Unit 2: Data Collection and Analysis I. Measurement and Observation There are two basic types of data collected in the lab: Quantitative : numerical information (e.g., the mass of the salt was 3.45 g) Qualitative : non-numerical, descriptive data (e.g., the color of the solution is magenta). Uncertainty in Measurement When you carry out an experiment or measurement you need to understand the true quality of your results. The terms scientists typically use are accuracy and precision—they are not the same. 1. Accuracy refers to degree of conformity with a standard (often called true, accepted or theoretical) value. There are times when a calculated value will be used as the standard. 2. Precision refers to how close measurements are to one another. Repeated measurements determine reproducibility or precision. Precision tells you how to report results. precision accuracy both neither Accuracy and Precision Four lab groups performed the same experiment three times to determine the melting point of naphthalene (moth balls). The accepted melting point is 79.0°C. Indicate whether the following sets of data are precise, accurate, both or neither. Precise, Accurate, Both or Reasoning Group Trial 1 Trial 2 Trial 3 Neither Average of the trials is accurate close to the accepted 1 76.2°C 79.5°C 81.3°C melting point of 79.0 All trials have values that are close to each precise 2 76.2°C 76.1°C 76.3°C other The trials are neither close to each other neither 3 86.4°C 82.8°C 81.2°C (precise) or close to the accepted value of 79.0 All trials are precise and both close to the accepted 4 79.1°C 78.9°C 79.2°C value of 79.0 General Chemistry Page 1 of 10 Unit 2: Data Collection and Analysis Qualitative or Glassware Function Quantitative Large mouth glass containers used to contain approximate Beaker qualitative volumes of liquid. Long tube with a stopcock that opens and closes. It is used to Buret quantitative precisely deliver solutions, especially in a titration. Glass container used to contain approximate volumes of liquid. Erlenmeyer Flask qualitative Small mouth accommodates a stopper for storage or shaking. Graduated Cylinder quantitative Used to measure and deliver approximate volumes of liquids. Pipet quantitative Used to precisely deliver variable quantities of liquid. Test Tube qualitative Glass cylinder that holds liquids being tested in an experiment. Designed to precisely contain a specific volume. Commonly used Volumetric Flask quantitative when accurately making aqueous solutions. ***In trying to decide which piece of equipment is the most accurate, always choose the one with the smallest measurement units and smallest diameter. II. Measurement and Significant Figures Results should always be reported to the correct number of significant figures. These will be discussed in more detail in the next unit. When making a measurement in the lab, always report the number of digits necessary to express results of measurement consistent with the measured precision. This means you are to report all certain digits plus one uncertain digit. Every time you take a measurement you should estimate between the lines. If the measurement is on a line, add a zero to show that you are estimating it to be exactly on the line. Always include one estimated digit. Remember that liquids form a curved surface called a meniscus. Measure to the bottom of the meniscus. A buret precisely measures the amount of liquid that is released through the stopcock. This is why a buret is marked “upside-down” compared to a graduated cylinder. The numbers increase going down a buret. Be careful of this when reading burets. General Chemistry Page 2 of 10 Unit 2: Data Collection and Analysis Example 2.1 Read the following ruler to the correct number of significant figures. A B C D E F centimeters A. 0.52 cm C. 1.58 cm E. 3.30 cm B. 0.79 cm D. 2.50 cm F. 3.68 cm Example 2.2 Read the following graduated cylinder to the correct number of significant figures. A. B. A. 37.7 mL B. 35.0 mL Read the following buret to the correct number of significant figures. Then calculate how much liquid was released from the buret. 20 mL Initial Initial: 15.0 mL Final Final: 18.3 mL 10 mL Released: 18.3 – 15.0 = 3.3 mL General Chemistry Page 3 of 10 Unit 2: Data Collection and Analysis III. Using Significant Figures Significant figures indicate with how much confidence or estimation a measurement is known. For example, the estimate “0.1” is quite different from the measurement “0.1000.” Likewise, the estimate “100” is quite different from the measurement “100.0.” Counting Significant Figures 1. All non-zero digits are significant (24 has two significant figures) 2. Leading zeros are never significant ( 0.0024 has two significant figures) 3. Middle or trapped zeros are significant ( 204 has three significant figures) 4. nTail zeros are significant if and only if there is a decimal point in the number. ( 24.0 has three significant figures, 240 has 2 significant figures) Example 2.3 Count and underline the significant figures in each of the following numbers: 4000 1 0.004 5 2 0.009 09 3 2.050×1024 4 3.990 4 100.0 4 1010 3 100. 3 Rounding A calculation cannot result in more significant figures than the numbers used to generate it. Jut because your calculator gives you an answer does not mean that answer is correct. You must round the answer correctly. If the digit to the right of the last digit to be kept is ≥ 5, increase the last digit by 1. If the digit to the right of the last digit to be kept is < 5, the last digit stays the same. Example 2.4 Round the following numbers to 3 significant figures: 123,499 -234,999 0.231 451 18.999 123,000 -235,000 0.231 19.0 Multiplication and Division with Significant Figures In multiplication and division, the answer can have no more significant figures than are in the measurement with the fewest number of significant figures. Exact numbers such as counting numbers and conversion factors (a ratio used to convert from one unit to another) are not included when counting significant figures. General Chemistry Page 4 of 10 Unit 2: Data Collection and Analysis Example 2.5 Perform the following mathematical functions and express the answers with the correct number of significant figures: 0.006 760 ÷ 32 1,234,000 ÷ 0.0000345 278.4 × 25.2 89.554 × 43.1 0.00021 3.58×1010 7020 3860 IV. Scientific Notation Scientific notation is used to represent numbers that are very large or very small. Rules for Scientific Notation To convert from decimal form to scientific notation: Move the decimal point to the left or the right so that only one nonzero digit remains to the left of the decimal point. The exponent is the number of places that you moved the decimal point. If you moved the decimal to the left, the exponent is positive. If you moved it to the right, the exponent is negative. To convert from scientific notation to decimal form: Move the decimal point to the right if the exponent is positive (add zeroes if needed). Move the decimal to the left if the exponent is negative (add zeroes if needed). A calculator can automatically show numbers in scientific notation if it is in scientific mode: SCI/ENG ENTER 2nd DRG ◄ select SCI ═ It can automatically show numbers in decimal form if it is in floating point mode: SCI/ENG ENTER 2nd DRG ► select FLO ═ Regardless of the mode in which the calculator is set, numbers in scientific notation should be entered using the “EE” button. Do NOT enter scientific notation using “× 10” or the “^” or “10x” buttons. These will make it more difficult to get the correct order of operations during calculations. To enter 1.0×10-14 in scientific notation: EE ENTER 1 . 0 2nd x-1 ( – ) 1 4 ═ Example 2.6 Convert the following numbers from decimal form to scientific notation: 75,100,000 -234,900 0.000 002 31 -0.000 035 49 7.51×107 -2.349×105 2.31×10-6 -3.549×10-5 General Chemistry Page 5 of 10 Unit 2: Data Collection and Analysis Example 2.7 Convert the following numbers from scientific notation to decimal form: 1.12×103 -2.35×105 1.12×10-3 -2.35×10-5 1,120 -235,000 0.001 12 -0.000 023 5 To correct INCORRECT scientific notation: Move the decimal point to the left or the right so that only one nonzero digit remains to the left of the decimal point. Increase the exponent if you moved the decimal to the left. Decrease the exponent if you moved it to the right. Example 2.8 Correct the following incorrect scientific notation: 36.7×101 -0.015×10-3 0.123×104 851.6×10-3 3.67×102 -1.5×10-5 1.23×103 8.516×10-1 Calculations in scientific notation: (Your calculator takes care of this for you.) . Addition and Subtraction: Exponents must be the same. Multiplication: Multiply the coefficients and add the exponents. Division: Divide the coefficients and subtract the exponents. Example 2.9 Perform the following mathematical functions and express the answers in correct scientific notation: 3.20×103 + 9.77×102 3.20×103 - 9.77×102 3.20×103 × 9.77×102 3.20×103 ÷ 9.77×102 4.18×103 2.22×103 3.13×106 3.28 X.