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.
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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
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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.
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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
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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. Algebraic Manipulation
Example 2.10 Rearrange the following equations to solve for the variable that is in bold/italics:
m m D D PV = nRT K = °C + 273 V V
m PV m = DV V R °C = K - 273 D nT
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XI. Density Density is the mass of a substance per unit volume or how much it weighs per given volume. It is an intensive physical property. mass D V The units for mass are grams. For liquids, the units for volume are milliliters and the units for density are grams/milliliter. For gases, the units for volume are liters and the units for density are grams/liter. Remember: 1 cm3 = 1 mL.
Water has a density of about 1.0 g/mL. Substances with densities less than 1.0 g/mL float on water. Substances with densities greater than 1.0 g/mL sink in water.
Example 2.11 Is ice more or less dense than liquid water? Ice floats on water, therefore it is less dense.
Example 2.12 A certain solid has a volume of 35.7 cm3 and a mass of 85 grams. What is its density? 85 g D 2.4 g 3 cm3 35.7 cm
Example 2.13 The density of liquid mercury is 13.6 g/mL. What is the mass of 35.0 mL of mercury? g mass 13.6 mL 35.0 mL 476 g
Example 2.14 If the density of gold is 19.3 g/cm3, what is the volume of 200 g of gold?
200 g 3 V 10 cm 19.3 g cm 3
Example 2.15 Find the density of a 500. g rectangular solid whose dimensions are 3.4 cm by 1.2 cm by 1.7 cm. V = (3.4 cm)(1.2 cm)(1.7 cm) = 6.936 cm3 (Don’t round significant digits until the end.) 500. g D 72 g 6.936 cm3 cm 3
Example 2.16 An empty graduated cylinder weighs 26.5 grams. When it is filled with an unknown liquid up to the 45.8 mL mark, the cylinder and the liquid together weigh 70.0 grams. What is the density of the unknown liquid? mass = 70.0 g – 26.5 g = 43.5 g
43.5 g g D 0.950 45.8 mL mL General Chemistry Page 7 of 10 Unit 2: Data Collection and Analysis
VII. Units of Measurement In 1960, scientists all over the world decided to begin using a standard system of seven base units for all measurements. They are known as the SI (Le Système International d’Unités).
mass kilogram (Kg) amount mole (mol) length meter (m) electric current Ampere (amp) time second (s) luminous intensity candela (cd) temperature Kelvin (K)
Mass (measure of quantity kilogram - The only standard which is still defined by an artifact. It is a metal of matter) cylinder, called the International Prototype Kilogram, which is kept in the International Bureau of Weights and Measures at Sevres, France. Length (distance covered meter - Defined in terms of the distance light travels in a vacuum in a specific by a straight line segment period of time. connecting two points.) Time (interval between two second - Defined in terms of electron transition in an atom. A very accurate occurrences) timepiece is called a chronometer, solid state digital timer or atomic clock. Temperature (measure Kelvin - Defined as the same size as the Celsius degree—1/100 of the of kinetic energy) difference between the freezing and boiling points of water. The Kelvin scale starts in a different place so that there are no negative temperatures. The lowest temperature possible in the universe is 0 K.
Derived Units Notice that the liter is not listed as a unit of volume. Volume is a derived unit which is sometimes expressed in cubic units or in liters. The standards that we will use are:
Volume L (liter) or mL or cm3 (milliliter and cubic centimeter are the same size) Pressure Pa (Pascal) Energy J (Joule)
Metric System Prefix Abbr. Sci. Not. Meaning Memorize giga G 1×109 1,000,000,000 1 G* = 1,000,000,000 * mega M 1×106 1,000,000 1 M* = 1,000,000 * kilo k 1×103 1,000 1 K* = 1,000 * hecto h 1×102 100 1 H* = 100 * deca da 1×101 10 1 D* = 10 * deci d 1×10-1 0.1 10 d* = 1 * centi c 1×10-2 0.01 100 c* = 1 * milli m 1×10-3 0.001 1,000 m* = 1 * micro μ 1×10-6 0.000 001 1,000,000 μ* = 1 * nano n 1×10-9 0.000 000 001 1,000,000,000 n* = 1 * * = g (gram) or L (liter) or m (meter) General Chemistry Page 8 of 10 Unit 2: Data Collection and Analysis
Example 2.17 Write the metric abbreviation for the following: one hundredth of a gram one billionth of a liter one tenth of a meter one thousand grams cg nL dm kg
1×103 gram 1×10-6 liters 1×10-2 meters 1/10 gram kg μL cm dg
Dimensional Analysis Dimensional analysis is a method of arranging conversion factors to convert any unit to any other unit.
Directions . Draw the dimensional analysis grid. . Write the given number and unit in the upper left corner. . Copy the unit from the upper left to the lower right corner. . Write the desired unit in the upper right corner. . Fill in the correct numerical relationship which exists between the two units. . Cancel any units which appear in both the numerator and the denominator of the grid. . Multiply everything together that is above the grid line. Divide by everything that is below. . Express your answer in the same number of significant figures as were given in the original problem. . The units which did not cancel are the units for your answer
Example 2.18 How many eggs are there in 10.25 dozen? 10.25 doz 12 eggs 123.0 eggs 1 doz
Example 2.19 How many hours are 190.7 minutes? 190.7 min 1 hr 3.178 hr 60 min
Metric system units (one step) If the two units in the problem are both metric units, and one of the units is a base unit (g, L or m), the problem is a one-step conversion.
Example 2.20 Convert 378.4 cm to meters. 378.4 cm 1 m 3.784 m 100 cm
Example 2.21 Convert 4.32×10-4 g to milligrams. -4 4.3210 g 1,000 mg 4.3210 1 mg 1 g
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Example 2.22 How many kiloliters are there in 4.56×10-7 L? -7 4.5610 L 1 kL 4.5610 10 kL 1,000 L
Example 2.23 Convert 88.1 km to meters. 88.1 km 1,000 m 8.8110 4 m 1 km
Metric system units (two step) If the two units in the problem are both metric units, but neither of the units is a base unit (g, L or m), the problem is a two-step conversion.
. Follow the directions for dimensional analysis to convert from the given unit to the base unit. . Add another section to the grid. . Repeat dimensional analysis to convert from the base unit to the desired unit.
Example 2.24 Convert 231 mm to km. 231 mm 1 m 1 km 2.3110-4 km 1,000 mm 1,000 m
Example 2.25 Convert 5.43 kL to dL. 5.43 kL 1,000 L 10 dL 5.4310 4 dL 1 kL 1 L
Example 2.26 Convert 6.99×108 kg to cg. 6.9910 8 kg 1,000 g 100 cg 6.991013 cg 1 kg 1 g
Example 2.27 How many kilometers are there in 45.2 centimeters? 45.2 cm 1 m 1 km 4.5210-4 km 100 cm 1,000 m
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