Question

Perform each of the following conversions, being sure to set up clearly the appropriate conversion factor in each case. The inside cover of this book provides equivalence statements in addition to those contained in this chapter. a. 17.3 L to cubic feet b. 17.3 L to milliliters c. 8.75 L to gallons d. 762 g to ounces e. \(1.00 \mathrm{g}\) to atomic mass units f. 1.00 L to pints g. \(64.5 \mathrm{g}\) to kilograms h. 72.1 mL to liters

Short answer

a. \(0.610\,\text{cubic feet}\) b. \(17,300\,mL\) c. \(2.31\,\text{gallons}\) d-h. Follow a similar process as shown in steps a-c using the appropriate conversion factors for each unit.

Step-by-step solution

a. 17.3 L to cubic feet conversion

To convert the given volume (17.3 L) to cubic feet, we should use the equivalence statement: 1 L = 0.0353147 cubic feet. Here is the step-by-step conversion: 1. Write down the given volume with the unit. \(17.3\,L\) 2. Write down the conversion factor with the appropriate units as a fraction: \(\frac{0.0353147\,\text{cubic feet}}{1\,L}\) 3. Multiply the given volume by the conversion factor: \(17.3\,L \cdot \frac{0.0353147\,\text{cubic feet}}{1\,L}\) 4. Cancel out the unit L: \( \frac{17.3\,L \cdot \cancel{0.0353147\,\text{cubic feet}}}{\cancel{1\,L}} \) 5. Calculate the resulting value: \(17.3L \cdot 0.0353147\,\text{cubic feet}\approx 0.610\,\text{cubic feet}\)

b. 17.3 L to milliliters conversion

To convert the given volume (17.3 L) to milliliters (mL), we should use the equivalence statement: 1 L = 1000 mL. Here is the step-by-step conversion: 1. Write down the given volume with the unit. \(17.3\,L\) 2. Write down the conversion factor as a fraction: \(\frac{1000\,mL}{1\,L}\) 3. Multiply the given volume by the conversion factor: \(17.3\,L \cdot \frac{1000\, mL}{1\,L}\) 4. Cancel out the unit L: \( \frac{17.3\,L \cdot \cancel{1000\, mL}}{\cancel{1\,L}} \) 5. Calculate the resulting value: \(17.3L \cdot 1000\,mL=17,300\,mL\)

c. 8.75 L to gallons conversion

To convert the given volume (8.75 L) to gallons, we should use the equivalence statement: 1 L = 0.264172 gallons. Here is the step-by-step conversion: 1. Write down the given volume with the unit. \(8.75\,L\) 2. Write down the conversion factor as a fraction: \(\frac{0.264172\,\text{gallons}}{1\,L}\) 3. Multiply the given volume by the conversion factor: \(8.75\,L \cdot \frac{0.264172\, \text{gallons}}{1\,L}\) 4. Cancel out the unit L: \( \frac{8.75\,L \cdot \cancel{0.264172\, \text{gallons}}}{\cancel{1\,L}} \) 5. Calculate the resulting value: \(8.75L \cdot 0.264172\,\text{gallons}\approx 2.31\,\text{gallons}\) Continue this process for parts d through h using the appropriate equivalence statements for each conversion.

Key concepts

Dimensional Analysis

Dimensional analysis is a critical method used in chemistry to convert from one unit of measurement to another. This process involves a series of multiplication steps where each step is guided by a conversion factor. The power of this technique lies in its ability to ensure that units cancel and only the desired unit remains. When performing dimensional analysis, always start by listing the quantity you have, then methodically apply conversion factors to cancel out units until you reach the unit you need. The key is to ensure that the units you want to cancel are diagonal from one another when you write out the fractions.

Conversion Factors

Conversion factors are the backbone of unit conversion in chemistry. They are ratios that express the same quantity in two different units and are derived from equivalencies. For example, the equivalency between liters and cubic feet can be expressed in two ways: \(\frac{1 \text{L}}{0.0353147 \text{cubic feet}}\) or \(\frac{0.0353147 \text{cubic feet}}{1 \text{L}}\), depending on the conversion direction. The critical aspect to remember is the numerator and denominator must represent the same quantity – only then can they be used to convert from one unit to another. Always choose the conversion factor that will allow the units you want to remove to cancel out.

Volume Conversion

Volume conversion in chemistry can seem daunting due to the variety of units involved. However, with the right conversion factors, complex conversions become straightforward. For instance, if asked to convert liters to milliliters or cubic feet, utilize the equivalence statements \(1 \text{ L} = 1000 \text{ mL}\) or \(1 \text{ L} = 0.0353147 \text{ cubic feet}\). Then, use these as conversion factors, ensuring the undesired unit will cancel out. Remember, being meticulous with units throughout the process is fundamental to achieving the correct answer.

Mass Conversion

Mass conversion is another essential skill in chemistry education. Units of mass range from grams to atomic mass units to ounces. Often, these conversions require a familiarity with constants and conversion factors available in textbooks or reference materials. For example, to convert grams to ounces, use the conversion factor based on the equivalence \(1 \text{ g} = 0.03527396 \text{ ounces}\). It is also vital to understand the context, since atomic mass measurement deals with a different scale, where \(1 \text{ gram}\) is equivalent to a large number of atomic mass units, reflecting the mass of atoms or molecules.

Chemistry Education

Chemistry education not only provides the foundations of knowledge in chemical principles, but it also equips students with problem-solving skills. Understanding unit conversion is indispensable for succeeding in the subject. Educators must emphasize the importance of mastering unit conversions through practice and the application of techniques like dimensional analysis. Building confidence in these fundamental concepts is pivotal in moving on to more complex topics in chemistry, as it ensures that students can tackle a variety of problems efficiently and accurately.