Name KEY Period CRHS Academic Chemistry Unit 2 - Measurement and Calculations Notes Key Dates Quiz Date Exam Date LAB Dates Notes, Homework,Exam Reviews and Their KEYS located on CRHS Academic Chemistry Website: https://cincochem.pbworks.com
Page 2 of 10 2.1 CONVERSION FACTORS, DIMENSIONAL ANALYSIS, AND UNITS OF MEASURE Conversion Factors A common practice in chemistry is to utilize conversion factors to convert from one unit to another. Conversion factors are derived from equalities and therefore conversion factors are equal to 1. Example of common equalities and common conversion factors: Equality Conversion Factor (h to days) Conversion Factor (day to h) 1 day = 24 h Equality Conversion Factor (min to h) Conversion Factor (h to min) 1 h = 60 min Equality Conversion Factor (s to min) Conversion Factor (min to s) 1 min = 60 s Using conversion factors The conversion factors are equal to one and you can use these ratios to convert a number from one unit to another by simply multiplying by the appropriate conversion factor. The process of keeping track of the units as you multiply by conversion factors is called Dimensional Analysis. Example: Convert 2.4 days to hours. You can also multiply a series of conversion factors together to complete a sequence of conversions. These conversions could be done one at time, but it is much easier to complete the series. Take caution to use Dimensional Analysis to insure correct units are obtained. Example: Convert 2.4 days to seconds Practice: How many inches are in 2.5 miles? ( 1 mile = 1760 yards)
Page 3 of 10 UNITS OF MEASURE IN CHEMISTRY For the most part, the METRIC system will be used in this course. The Standard International (SI) units for length, mass, and volume are shown below. These units are recognized globally in the scientific community. The metric system is based on the decimal system, i.e. multiples of 10, which makes it easy to carry out math and calculations, compared to the English units for weight (pound & ounces) or length (inches & feet& miles). Prefixes for Metric System kilo (k) 1000 times greater hector (h) 100 times greater deca (da) 10 times greater Increasing Base Units Length Meter (m) Mass Gram (g) Volume Liter (L) deci (d) 10 time smaller centi (c) 100 times smaller milli (m) 1000 times smaller Metric Conversion Factors Used in Chemistry 1 km = 1000 m 1 kg = 1000 g 1 L = 1000 ml 1 m = 100 cm 1 g = 1000 mg 1 m = 1000 mm Practice: 1. Convert 25.5 g to kg 2. Convert 3.56 kg to mg 3. 0.052 km = cm 4. 38129 ml = L 5. If 1.00 lb = 454 g and 1000 g = 1 kg, then how many kg is 2000 lb?
Page 4 of 10 2.2 SIGNIFICANT FIGURES Significant figures are the digits in a measurement that you can prove are true on a measuring device plus one unknown, or uncertain digit that you estimate. When any measurement falls BETWEEN 2 lines on a measuring device, then you WILL estimate the final digit. This is the doubtful digit. When a measurement falls on a line, your doubtful digit is zero (in the graphic, 43.0 ml). For example, a ruler: 1 2 3 4 5 6 measurement is 3.7 cm. We are certain of the first digit, the 3, but we are not certain of the second digit, estimate the.7. Therefore the.7 is our doubtful digit. Given a measurement, we can COUNT how many significant figures are present in that number. This is important, because in science, our work is only as good as our measurements. How to determine number of significant figures in a measurement. (ADD HANDS NMOMINC) Pacific Ocean Is a decimal Absent or Present? Atlantic Ocean Determine if the decimal is Absent or Present. Decimal is Absent (Atlantic) - From RIGHT of the number (the Atlantic side), find the first non-zero digit and count Right to Left until you reach the end of the number. Ex: 6050 3 sig figs Ex: 6051 4 sig figs Decimal is Absent (Pacific) -From LEFT of the number (the Pacific side), find the first non-zero digit and count Left to Right until you reach the end of the number. Ex: 700.70 5 sig figs Ex: 0.0070 2 sig figs
Page 5 of 10 Practice How many significant figures 65000 2 0.00005 1 1.0040 5 0.00341 3 40300 3 200300 4 5.300 4 870 2 37.76 4 0.61 2 600.0 4 0.1707 4 Adding/Subtracting arrange numbers in a. Line up the. Omit any digits to the right of a column that contains a doubtful digit (think place value). Units must match! Practice: 2.43 cm + 21.1 cm 23.53-23.5 cm 27.789 m + 6.1 m 33.889 33.9 m Round off after you add all the numbers together 87 ml + 11.87 ml = 98.87 ml 99 ml Multiplying/Dividing the number of sigfigs in your product or quotient is the same as the number in the operation with the least sigfigs. When using a calculator, round to the sigfig needed. Units must stay in the place they are located in the operation! Practice: 5.12 m x 223 m = 1141.76 1140 m 2 4.750 g x 2.00 g = 9.5 9.50 g 2 2.483 m 0.52 s = 4.775 4.8 m/s Combining Operations First, observe the order of operations (_PEMDAS ) when considering sigfigs. For each step, you must determine sigfigs, then use that result in the next step of the operation. Keep track of the units. Practice: (2.3 cm + 4.37 cm) x 38.2 cm = _254.79 cm 2 250 cm 2 (2 Sig Fig s!) Final answer can only be 2 sig figs
Page 6 of 10 2 SF s! 62.2 kg 2.0 kg + 47.3 kg = 31.1 + 47.3 = 78.4 78 kg Note: PEMDAS perform operations in this order. 1. Parenthesis 2. Exponent 3. Multiply 4. Divide 5. Add 6. Subtract 7. 2.3 SCIENTIFIC NOTATION Scientific notation is used to express very large and very small numbers. Often in science we measure and count extremely small and large numbers. Scientific notation makes our work easier (promise!). *The number of sig figs does not change when converting to or from scientific notation. General formula: a x 10 n The coefficient (number in front) is always between 1 and 10. For very large numbers (greater than 10), n is positive. For very small numbers (less than 1), n is negative. To convert TO scientific notation from ordinary notation: 1. Move the decimal point one digit at a time so the coefficient is between 1 and 10. 2. Count how many places you moved the decimal point. 3. This will be the exponent, or n. 4. For large numbers, n is positive 5. For small numbers, n is negative. Practice: 91.4 m = 9.14 x 10 1 m 0.000 000 000 154 m = 1.54x10-10 m 6,378,000 m = 6.378 x 10 6 m 34,071,000 m = 3.4071 x 10-7 m
Page 7 of 10 To convert FROM scientific notation to ordinary notation, move the decimal point the number of places signified by the exponent n. 1. For a positive n, move the decimal to the right to make the number large. 2. For a negative n, move the decimal to the left to make the number smaller. 3. No decimal present = an implied decimal after the ones place. Term - Ordinary notation a method of expressing numerical values in which the entire number is expressed in the notation. Practice Conversions: 4 x 10 7 m = 40,000,000 m 2 x 10-3 m = 0.002 m 1.8 x 10 3 m = 1800 m 3.499 x 10 4 m = 34990 m 0.670005 cm = 6.70005 x 10-1 cm 31,580,000 s = 3.158 x 10 7 s 0.0000018 km = 1.8 x 10-6 km 7.8 x 10 5 mm = 780,000 mm Practice Math Problems with Scientific Notation: (2.43 x 10 4 ) x (4.43 x 10 5 ) = 1.08 x 10 10 251 x (6.5 x10-5 ) = 1.6 x 10-2 or 0.016 0.0023 x (3 x 10 7 ) /( 4.3 x 10 13 ) = 1.6 x 10-9 (6.02x10-23 ) /[ (2.3 x 10 16 ) x (4.3 x 10 15 )] = 6.1 x 10-55 How many lithium (Li) atoms in 25.0 g of Li? (1.00 mol Li = 6.02x10 23 Li atoms & 1 mol Li = 6.94 g Li)
Page 8 of 10 2.4 ACCURACY AND PRECISION AND QUALITATIVE VS. QUANTITATIVE DATA Accuracy describes how close a measurement is to the known or true value of the object measured. Precision is both: o the number of significant figures in a measurement, where more digits is more precision, and; o the repeatability of the measurement A measurement system that is both accurate and precise is considered valid. Accurate & Precise Accurate not precise Precise not accurate not precise not accurate Example: Jennie massed an object known to have a mass of 100.0 g. She measured the object three times with the same device: 175.6 g, 175.3 g, and 175.8 g. Were her measurements accurate? Precise? Explain. Precise because correct number of sig figs and repeatable, but not accurate Practice: 1. Curtis measured a known 34.57 cm length of twine. The first measurement was 34 cm. Is this an accurate measurement? _NO_ Why or why not? 4 is the doubtful digit in first measurement, so it wasn t accurate to 2 nd decimal place Is this a precise measurement? _NO Why or why not? 4 is the doubtful digit in first measurement, so it wasn t precise to 2 nd decimal place 2. The second measurement was 34.58 cm. Is this an accurate measurement? _Yes_ Why or why not? The diiference is within the doubtful digit Is this a precise measurement? No_ Why or why not? 1 st measurement did not have enough significant figures to allow average to be classified as precise
Page 9 of 10 QUALITATIVE vs. QUANTITATIVE DATA Qualitative data is descriptive and non-numerical. (Examples: color and phase of matter). Quantitative data gives results in a definite form, usually in numerical form with units. (Examples: length and mass) Practice: Describe the following as Qualitative or Quantitative Mass Quantitative Rough Qualitative Color Qualitative Volume Quantitative Length Quantitative Turbulent Qualitative Smooth Qualitative Radius Quantitative Temperature _ Quantitative Hazy Qualitative Time Quantitative Soft Qualitative
Page 10 of 10