Conversion factors mole ratios

We now want to use this equivalence statement to obtain the conversion factor (mole ratio) that we need. Because we want to go from moles of H2O to moles of O2, we need the mole ratio... 

Use units as a check to see that you have used the correct conversion factors (mole ratios). 

Fig. 8-1 The conversion of moles of one reagent to moles of another, using a ratio of the coefficients of the balanced chemical equation as a factor label...

At a lower temperature, in contrast, even Me3Al was able to accelerate the polymerization of MM A. At -40 °C, for example, after a 3 molar amount of Me3Al had been added to the polymerization system ([MMA]q/[2 (X=Me)]o=100,11% conversion) 91% conversion was attained in the following 1 h. Furthermore, the polymer formed here had a narrow MWD as indicated by the Mw/Mn ratio of 1.17, and the Mn value (9700) was close to that expected (9100) from the mole ratio of the monomer reacted to the initiator. In this case, the polymerization was observed to proceed without any change in color of the system. Thus, the polymerization temperature is one of the important factors to achieve the clean and rapid polymerization with trialkylaluminums. 

This factor, which is commonly called the mole ratio for the reaction, allows us to relate the moles of oxygen molecules consumed to the moles of water molecules produced. We use it in the same way we use a conversion factor when we are converting units, as illustrated in Appendix IB ... 

The balanced chemical equation for a reaction is used to set up the conversion factor from one substance to another and that conversion factor, the mole ratio for the reaction, is applied to the moles given to calculate the moles required. 

Use molar mass of Cl2 Use coefficients in as a conversion factor the balanced equation to find mole ratios... 

We need to calculate the amount of methyl tert-bu tyl ether that could theoretically be produced from 26.3 g of isobutylene and compare that theoretical amount to the actual amount (32.8 g). As always, stoichiometry problems begin by calculating the molar masses of reactants and products. Coefficients of the balanced equation then tell mole ratios, and molar masses act as conversion factors between moles and masses. 

In the above relationship, the left-hand side term, being ratio of two activity coefficient terms is independent of the standard state chosen. The activity coefficient (generally termed /) based on 1 weight percent solution as the standard state, can very well be used. On the right hand side, N or the mole- (or atom-) fraction, would be replaced by weight per cent of solute and the interaction coefficient would have to absorb within it the corresponding conversion factor for composition. In this form, the interaction coefficient is generally represented by the symbol e . 

The chemical formula for a compound gives the ratio of atoms of each element in the compound to atoms of every other element in the compound. It also gives the ratio of dozens of atoms of each element in the compound to dozens of atoms of every other element in the compound. Moreover, it gives the ratio of moles of atoms of each element in the compound to moles of atoms of every other element in the compound. For example, a given quantity of H2O has 2 mol of H atoms for every mole of O atoms, and a given quantity of CH4 has 1 mol of C atoms for every 4 mol of H atoms. The mole ratio from the formula can be used as a factor to convert from moles of any element in the formula to moles of any other element or to moles of the formula unit as a whole. In Figure 7.2, these additional conversions have been added to those already presented in Figure 7.1. 

The number of moles of an element in a mole of componnd can also be used to calculate the number of moles of the compound involved in a reaction. The ratio of the number of moles of an element within a compound to the number of moles of the compound is determined by the compound s chemical formula (Section 7.3). Thns, the snbscripts of the formula may be used to form conversion factors. 

Because molarity is a ratio, like speed and density, it can be used as a conversion factor. Wherever it appears, the symbol M can be replaced by the ratio moles per liter (mol/L) or millimoles per milliliter (mmol/mL). For example, a concentration of 3.11 M can be used as any of the following factors ... 

The concentration of a solute depends on the quantities of both the solute and the solution (or solvent). Molarity is defined as the number of moles of solute per liter of solution. Molarity is calculated by dividing the number of moles of solute by the volume of the solution in liters, or alternatively, by dividing the number of millimoles of solute by the milliliters of solution. Because molarity is a ratio, it can be used as a conversion factor to change the volume of solution into the number of moles of solute, or vice versa. 

Let s say that you want to find an empirical formula from the percentage composition. First, convert the mass percentage of each element to grams. Second, convert from grams to moles using the molar mass of each element as a conversion factor. (Keep in mind that a formula for a compound can be read as a number of atoms or as a number of moles.) Third, as shown in Sample Problem C, compare these amounts in moles to find the simplest whole-number ratio among the elements in the compound. 

The coefficients in a balanced chemical equation show the relative numbers of moles of the substances in the reaction. As a result, you can use the coefficients in conversion factors called mole ratios. Mole ratios bridge the gap and can convert from moles of one substance to moles of another, as shown in Skills Toolkit 1. 

The thought process in solving stoichiometry problems can be broken down into three basic steps. First, change the units you are given into moles. Second, use the mole ratio to determine moles of the desired substance. Third, change out of moles to whatever unit you need for your final answer. And if you are given moles in the problem or need moles as an answer, just skip the first step or the last step As you continue reading, you will be reminded of the conversion factors that involve moles. 

Think through the three basic steps used to solve stoichiometry problems change to moles, use the mole ratio, and change out of moles. Know which conversion factors you will use in each step. 

Write the conversion factors— including the mole ratio—in order so that you change the units of the given substance to the units needed for the answer. 

The conversion factor for converting between mass and amount in moles is the molar mass of the substance. The molar mass is the sum of atomic masses from the periodic table for the atoms in a substance. Skills Toolkit 3 shows how to use the molar mass of each substance involved in a stoichiometry problem. Notice that the problem is a three-step process. The mass in grams of the given substance is converted into moles. Next, the mole ratio is used to convert into moles of the desired substance. Finally, this amount in moles is converted into grams. 

When reactants are liquids, they are almost always measured by volume. So, to do calculations involving liquids, you add two more steps to the sequence of mass-mass problems—the conversions of volume to mass and of mass to volume. Five conversion factors—two densities, two molar masses, and a mole ratio—are needed for this type of calculation, as shown in Skills Toolkit 4. 

Because the conversion factor is a ratio of whole numbers, the number of significant digits is based on the moles of AI2O3. Therefore, the answer is expressed correctly with three significant figures. As predicted, the answer is twice the number of moles of AI2O3. 

Example Problem 11-8 illustrated how to find the number of moles of a compound contained in a given mass. Now, you will learn how to calculate the number of representative particles—molecules or formula units—contained in a given mass and, in addition, the number of atoms or ions. Recall that no direct conversion is possible between mass and number of particles. You must first convert the given mass to moles by multiplying by the inverse of the molar mass. Then, you can convert moles to the number of representative particles by multiplying by Avogadro s number. To determine numbers of atoms or ions in a compound, you will need conversion factors that are ratios of the number of atoms or ions in the compound to one mole of compound. These are based on the chemical formula. Example Problem 11-9 provides practice in solving this type of problem. 

You are given the masses of the elements found in a known mass of ilmenite and must determine the empirical formula of the mineral. Convert the known masses of each element to moles using the conversion factor that relates moles to grams, the inverse of molar mass. Then, find the smallest whole-number ratio of the moles of the elements. 

Mole ratios You have seen that the coefficients in a chemical equation indicate the relationships among moles of reactants and products. For example, return to the reaction between iron and oxygen described in Table 12-1. The equation indicates that four moles of iron react with three moles of oxygen. It also indicates that four moles of iron react to produce two moles of iron(III) oxide. How many moles of oxygen react to produce two moles of iron(III) oxide You can use the relationships between coefficients to write conversion factors called mole ratios. A mole ratio is a ratio between the numbers of moles of any two substances in a balanced chemical equation. As another example, consider the reaction shown in Figure 12-2. Aluminum reacts with bromine to form aluminum bromide. Aluminum bromide is used as a catalyst to speed up a variety of chemical reactions. 

To solve the problem, you need to know how the unknown moles of hydrogen are related to the known moles of potassium. In Section 12.1 you learned to use the balanced chemical equation to write mole ratios that describe mole relationships. Mole ratios are used as conversion factors to convert a known number of moles of one substance to moles of another substance in the same chemical reaction. What mole ratio could be used to convert moles of potassium to moles of hydrogen In the correct mole ratio, the moles of unknown (H2) should be the numerator and the moles of known (K) should be the denominator. The correct mole ratio is... 

This mole ratio can be used to convert the known number of moles of potassium to a number of moles of hydrogen. Remember that when you use a conversion factor, the units must cancel. 

Determine the moles of the unknown substance from the moles of the given substance. Use the appropriate mole ratio from the balanced chemical equation as the conversion factor. 

The next thing to determine are the given and unknown substances. In this problem, ethane is the given substance and carbon dioxide is the unknown. Our task will be to convert from moles of ethane to moles of carbon dioxide. We will do this using the mole ratio, which is based on the equality of 2 moles C2Hg = 4 moles CO2. In simple terms, the ratio tells you that you will always produce twice as many moles of CO2 as the number of moles of ethane. To solve the problem, we will use the mole ratio as the conversion factor to change units from ethane to carbon dioxide. 

The ratio of moles of P4O10 to moles of P (which came from the subscripts in the chemical formula, P4O10) provided the key conversion factor that allowed us to convert from units of phosphorus to units of tetraphosphorus decoxide. 

There is a shortcut for this calculation. We can collapse all five of the conversion factors above into one. The reaction equation tells us that there are six moles of H2O for each mole ofP40io. The molecular masses of these substances tell us that each mole of H2O weighs 18.0153 g, and each mole of P4O10 weighs 283.889 g. Thus the mass ratio of H2O to P4O10 is six times 18.0153 g to one times 283.889 g. 

Step 5 Convert from moles of substance 1 to moles of substance 2 using their coefficients from the balanced equation to create a molar ratio to use as a conversion factor. 

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