Measurement and Units Study Guide (page 2)
Chemistry is an experimental science. Measuring and calculating the amount of a substance, the temperature of a reaction system, or the pressure of the surroundings are a few ways to help you understand experiments.
Units of Measurement
Quantitative calculations and qualitative interpretations are fundamental to fully grasp the concepts of chemistry. Quantitative values must include a number and a unit. Two common units of measurement are the conventional (English) system and the metric system. The conventional set of units includes inches, feet, miles, gallons, and pounds. These units, although common in the United States, are not used in science or by most of the world. However, the metric system is becoming more common in the United States. The metric system's base-10 units are easier to use and essential for scientific calculations. However, because most readers of this book are more familiar with the conventional system, it will be necessary to convert to and from the metric system.
Prefixes are used in both systems, but they are more commonly used in the metric system because the metric system is base-10.
The modern metric system uses SI (Système Internationale d'Unités) units that have seven base units (see Table 3.2). All other units are derived from these base units such as area (m2), volume (m3 or 1,000 liters), speed (m/s2), force (kg m/s2 or newton, N), and energy (kg m2/s2 or joule).
Uncertainty and Error
Uncertainty expresses the doubt associated with the accuracy of any single measurement. Accuracy establishes how close in agreement a measurement is with the accepted value. The precision of a measurement is the degree to which successive measurements agree with each other (the average deviation is minimized). Error is the difference between a value obtained experimentally and the standard value accepted by the scientific community. Consider the bull's-eye target patterns in Figure 3.1.
The number of significant figures in any physical quantity or measurement is the number of digits known precisely to be accurate. The last digit to the right is inaccurate. The rules for counting significant figures are as follows:
- All nonzero digits are significant.
- Zeros between nonzero digits are significant figures.
- Zeros that locate the decimal place (placeholder) on the left are nonsignificant.
- Trailing zeros to the right of the decimal point are significant if a decimal point is present.
Significant Figures in Calculations
Multiplication and division: The answer will have the same number of significant figures as the least precise number.
56.2 * 0.25 = 14.05 = 14 (0.25 is limiting with two significant figures)
13.38 ÷ 12 .3 = 1.0878 = 1.09 (12.3 is limiting with three significant figures)
Addition and subtraction: The answer will have the same number of decimal places as the least precise number.
12.01 + 1.008 = 13.018 = 13.02 (12.01 is limiting with two decimal places)
65.2 – 12.95 = 52.25 = 52.3 (65.2 is limiting with one decimal place)
When more than one operation is involved in a calculation, note the number of significant figures in each operation, but round only the final answer.
27.43 + 3.32 * 25.61 = 27.43 + 85.0252 = 112.4552 = 113 (Three significant figures)
Dimensional Analysis (Factor-Label Method)
Dimensional analysis is the method to convert a number from one unit to another using a conversion factor. Conversion factors establish a relationship of equivalence in measurements between two different units. Examples of conversion factors are tabulated in Table 3.1 (metric prefixes) and Table 3.3 (common conversion factors).
Within the metric system, the prefix relationship is used (see Table 3.3). It is expressed as a fraction. For instance, for 1 kg = 2.2 lb., the conversion factor is 1 kg/2.2 lb. or 2.2 lb./1 kg.
|185 lbs.||kg||185 lbs. * = 83.9 kg|
|4.0 ft.||cm||4.0 ft.* = 120 cm|
|235 mL||qt.||235 mL * = 0.249 qt.|
|256 kB||GB||256 kB * = 2.56 * 10–4GB|
|(B is a byte)|
|2 ft., 3.5 in.m||2'3"||= 27.5 in.*|
|= .699 m|
Temperature is the measure of thermal energy (the total energy of all the atoms and molecules) of a system. The SI unit for temperature is Kelvin, but most scientific thermometers use the centigrade (Celsius) scale. However, most are more familiar with the Fahrenheit scale. Because many chemical calculations require Kelvin temperature, scientists frequently convert from degrees Celsius to Kelvin and from Kelvin to degrees Celsius.
°F to °C: °C = (°F – 32)
°C to °F: °F = °C + 32
K to °C: °C = K – 273.15
°C to K: K = °C + 273.15
Room temperature is 70° F. What is 70° F in Celsius and Kelvin scales?
°C = (°F – 32)= (70 – 32) = 21.11 = 21° C
K = °C + 273.15 = 21.11 + 273.15 = 294.26 = 294 K
Practice problems for these concepts can be found at - Measurement and Units Practice Questions
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