CHAPTER 2 - MEASUREMENTS - APC_SHSCHEM1 - Finalized.pdf

Measurements Lecture Chapter 2 – SHCHEM1 Natural Science Cluster Prepared by: Mc. Benrick Porras Outline of Discussion At the end of the lecture session, the student/staff should be able to know the following: Scientific Notations Significant Figures...

Measurements Lecture Chapter 2 – SHCHEM1 Natural Science Cluster Prepared by: Mc. Benrick Porras Outline of Discussion At the end of the lecture session, the student/staff should be able to know the following: Scientific Notations Significant Figures Accuracy and Precision SI and Metric System Mass and Weight Volume Density Temperature Scales Dimensional Analysis in Problem Solving 1 Introduction – The Importance of Units Mars Climate Orbiter Costs about $125 Million. 638-kg robotic space probe whose purpose is to study Mars climate, atmosphere, surface changes. Serve as a communication relay in the Mars Surveyor ’98 for Mars Polar Lander. Launched on December 11, 1998. Figure 1. A Boeing Delta II 7425 expendable launch vehicle lifts off with NASA’s Mars Climate Orbiter on Dec. 11, 1998 1 Introduction – The Importance of Units The space probe is supposed to orbit Mars Mars Climate Orbiter was Main Reason? Mistake in Unit destroyed by heat as a result. Conversion !! The space probe is 100 km lower than expected! 1 Introduction – The Importance of Units Main Reason? Mistake in Unit Conversion !! Uses metric system. Uses English unit system. Assumed that the thrust Specified the thrusts in is expressed in Newtons. pounds. JPL thought that the data they received was in Newton, hence they treated it as 1N. However, in reality 1 lb = 4.45 N Maybe we got lost in translation! 1 1 gram of the element hydrogen is equal to 602,200,000,000,000,000,000,000 hydrogen atoms Each hydrogen atom has a mass of 0.0000000000000000000000016735 g 0.000000000004578 x 0.000000000000000000000546 This is too much! Is there a simplified way to express them? 1 Scientific Notation is a simplified way of expressing large or small numbers. 𝒏 𝑵 𝒙 𝟏𝟎 N is a number between 1 – 10 n is the exponent, either positive or negative integer (whole number) STEPS IN SCIENTIFIC NOTATION Identify the N (a number between 1 – 10) Move the decimal/”imaginary decimal” either to the left or to the right (it depends) so that we could get to the N. If decimal point moves to the right, n is negative. If decimal point moves to the left, n is positive. 1 Scientific Notation is a simplified way of expressing large or small numbers. STEPS IN SCIENTIFIC NOTATION Identify the N (a number between 1 – 10) Move the decimal/”imaginary decimal” either to the left or to the right (it depends) until there is only one non-zero digit to the left of the decimal point. If decimal point moves to the right, n is negative. If decimal point moves to the left, n is positive. 1.) 5 6 8.7 6 2 - Decimal point moves to the left to give us 5.68762. - Since the decimal point moves 2 times, therefore n = 2 - Scientific notation: 5.68762 x 102 1 Scientific Notation is a simplified way of expressing large or small numbers. STEPS IN SCIENTIFIC NOTATION Identify the N (a number between 1 – 10) Move the decimal/”imaginary decimal” either to the left or to the right (it depends) until there is only one non-zero digit to the left of the decimal point. If decimal point moves to the right, n is negative. If decimal point moves to the left, n is positive. 2.) 0. 0 0 0 0 0 0 0 0 0 7 2 6 - Decimal point moves to the right to give us 7.26. - Since the decimal point moves 10 times, therefore n = -10 - Scientific notation: 7.26 x 10-10 1 Scientific Notation is a simplified way of expressing large or small numbers. STEPS IN SCIENTIFIC NOTATION Identify the N (a number between 1 – 10) Move the decimal/”imaginary decimal” either to the left or to the right (it depends) until there is only one non-zero digit to the left of the decimal point. If decimal point moves to the right, n is negative. If decimal point moves to the left, n is positive. 3.) 0.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 6 7 3 5 - Decimal point moves to the right to give us 1.6735 - Since the decimal point moves 24 times to the right, therefore n = -24 - Scientific notation: 1.6735 x 10-24 1 Scientific Notation is a simplified way of expressing large or small numbers. STEPS IN SCIENTIFIC NOTATION Identify the N (a number between 1 – 10) Move the decimal/”imaginary decimal” either to the left or to the right (it depends) until there is only one non-zero digit to the left of the decimal point. If decimal point moves to the right, n is negative. If decimal point moves to the left, n is positive. 4.) 6 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - Decimal point moves to the left to give us 6.022 - Since the decimal point moves 24 times to the left, therefore n = 23 - Scientific notation: 6.022 x 1023 1 Scientific Notation is a simplified way of expressing large or small numbers. Addition and Subtraction of Scientific Notations 1. Ensure the Exponents Are the Same ✓ Same Exponent: If the numbers have the same exponent, you can directly add or subtract the coefficients. ✓ Different Exponents: If the exponents are different, you must first adjust one of the numbers so that both exponents are the same. 2. Preform addition/subtraction of the N values while keeping the 10n value. 1: Addition with Same Exponent 2. Subtraction with different Exponent 5.3 × 103 + 2.4 × 103 (6.2 × 106) − (4.3×105) Step 1: The exponents are the same. Step 1: Convert 4.3×105 to 0.43 × 106 to match Step 2: Add the coefficients: 5.3 + 2.4 = 7.7. exponents. Result: 7.7×103 Step 2: Subtract the coefficients: 6.2 − 0.43 = 5.77. Result: 5.77×106 1 Scientific Notation is a simplified way of expressing large or small numbers. Multiplication and Division of Scientific Notations 1. Multiply/Divide the N1 and N2 the usual way. 2. Add the exponents together if the operation is multiplication. 3. Subtract the exponents together if the operation is division. 3: Multiplication of Scientific Notations 4: Division of Scientific Notations (8.0 × 104) x (5.0 × 102) = (8.0 x 5.0) 104+2 (6.9 × 107)/(3.0 × 10-5) = (6.9 / 3.0) 107-(-5) = 40 x 106 = 2.3 x 1012 = 4.0 x 107 (4.0 × 10-5) x (7.0 × 103) = (4.0 x 7.0) 10-5+3 (8.5 × 104) x (5.0 × 109) = (8.5 / 5.0) (104-9) = 28 x 10-2 = 1.7 x 10-5 = 2.8 x 10-1 1 Scientific Notation is a simplified way of expressing large or small numbers. Addition and Subtraction of Scientific Notations 1. Ensure the Exponents Are the Same ✓ Same Exponent: If the numbers have the same exponent, you can directly add or subtract the coefficients. ✓ Different Exponents: If the exponents are different, you must first adjust one of the numbers so that both exponents are the same. 2. Preform addition/subtraction of the N values while keeping the 10n value. Multiplication and Division of Scientific Notations 1. Multiply/Divide the N1 and N2 the usual way. 2. Add the exponents together if the operation is multiplication. 3. Subtract the exponents together if the operation is division. 1 Express the answers to the following calculations in scientific notations: a. 0.0095 + (8.5 x 10-3) b. 653 / (5.75 x 10-8) c. 850, 000 – (9.0 x 105) d. (3.6 x 10-4) x (3.6 x 106) 1 Measurements Average English System Enjoyer 3 feet is 1 yard, and It doesn’t make any 1760 yard is 1 mile. sense! Average SI System Enjoyer 1 km = 1000 m Yes 1 m = 1000 mm Why are measurements important? In Science, experiments are done. Numerical values or data are obtained from these. 52. 3 What’s wrong with this data? Measurements always have a numerical value (magnitude) AND a unit. 52. 3 km makes more sense. 1 Accuracy and Precision ACCURACY = CORRECT Accuracy – how close a measurement is to the true value. PRECISION = CONSISTENT Precision – how close a set of measurements are to each other. Accurate and Precise but NOT NOT accurate and Precise accurate NOT precise 1 Accuracy and Precision Accuracy – how close a measurement is to the true value. Precision – how close a set of measurements are to each other. STUDENT A STUDENT B STUDENT C 1.964 g 1.970 g 2.000 g 1.971 g 1.972 g 2.002 g True value = 2.000 g 1.978 g 1.968 g 2.001 g Average 1.971 g 1.970 g 2.001 g Practice: Four mass measurements of a metal cube were made using a laboratory balance. The results are 24.02 g, 23.99 g, 23.98 g, and 23.97 g. The actual mass of the metal cube is 25.00 g. Are the mass measurement accurate? Are the mass measurement precise? 1 Significant Figures - refers to the number of important single digits which is meaningful in measurement. Not very precise 82 grams Significant figures are used to make sure our answers Spring Balance isn’t more precise than the numbers we’ve started with. The Rock painted on a Rock. Very precise 82.1234 grams Analytical Balance 1  Significant Figures - refers to the number of important single digits which is meaningful in measurement. 𝒎𝒂𝒔𝒔 𝝆= 82 grams = 1.576923077 g/mL 𝑽𝒐𝒍𝒖𝒎𝒆 52 mL Doesn’t make sense because suddenly, it became super precise. The Rock painted Using significant figures: on a Rock. The answer isn’t 82 grams more precise than = 1.6 g/mL 52 mL the numbers we’ve Graduated Cylinder started with. 1 Significant Figures - refers to the number of important single digits which is meaningful in measurement. 1st Friend: Let’s meet at the Mall in Makati (Not very precise) San Lorenzo Place Mall in Edsa cor. Chino Roces Ave., Makati City. (Super super precise) 2nd Friend: You Significant figures are used to I think its in some street (Not very precise, again) make sure our answers isn’t more precise than the numbers we’ve started with. 1 Guidelines for using significant figures Other Examples: 1. 845 – 3 Significant Figures 2. 40, 501 – 5 Significant figures 3. 0.0000345 – 3 Significant figures 4. 40.062 – 5 significant figures 5. 3.040 – 4 significant figures 6. 0.090 – 2 Significant figures 1 Guidelines for using significant figures Exercise: Determine how many significant figures are there in the following measurements. 1. 394 cm 2. 5.03 3. 0.714 cm 4. 0.0052 5. 2.720 x 1022 atoms 1 Guidelines for using significant figures Exercise: Determine how many significant figures are there in the following measurements. 1. 394 cm – 3 sig fig 2. 5.03 – 3 sig fig 3. 0.714 cm – 3 sig fig 4. 0.0052 – 2 sig fig 5. 2.720 x 1022 atoms – 4 sig fig 1 Guidelines for using significant figures Addition and Subtraction When adding or subtracting the set of data with varied number of significant figures, the data which the least number of decimal places will determine the number of the sum or difference of the data. 1 Guidelines for using significant figures Multiplication and Division When multiplying or dividing the set of data with varied number of significant figures, the data which the least significant figures will determine the number of product or quotient of the data. 1 Guidelines for using significant figures Examples: 1. 12, 343. 2 g + 0.1893 g = 2. 55.97 L – 2.386 L = 3. 7.52 m x 6.9232 m = 4. 0.0239 kg / 46.5 mL = 1 Guidelines for using significant figures 1 Solving for using significant figures 1 Solving for using significant figures 1 Solving for using significant figures 1 The International System of Units, abbreviated as SI, is the main system of measurement units used in science. Taken from Chemistry: The Central Science, 14th Ed. By Brown 1  The International System of Units, abbreviated as SI, is the main system of measurement units used in science. Taken from Chemistry: The Central Science, 14th Ed. By Brown 1  The International System of Units, abbreviated as SI, is the main system of measurement units used in science. Taken from Chemistry: The Central Science, 14th Ed. By Brown What is the name of the unit that equals (a) 10-9 gram, (b) 10-6 second, (c) 10-3 meter? 1  TEMPERATURE Temperature, a measure of the hotness or coldness of an object, is a physical property that determines the direction of heat flow. Heat always flows spontaneously from a substance at higher temperature to one at lower temperature. 1 TEMPERATURE Temperature, a measure of the hotness or coldness of an object, is a physical property that determines the direction of heat flow. Heat always flows spontaneously from a substance at higher temperature to one at lower temperature. A weather forecaster predicts the temperature will reach 31 °C. What is this temperature (a) in K, (b) in °F 1 Sample Problems - TEMPERATURE 1  Derived SI Units A derived unit is obtained by multiplication or division of one or more of the base units. Some examples of derived units includes SI unit for speed (m/s), acceleration (m/s2), and area (m2). 𝒎𝒂𝒔𝒔 𝝆= 𝑽𝒐𝒍𝒖𝒎𝒆 Volume – SI derived unit for volume is Density – SI derived unit for density is cubic meter (m3) kg/m3 1  Derived SI Units A derived unit is obtained by multiplication or division of one or more of the base units. Some examples of derived units includes SI unit for speed (m/s), acceleration (m/s2), and area (m2). Volume – SI derived unit for volume is cubic meter (m3) 1  Derived SI Units A derived unit is obtained by multiplication or division of one or more of the base units. Some examples of derived units includes SI unit for speed (m/s), acceleration (m/s2), and area (m2). A piece of platinum metal with a density of 21.5 g/cm3 has a volume of 𝒎𝒂𝒔𝒔 4.49 cm3. What is its mass? 𝝆= 𝑽𝒐𝒍𝒖𝒎𝒆 Density – SI derived unit for density is kg/m3. However, this is very large when it comes to chemical applications, we can use g/cm3 as alternative. 1 Sample Problems – Density and Volume Measurements 1 Sample Problems – Density and Volume Measurements 1 Sample Problems – Density and Volume Measurements 1 Sample Problems – Density and Volume Measurements 1 Sample Problems – Density and Volume Measurements What would be the radius of a cylindrical object having a height of 10 cm, mass of 15 g, and a density of 15 g/cm3 ? The formula for the volume of cylinder is Vcylinder = πr2h where h stands for height. 1 Dimensional Analysis In Problem Solving 1. Determine which unit conversion factor(s) are needed 2. Carry units through calculation. 3. If all units cancel except for the desired unit(s), then the problem was solved correctly. Desired Unit Given Unit x = Desired Unit Given Unit How many mL are in 1.63 L? 1 Dimensional Analysis In Problem Solving Desired Unit Given Unit x = Desired Unit Given Unit 1 Dimensional Analysis In Problem Solving Desired Unit Given Unit x = Desired Unit Given Unit 1 kg = 2.205 lbs 1 Dimensional Analysis In Problem Solving Desired Unit Given Unit x = Desired Unit Given Unit 1 Dimensional Analysis In Problem Solving Desired Unit Given Unit x = Desired Unit Given Unit 1 Dimensional Analysis In Problem Solving Desired Unit Given Unit x = Desired Unit Given Unit 1 mi = 1.61 km 1 1