Measurement

Types of Observations and Measurements We make QUALITATIVE observations of reactions — changes in color and physical state. We also make QUANTITATIVE MEASUREMENTS, which involve numbers. Use SI units — based on the metric system

The International System of Units (SI System)

Units Quantity Base Unit Abbreviation Length Meter m Mass Gram g Volume Liter l Time Second s Temperature Kelvin K Amount Mole mol

Temperature On the Celsius scale, the freezing point of water is 0°C and the boiling point is 100°C. On the Kelvin scale, the freezing point of water is 273.15 kelvins (K), and the boiling point is 373.15 K. The zero point on the Kelvin scale, 0 K, or absolute zero, is equal to 273.15 °C.

Celsius & Kelvin Because one degree on the Celsius scale is equivalent to one kelvin on the Kelvin scale, converting from one temperature to another is easy. You simply add or subtract 273, as shown in the following equations.

Temperature Scales

SI Units Prefix Symbol Factor mega- M 106 kilo- k 103 BASE UNIT ----- 100 deci- d 10-1 centi- c 10-2 milli- m 10-3 micro- 10-6 nano- n 10-9 pico- p 10-12

Number vs. Quantity Quantity - number + unit UNITS MATTER!!

M V D = C. Derived Units 1 cm3 = 1 mL 1 dm3 = 1 L Combination of base units. Volume (m3 or cm3) length  length  length Density (kg/m3 or g/cm3) mass per volume 1 cm3 = 1 mL 1 dm3 = 1 L D = M V

Accuracy vs. Precision ACCURATE = CORRECT PRECISE = CONSISTENT 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

Accuracy defined: The accuracy of a measurement is how close a result comes to the true value.

Precision : Precision indicates how close together or how repeatable the results are.  A precise instrument will give very nearly the same result each time it is used.

An Example

Every experimental measurement has a degree of uncertainty Every experimental measurement has a degree of uncertainty. We can see the markings between 1.6-1.7 cm but we can’t see the markings between the .6-.7 so we must guess. We record 1.67 cm as our measurement (the last digit, 7, was a guess so we stop there).

This is why measured numbers have a degree of error. All but one of the figures is known with certainty. To indicate the precision of a measurement, the value recorded should use all the digits known with certainty.

Percent Error Indicates accuracy of a measurement Where l error l is your measured (experimental) value minus the accepted value

Sample percent error problem:

Practice problem: 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.

Scientific Notation Used to express very small and very large numbers It is written as a product of two numbers: The coefficient – always greater than or equal to 1 and less than 10 The power (or exponent) – represents how many times the coefficient must be multiplied by 10 Ex. 8.4 x 104 The exponent is equal to the number of places the decimal is moved to the left or right

Scientific Notation 65,000 kg  6.5 × 104 kg Converting into Sci. Notation: Move decimal until there’s 1 digit to its left. Places moved = exponent. Large # (>1)  positive exponent Small # (<1)  negative exponent Only include sig figs. (more on this in a bit)

Scientific Notation Practice Problems 2,400,000 g 0.00256 kg 7  10-5 km 6.2  104 mm 2.4  106 g 2.56  10-3 kg 0.00007 km 62,000 mm

Adding and Subtracting with Scientific Notation If you are not using a calculator than the exponents must be the same. Ex: You want to calculate the sum of 5.4 x 103 and 8.0 x 102. First rewrite the second number so that the exponent is 3. 8.0 x 102 = .80 x 103 Now add the numbers. (5.4 x 103) = (0.80 x 103) = (5.4 + .80) x 103 = 6.2 x 103 Follow the same rule when you subtract. (3.42 x 10-5)-(2.5 x 10-6) = (3.42 x 10-5) – (0.25 x 10-5) = (3.42-0.25) x 10-5 = 3.17 x 10-5

Multiplying and Dividing with Scientific Notation Multiply/divide the coefficients and add/subtract the exponents Ex: (3x104) x (2x102) = (3x2) x 104+2 = 6x106 (3.0x105) (6.0x102) = (3 6)x105-2 = 0.5x103 = 5.0x102

Type on your calculator: Scientific Notation Calculating with Sci. Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your calculator: EXP EE EXP EE ENTER EXE 5.44 7 8.1 ÷ 4 = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

Significant Figures

Significant figures indicate the precision of a measurement They are very important in chemistry Recording significant figures (sig figs) Sig figs in a measurement include the known digits plus a final estimated digit

Counting Sig Figs You will always count all nonzero digits as well as any zeros between two significant figures For numbers with no decimal Start from the right Skip any zeros at the end Once you come to the first non-zero digit, count EVERY number from then on For numbers with a decimal Start from the left Skip the zeros at the beginning of the number Then count as those with no decimal, even zeros after nonzero digits Review: count all numbers EXCEPT: Leading zeros  0.0025 Trailing zeros without a decimal point  2, 500

Counting Sig Fig Examples 4 sig figs 23.50 402 5,280 0.080 3 sig figs 3 sig figs 2 sig figs

Sig Fig Problems – your turn: Value Number of significant digits 1) 34608 2)  0.34680                3)  34.680                4)  0.3468                  5) 346.80 6)  3.4608                7) 0.034608 8)  0.3468                    9)  0.00034680 10)  0.0000034608

Answers to Sig Fig Problems Value Number of significant digits 1) 34608 5 2) 0.34680      5          3) 34.680    5           4) 0.3468  4                 5) 346.80 5 6) 3.4608     5            7) 0.034608 5 8) 0.3468    4                 9) 0.00034680 5 10) 0.0000034608 5

Calculating with Sig Figs Add/Subtract The number with the lowest decimal value determines the place of the last sig fig in the answer. 3.75 mL +4.1 mL 7.85 mL 7.9 mL

Calculating with Sig Figs Multiply/Divide The number with the fewest sig figs determines the number of sig figs in the answer (13.91g/cm3)(23.3cm3) = 324.103g 4 SF 3 SF 3SF 324 g

Calculating with Sig Figs Exact numbers do not limit the number of sig figs in the answer Counting numbers = 12 students Exact conversions = 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm

Practice 15.30 g 6.4 mL = 5.761m x 6.20m = 18.9 g – 0. 84 g = 1.6 mL + 0.62mL =

Think Time 10/26/15 How many sig. figs. 10.03 cm Expand 6.22 x 10-4 g Calculate using sig. fig. rules: 23.1 g/55.77 mL = g/mL or g/cm3 is the derived unit for _________. Remember Friday’s Lab

a.k.a. Factor Label Method Dimensional Analysis a.k.a. Factor Label Method

Dimensional Analysis Units, or “labels” are cancelled or “factored” out (hence the name, factor labeling)

Dimensional Analysis Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

SI Units Prefix Symbol Factor mega- M 106 kilo- k 103 BASE UNIT ----- 100 deci- d 10-1 centi- c 10-2 milli- m 10-3 micro- 10-6 nano- n 10-9 pico- p 10-12

Dimensional Analysis 1 in 2.54 cm = 1 2.54 cm 2.54 cm 1 in 2.54 cm 1 = Lining up conversion factors: = 1 1 in 2.54 cm 2.54 cm 2.54 cm 1 = 1 in 2.54 cm 1 in 1 in

Use Dimensional Analysis to Convert Between Metric Units Express 750 dg in grams

Dimensional Analysis 65 g 1000mg 1 g = 65,000 mg g mg  How many milligrams are there in 65 grams of salt? g mg 65 g 1000mg 1 g = 65,000 mg 

Dimensional Analysis 1 g 1000 mg 1 kg 1000 g = 0.0135 kg g kg  How many kilograms are in 13,500 milligrams of iron? g kg 13500 mg 1 g 1000 mg 1 kg 1000 g = 0.0135 kg 

SI Prefix Conversions 0.2 32 45,000 0.0805 1) 20 cm = ______________ m 2) 0.032 L = ______________ mL 3) 45 m = ______________ nm 4) 805 dm = ______________ km 32 45,000 0.0805

Dimensional Analysis 1.00 qt 1 L 1.057 qt 1000 mL 1 L = 946 mL qt mL  How many milliliters are in 1.00 quart of milk? qt mL 1.00 qt 1 L 1.057 qt 1000 mL 1 L = 946 mL 

Dimensional Analysis 8.0 cm 1 in 2.54 cm = 3.2 in cm in Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? cm in 8.0 cm 1 in 2.54 cm = 3.2 in

Dimensional Analysis 550 cm 1 in 2.54 cm 1 ft 12 in 1 yd 3 ft = 6.0 yd Taft football needs 550 cm for a 1st down. How many yards is this? cm yd 550 cm 1 in 2.54 cm 1 ft 12 in 1 yd 3 ft = 6.0 yd

Dimensional Analysis 1.3 m 100 cm 1 m 1 piece 1.5 cm = 86 pieces cm A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire? cm pieces 1.3 m 100 cm 1 m 1 piece 1.5 cm = 86 pieces

Dimensional Analysis 1.5 lb 1 kg 2.2 lb 1000 g 1 kg 1 cm3 19.3 g You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. lb cm3 1.5 lb 1 kg 2.2 lb 1000 g 1 kg 1 cm3 19.3 g = 35 cm3