Problem solving conversion factors

In problem solving, conversion factors are used to cancel the given unit and to provide the needed unit for the answer. 

The mass percent gives us the mass of sugar in 100 g of solution. This information can be used to make a conversion factor to solve the problem. Two conversion factors can be written ... 

Chemistry is full of calculations. Our basic goal is to help you develop the knowledge and strategies you need to solve these problems. In this chapter, you will review the Metric system and basic problem solving techniques, such as the Unit Conversion Method. Your textbook or instructor may call this problem solving method by a different name, such as the Factor-Label Method and Dimensional Analysis. Check with your instructor or textbook as to for which SI (Metric) prefixes and SI-English relationships will you be responsible. Finally, be familiar with the operation of your calculator. (A scientific calculator will be the best for chemistry purposes.) Be sure that you can correctly enter a number in scientific notation. It would also help if you set your calculator to display in scientific notation. Refer to your calculator s manual for information about your specific brand and model. Chemistry is not a spectator sport, so you will need to Practice, Practice, Practice. 

The thermochemical data for the chemical compounds that follow in this appendix are extracted directly from the JANAF tables [ JANAF thermochemical tables, 3rd Ed., Chase, M. W., Jr., Davies, C. A., Davies, J. R., Jr., Fulrip, D. J., McDonald, R. A., and Syverud, A. N.,./. Phys. Chem. Ref. Data 14, Suppl. 1 (1985)]. The compounds chosen from the numerous ones given are those believed to be most frequently used and those required to solve some of the problem sets given in Chapter 1. Since SI units have been used in the JANAF tables, these units were chosen as the standard throughout. Conversion to cgs units is readily accomplished by use of the conversion factors in this appendix (Table Al). Table A2 contains the thermochemical data. 

Solve these kinds of problems by using the definition of molarity and conversion factors. In parts (b) and (c), you must first convert your mass in grams to moles. To do so, you divide by the molar mass from the periodic table (flip to Chapter 7 for details). In addition, be sure you convert milliliters to liters. 

Again, conversion factors are the way to approach these kinds of problems. Each problem features a certain volume of solution that contains a certain solute at a certain concentration. To begin each problem, convert your volume into liters — part (c) has already done this for you. Then rearrange the molarity formula to solve for moles ... 

Desflurane has a heat of vaporization of 45 cal/g. How much heat does des-flurane absorb from the surroundings when 2 g vaporize To solve this problem, just use the heat of vaporization as a conversion factor. 

The physical sciences use a problem-solving approach called dimensional analysis. Dimensional analysis requires conversion factors. A conversion factor is a numerator and a denominator that are equal to each other. Some conversion factors are... 

Using Dimensional Analysis and Conversion Factors in Problem Solving... 

Look at the four-step problem-solving format above. A Mole-to-gram problem is solved in the same way, except that you write the given followed by the last two conversion factors. Therefore, it is a three-step problem rather than a four-step problem. 

As you study this example, look back at the four-step strategy for solving gram-to-gram problems. Note that we will follow the same pattern except for omitting the last conversion factor. 

The conversion factor problem-solving technique has been used throughout this book, especially in the units on moles and stoichiometry. These problem solutions are generally in a format like this ... 

There are a variety of problem-solving strategies that you will use as you prepare for and take the AP test. Dimensional analysis, sometimes known as the factor label method, is one of the most important of the techniques for you to master. Dimensional analysis is a problem-solving technique that relies on the use of conversion factors to change measurements from one unit to another. It is a very powerful technique but requires careful attention during setup. The conversion factors that are used are equalities between one unit and an equivalent amount of some other unit. In financial terms, we can say that 100 pennies is equal to 1 dollar. While the units of measure are different (pennies and dollars) and the numbers are different (100 and 1), each represents the same amount of money. Therefore, the two are equal. Let s use an example that is more aligned with science. We also know that 100 centimeters are equal to 1 meter. If we express this as an equation, we would write ... 

The metric system problem, part (a), can be solved without paper and pencil— by moving the decimal point in 5.200 three places to the right. The English system conversion, part (b), requires that we remember the number of yards per mile (harder than the 1000 m/km metric conversion factor) and that we use pencil and paper or a calculator to do the arithmetic. The conversion factor 1000 is used for kilograms, kilohters, kilowatts, and any other factor involving the prefix kilo-. The English conversion factor 1760 yd/mile is not used in any other conversion. 

Consider the reaction of phosphorus with chlorine as shown in the previous equation. Of course, the chemist is not required to place exactly 2 mol of P and 3 mol of CI2 in a reaction flask. The equation gives the reacting ratio. Ratios of coefficients from balanced chemical equations can be used as conversion factors for solving problems. 

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. 

What is the key conversion factor needed to solve all stoichiometry problems ... 

Dimensional analysis often uses conversion factors to solve problems that involve units. A conversion factor is a ratio of equivalent values. 

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. 

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... 

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. 

As you saw in Chapter 1, one of the convenient features of the metric system is that the relationships between metric units can be derived from the metric prefixes. These relationships can easily be translated into conversion factors. For example, milli- means 10 (or 0.001 or 1/1000), so a milliliter (mL) is 10 liters (L). Thus there are 1000 or 10 milliliters in a liter. (A complete list of the prefixes that you need to know to solve the problems in this text is in Table 1.2.) Two possible sets of conversion factors for relating milliliters to liters can be obtained from these relationships. 

Being asked to convert from volume into mass is the tip-off that we can use the density of water as a conversion factor in solving this problem. We can find water s density on a table of densities, such as Table 8.2. 

But there is a faster way to solve this problem, eliminating the need for the conversion from grams Fe to mole Fe. A conversion factor in terms of g Fe and atoms Fe can be assembled from the following equality that allows a one-step solution to the problem ... 

There is a lesson here Choose or develop the most efficient conversion factor to solve the problem. If you re converting grams to atoms, find the equality that relates grams and atoms for the conversion factor. If it s mole to atoms, find the connection between mole and atoms. Use the units g Fe, mole Fe, and atoms Fe to guide the correct use of the conversion factor. 

The relationship between the molar mass of BaF2 and Avogadro s number of formula units provides the conversion factor needed to solve the problem. 

First, convert kilogram to gram 1.000 kg of NaCl equals 1,000 g of NaCl. A 2.5%(m/v) solution of sodium chloride contains 2.5 g of NaCl in 100 mL of solution. This relationship provides the conversion factor needed to solve the problem. The answer has two significant figures ... 

The units of molarity are mole/liter (of solution), but they are commonly replaced with a capital M, which symbolizes molarity. Yet, there will be times when you will need to replace M with mole/liter when analyzing units and solving problems. If a sodium hydroxide solution is labeled 2 M (read as two-molar), it means that 2 moles of NaOH are dissolved in 1 L of solution, 2 moles/liter. If you need to brush up on mass-mole conversions, review the pertinent material in Chapter 5. In all the problems dealing with molar solutions, molarity will be written as a conversion factor to emphasize the canceling and retention of units, just as was done with the percent concentrations. The molarity term for a solution that is 0.55 M in NaOH could be written in four ways to make the required conversion factor ... 

The conversion factor in Example 1.5 may be written as 4 qt/1 gal or 1 gal/ 4 qt, because both are equal to 1. However, only the first factor, 4 qt/1 gal, will give us the units we need to solve the problem. If we had set up the problem incorrectly, we would obtain... 

The decimal point is moved three positions to the right.) This problem can be solved by using conversion factors ... 

To convert one unit to another, we must set up a conversion factor or series of conversion factors that relate two units. The proper use of these conversion factors is referred to as the factor-label method. This method is used either to convert from one unit to another within the same system or to convert units from one system to another. It is a very useful problem-solving tool. 

---