obtained in moles, the calculation is finished with step 3. If the mass of the unknown is to be determined, you must go on to step 4. 

What about the reactant sulfur, which you know is in excess How much of it actually reacted You can calculate the mass of sulfur needed to react completely with 1.410 mol of chlorine using a mole-to-mass calculation. The first step is to multiply the moles of chlorine by the mole ratio of sulfur to chlorine to obtain the number of moles of sulfur. Remember, the unknown is the numerator and the known is the denominator. 

For most practical purposes we are interested in the masses of reactants and products, because those are the quantities that are directly measured. In this case, the molar masses (calculated from a table of atomic masses) are used to convert the number of moles of a substance (in moles) to its mass (in grams), as illustrated by Example 2.6. Sometimes, however, we are also interested in knowing the number of molecules in a sample. The mole allows us to convert easily from mass to numbers of molecules as follows ... 

The average mole mass of silicate anions and the average number of Si04 tetrahedrons in the particular anion can be calculated according to the equations... 

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