Sci 401 General Chemistry Measurements PDF

Sci 401 GENERAL CHEMISTRY ©2021 Batangas State University 1 MEASUREMENTS SI UNITS BASIC TYPES OF QUANTITY SIGNIFICANT FIGURES 2 ©2021 Batangas State University  Measurement Observations in science can either be qualitative or quantitative....

Sci 401 GENERAL CHEMISTRY ©2021 Batangas State University 1 MEASUREMENTS SI UNITS BASIC TYPES OF QUANTITY SIGNIFICANT FIGURES 2 ©2021 Batangas State University  Measurement Observations in science can either be qualitative or quantitative. Qualitative observation does not involve a number. A quantitative observation is called a measurement, which always has two parts: a number and a scale (called a unit). Both parts must be present for the measurement to be meaningful. 6 kilograms unit number 3 ©2021 Batangas State University  Measurement Scientists recognized long ago that standard systems of units had to be adopted if measurements were to be useful. The two major systems are the English system used in the United States and the metric system used by most of the rest of the industrialized world. In 1960, an international agreement set up a system of units called the International System (le Syste me International in French), or the SI system. This system is based on the metric system and units derived from the metric system. 4 ©2021 Batangas State University  Measurement Physical Quantity Name of Unit Abbreviation Mass kilogram kg Length meter m Time second s Temperature kelvin K Electric current ampere A Amount of substance Mole mol Luminous intensity candela Cd 5 ©2021 Batangas State University  Measurement To express small or large measured quantities in terms of a few simple digits, prefixes are used with these base units and other derived units. These prefixes multiply the unit by various powers of 10. 6 ©2021 Batangas State University  Basic Types of Quantity Fundamental Quantities It is referred to as the basic quantities. Quantities which are measured by the direct method. The units assigned to the fundamental quantities are called fundamental units. The fundamental units meter, kilogram and second (MKS) are the standard units for length, mass, and time, respectively. However, for smaller quantities, centimeter, gram, and second (CGS) are used as fundamental units. 7 ©2021 Batangas State University  Basic Types of Quantity Derived Quantities Quantities that emanate or a result of the combination of fundamental quantities after a set of operations. Area, volume, and density are some examples of derived quantities. Area square meter m2 Volume cubic meter m3 Density kilogram per cubic meter kg/m3 8 ©2021 Batangas State University  Basic Types of Quantity One physical quantity that is very important in chemistry is volume, which is not a fundamental SI unit but is derived from length. The most common conversion factors for volume is shown below: 1 L = 1 (dm)3 = (10 cm)3 = 1000 cm3 1cm3 = 1 mL 1L = 1000 cm3 = 100o mL 9 ©2021 Batangas State University  Significant Figures It is very important to realize that a measurement always has some degree of uncertainty. The uncertainty of a measurement depends on the precision of the measuring device. Consider the measurement of the volume of a liquid using a burette. 10 ©2021 Batangas State University  Significant Figures The first three numbers (20.1) remain the same regardless of who makes the measurement; these are called certain digits. The digit to the right of the 1 must be estimated and therefore varies; it is called an uncertain digit. We customarily report a measurement by recording all digits that are known with certainty plus the first uncertain digit. These numbers are called the significant figures of a measurement. 11 ©2021 Batangas State University  Significant Figures Rules for counting Significant Figures 1. Non-zero Integers These always count as significant figures. The number 1458 has four (4) non-zero digits, all of which count as significant figures. 2. Zeros a. Leading zeros are zeros that precede all the non- zero digits. These do not count as significant figures. The number 0.0025, the three zeros simply indicate the position of the decimal point. This number has only two (2) significant figures. 12 ©2021 Batangas State University  Significant Figures Rules for counting Significant Figures b. Captive zeros are zeros between non-zero digits. These always count as significant figures. The number 1.008 has four (4) significant figures. c. Trailing zeros are zeros at the right end of the number. They are significant only if the number contains a decimal point. The number 100 has only one significant figure, whereas the number 1.00 x 102 has three (3) significant figures. The number one hundred written as 100. also has three (3) significant figures. 13 ©2021 Batangas State University  Significant Figures Rules for counting Significant Figures 3. Exact Numbers These involve numbers that were not obtained using measuring devices but were determined by counting: 10 experiments, 3 apples, 8 molecules. They can be assumed to have an infinite number of significant figures. Other examples of exact numbers are the 2 in 2πr (the circumference of a circle) and the 4 and the 3 in 4/3πr3 (the volume of a sphere). Exact numbers also can arise from definitions such as 1 inch is defined as exactly 2.54 centimeters. 14 ©2021 Batangas State University  Significant Figures Exponential Notation The number 1.00 x 102 is written in exponential notation or scientific notation. This type of notation has at least two advantages: a. the number of significant figures can be easily indicated b. fewer zeros are needed to write a very large or very small number. For example, 0.000060 is much more conveniently represented as 6.0 x 10-5. (The number has two significant figures.) It is often necessary to set the decimal point using the power-of-10 notation to avoid introducing the appearance of unwanted significant figures. 15 ©2021 Batangas State University  Significant Figures Scientific Notation 16 ©2021 Batangas State University  Significant Figures Scientific Notation For 2300000, to change it into scientific notation: 17 ©2021 Batangas State University  Significant Figures Scientific Notation The speed of light is 300,000km/s. We can write this number as 3.0 X 105km/s. The mass of a carbon atom is 0.000000000000000000000002 grams. We can write this as 2.0 X 10-23 grams. The number of hydrogen atoms in 1 gram of hydrogen is 623,000,000,000,000,000,000,000. We can write this as 6.23 X 1023. You can see why we write in scientific notation. 18 ©2021 Batangas State University  Significant Figures Rules for Significant Figures in Mathematical Operations a. For multiplication or division, the number of significant figures in the result is the same as the number in the least precise measurement used in the calculation. For example, consider the calculation: 4.56 x 1.4 = 6.38 Final answer = 6.4 The product should have only two significant figures, since 6.4 has only two significant figures. 19 ©2021 Batangas State University  Significant Figures Rules for Significant Figures in Mathematical Operations b. For addition and subtraction, the result has the same number of decimal places as the least precise measurement used in the calculation. For example, consider the sum: 22.13 17.0 + 2.024 41.154 Final answer is 41.2 since 17.0 has only one decimal place. 20 ©2021 Batangas State University  Precision and Accuracy Two terms often used to describe the reliability of measurements are precision and accuracy. Accuracy refers to the agreement of a particular value with the true value. Precision refers to the degree of agreement among several measurements of the same quantity. Precision reflects the reproducibility of a given type of measurement. 21 ©2021 Batangas State University  Precision and Accuracy Two different types of errors are illustrated in Figure. large random error A random error (also called an (poor technique) indeterminate error) means that a measurement has an equal probability of being high or low. This type of error occurs in estimating the value of the last digit of a measurement. 22 ©2021 Batangas State University  Precision and Accuracy The second type of error is called small random systematic error (or determinate error). errors but large This type of error occurs in the same systematic error direction each time; it is either always high or always low. small random errors but no 23 ©2021 Batangas State University systematic error  Dimensional Analysis 24 ©2021 Batangas State University  Dimensional Analysis Some equivalents in the English and metric system are given as follow: Volume Length Mass SI Unit: cubic meter SI Unit: meter (m) SI Unit: kilogram (kg) (m3) 10-3 m3 1m 1.0936yards 1 pound 453.59 grams 1L 1 dm3 (lb) 0.45359 kg 1.0567 quarts 1 cm 0.39370 inch 16 ounces 4 quarts 1 inch 2.54 centimeters 1000 grams 1 gallon 8 pints 1 kg 1 km 0.62137 miles 2.2046 lbs 3.7854 Liters 1 quart 32 fluid ounces 1 mile 5280 feet 1 ton 2000 lbs 0.94633 Liter 1.6093 km 907.185 kg 1 10-10 m 1 Metric 1000 kg 25 ©2021 Batangas State University angstrom 100 picometers ton (MT) 2204.6 lbs  Dimensional Analysis 26 ©2021 Batangas State University  Dimensional Analysis Example 2: A student has entered a 10.0 km run. How long is the run in miles? kilometer meter yards miles Solution: Equivalence statements: 1km=1000m 1m=1.094yd 1760yd=1mi 27 ©2021 Batangas State University  Dimensional Analysis 1km=1000m 1m=1.094yd 1760yd=1mi 28 ©2021 Batangas State University  Dimensional Analysis 29 ©2021 Batangas State University  Dimensional Analysis 30 ©2021 Batangas State University  Temperature 31 ©2021 Batangas State University