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Measuring Matter Holt Modern Chemistry (2006) Chapter 2 Using Measuring Instruments (Lab Technique) Measuring Volume Temperature Mass Measuring Volume Graduated Cylinders – used for measuring volume The glass cylinder has etched marks to indicate volumes, a pouring lip, and quite often, a plastic bumper to prevent breakage. Keep the bumper pushed toward the top. Sit the graduated cylinder on a flat surface. Get down to eye level ! ! ! And . . . . Read the Meniscus Always read volume from the bottom of the meniscus. The meniscus is the curved surface of a liquid in a narrow cylindrical container. Try to avoid parallax errors. Parallax errors arise when a meniscus or needle is viewed from an angle rather than from straight-on at eye level. Incorrect: viewing the Correct: Viewing the meniscus meniscus from an angle at eye level Measuring Volume Determine the volume contained in a graduated cylinder by reading the bottom of the meniscus at eye level. Read the volume using all certain digits and one uncertain digit. Certain digits are determined from the calibration marks on the cylinder. The uncertain digit (the last digit of the reading) is estimated. Use the graduations to find all certain digits There are two unlabeled graduations below the meniscus, and each graduation represents 1 mL, so the certain digits of the reading are… 52 mL. Estimate the uncertain digit and take a reading The meniscus is about eight tenths of the way to the next graduation, so the final digit in the reading is 0.8 mL . The volume in the graduated cylinder is 52.8 mL. 10 mL Graduate What is the volume of liquid in the graduate? 6 . _ _ mL _ 6 2 25mL graduated cylinder What is the volume of liquid in the graduate? 1 _ 5 _ 1 . _ mL 100mL graduated cylinder What is the volume of liquid in the graduate? _ _ 7 5 2 . _ mL Self Test Examine the meniscus below and determine the volume of liquid contained in the graduated cylinder. The cylinder contains: 7 _ _ _ 6 . 0 mL Measuring Temperature The Thermometer o Determine the temperature by reading the scale on the thermometer at eye level. o Read the temperature by using all certain digits and one uncertain digit. o Certain digits are determined from the calibration marks on the thermometer. o The uncertain digit (the last digit of the reading) is estimated. o On most thermometers encountered in a general chemistry lab, the tenths place is the uncertain digit. Do not allow the tip to touch the walls or the bottom of the flask. If the thermometer bulb touches the flask, the temperature of the glass will be measured instead of the temperature of the solution. Readings may be incorrect, particularly if the flask is on a hotplate or in an ice bath. Reading the Thermometer Determine the readings as shown below on Celsius thermometers: 8 7 4 _ _ . _ C _ _ 0 3 5 . _ C Measuring Mass - The Beam Balance Our balances have 3 beams – the uncertain digit is the hundredths place ( _ _ _ . _ _ ) Balance Rules In order to protect the balances and ensure accurate results, a number of rules should be followed: Always check that the balance is level and zeroed before using it. Never weigh directly on the balance pan. Always use a piece of weighing paper to protect it. Do not weigh hot or cold objects. Clean up any spills around the balance immediately. Mass and Significant Figures o Determine the mass by reading the riders on the beams at eye level. o Read the mass by using all certain digits and one uncertain digit. oThe uncertain digit (the last digit of the reading) is estimated. o On our balances, the hundredths place is uncertain. Determining Mass 1. Place object on pan 2. Move riders along beam, starting with the largest, until the pointer is at the zero mark Check to see that the balance scale is at zero ? _ ? . _ ? _ ? _ ? _ Read Mass 5 1 _ . 0 0 _ _ 0 _ _ Read Mass More Closely Self-Test _ _ _ . _ _ 1 3 7 3 9 Units of Measurement (Section 2-2) Types of Observations There are two types of observations Qualitative: descriptive (color smell, etc…) Quantitative: numerical (mass, density, etc…) These notes will deal with quantitative. Quantity something that has magnitude, size, or amount. NOT the same as a measurement!! Ex: measurement Quantity Teaspoon ----------- volume Feet ----------- length SI Units Standard International Units adopted in 1960 by the General Conference on Weights & Measures. SI Base Units (see page 34) SI Prefixes (see page 35) SI Derived Units- combinations of base units (see page 36) Mass: the amount of matter in an object (SI: kg) Weight: the amount of gravitational pull on matter Volume: the amount of space occupied (SI: m3 or mL) Density: the ratio of mass to volume (SI: kg/m3) D = m/v or - ÷ M÷ D xV Conversions (using dimensional analysis) Going from one unit of measurement to another. Use a “line of equality” as a conversion factor For example: 1 meter = 100 cm Each “line of equality” gives two conversion factors 1 meter 100 cm and 100 cm 1 meter Since the factor on top “equals” the factor on the bottom, as a fraction (conversion factor) together they equal “1” Because the fraction equals “one”, it can be used as a multiplier without changing the quantity But since the unit of measurements are different, they can be used in combinations to cancel out unwanted units Lets practice!! Example 1: Express a mass of 5.712 grams in milligrams. We will use a bracket for conversion problems. The given in this problem is 5.712 g. Write it as a fraction in the first part of the bracket. 5.712 g 1 Example 1: Express a mass of 5.712 grams in milligrams. (continued) You want to change the unit to milligrams. Use the “line of equality” 1 g = 1000 mg Since you want to get rid of grams, place 1 g on the bottom to cancel-out the grams on the top. Then place 1000 mg on top. 5.712 g 1000 mg 1 1g Example 1: Express a mass of 5.712 grams in milligrams. (continued) The grams on top will cancel-out the grams on bottom. Then multiple the top numbers together; multiple the bottom numbers together. Final step, divide the top total by the bottom total. DON’T FORGET TO WRITE THE NEW UNIT IN YOUR ANSWER! 5.712 g 1000 mg 5712 mg = = 5712 mg 1 1g 1 Example 2: Express a mass of 0.014 mg in grams. 0.014 mg 1 g = 0.000014 g 1000 mg Example 3: Express a length of 16.45 m in km. 16.45 m 1 km = 0.01645 km 1000 m Using Scientific Measurements (Section 2-3) Accuracy vs. Precision Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT Accurate? Accurate? Accurate? Accurate? Yes! NO! NO! Yes!* Precise? Precise? Precise? Precise? Yes! Yes! NO! NO! *The average is accurate Let’s use a golf analogy Accurate? No Precise? Yes Accurate? Yes Precise? Yes Precise? No Accurate? Maybe? Accurate? Yes Precise? We can’t say! Percent Error Indicates accuracy of a measurement experiment al accepted % error x 100 accepted your value accepted value B. Percent Error A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. 1.40 g/mL 1.36 g/mL % error 100 1.36 g/mL % error = 2.94 % C. Significant Figures (Sig Figs) Indicate precision of a measurement. Recording Sig Figs Sig figs in a measurement include the known digits plus a final estimated digit 2.33 cm C. Significant Figures Counting Sig Figs Count all numbers EXCEPT: • Leading zeros -- 0.0025 • Trailing zeros without a decimal point -- 2,500 C. Significant Figures Counting Sig Fig Examples 1. 23.50 4 sig figs 2. 402 3 sig figs 3. 5,280 3 sig figs 4. 0.080 2 sig figs C. Significant Figures Calculating with Sig Figs - The # with the fewest sig Multiply/Divide figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = 324.103g 4 SF 3 SF 3 SF 324 g C. Significant Figures Calculating with Sig Figs (con’t) Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 3.75 mL 224 g + 4.1 mL + 130 g 7.85 mL 7.9 mL 354 g 350 g C. Significant Figures Calculating with Sig Figs (con’t) ExactNumbers do not limit the # of sig figs in the answer. For example: • Counting numbers: 12 students • Exact conversions: 1 m = 100 cm • “1” in any conversion: 1 in = 2.54 cm Rounding Sig Fig Rules Ex: round to 3 sf rule 42.68g 42.7g……………greater than 5, round up 17.32g 17.3g…………...less than 5, stays the same 2.7851m 2.79m… ………..a 5, round up (there are more specific rules here, but we will leave that to A.P. Chemistry! ) C. Significant Figures Practice Problems 5. (15.30 g) ÷ (6.4 mL) 4 SF 2 SF = 2.390625 g/mL 2.4 g/mL 2 SF 6. 18.9 g - 0.84 g 18.06 g 18.1 g D. Scientific Notation 65,000 kg 6.5 × 104 kg Converting into Sci. Notation: Movedecimal until there’s 1 digit to its left. Places moved = exponent. Large# (>1) positive exponent Small # (<1) negative exponent Only include sig figs. D. Scientific Notation Practice Problems 7. 2,400,000 g 2.4 106 g 8. 0.00256 kg 2.56 10-3 kg 9. 7 10-5 km 0.00007 km 10. 6.2 104 mm 62,000 mm D. Scientific Notation Calculating with Sci. Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your calculator: EXP EXP EXE 5.44 7 ÷ 8.1 4 EE EE ENTER = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol E. Graphical Analysis (Proportions) Direct Proportion y x k y x Inverse Proportion y xy k x Basic Temperature Conversions Temperature Scales Fahrenheit Celsius Kelvin Temperature Conversion Equations 4 equations to use: oF = 9/5oC + 32 oC = 5/9 (oF-32) K = oC + 273 oC = K – 273 Helpful Hints Identify the equation needed. Plug in the numbers to solve Remember the math rules: • Solve what is in parenthesis first • Solve Multiplication & Division before addition and subtraction Show all work Put box around final answer Practice Problem #1 240oC = ____K K = oC + 273 K = 240 + 273 K = 513 Practice Problem #2 50oF = ____ oC oC = 5/9 (oF-32) oC = 5/9 (50-32) oC = 0.55 (18) oC = 10 Practice Problem #3 510K = ____ oC oC = K – 273 oC = 510 – 273 oC = 237 Practice Problem #4 20 oC = ____ oF oF = 9/5oC + 32 oF = 9/5o(20) + 32 oF = 1.8(20) + 32 oF = 36 + 32 oF = 68 The End Common Metric Prefixes Prefix Symbol Factor Numerically Name giga G 109 1 000 000 000 billion** mega M 106 1 000 000 million kilo k 103 1 000 thousand centi c 10-2 0.01 hundredth milli m 10-3 0.001 thousandth micro μ 10-6 0.000 001 millionth nano n 10-9 0.000 000 001 billionth** SI Derived Units- combinations of base units Quantity Symbol Unit Abbreviatio Derivation n Area A square meter m2 LxW Volume V cubic meter m3 LxWxH Density D kilograms per kg mass cubic meter m3 volume Molar mass M kilograms per kg mass mole mol amt. of sub. Molar volume Vm cubic meters m3 volume per mole mol amt. of sub. Energy E joule J force x length SI Base Units Base quantity Name Symbol length meter m mass kilogram kg time second s electric current ampere A thermodynamic temperature kelvin K amount of substance mole mol luminous intensity candela cd

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