The Scientific Method: A logical series of steps The Scientific Method: A logical series of steps scientists follow when solving problems.

Orange Grove Experiment Hypothesis: If we add fertilizer to the soil, then we will grow large oranges.

Orange Grove Purpose: Discover how to grow the biggest oranges.

Example The independent variables (manipulated variables) in the orange grove experiment could be: Fertilizer Other ideas? The dependent variable (responding variable) is Orange size Controlled Variables?

Controlled Experiments Controlled experiments only test one variable at a time Independent Variable (manipulated variable) – is the variable being tested to see if a change occurs Dependent Variables (responding variable) – are all of the observations and data you record during your experiment “DRY MIX” Controlled Variables – are all of the other things that you must keep constant so they do not influence your results

The SI System of Measurement (le Système International, SI)

The Nature of Measurement A Measurement is a quantitative observation consisting of TWO parts Part 1 - number Part 2 - scale (unit) Examples: 20 grams 6.63 x 10-34 Joule·seconds

The Fundamental SI Units (le Système International, SI)

SI Prefixes Common to Chemistry Unit Abbr. Exponent Kilo k 103 Deci d 10-1 Centi c 10-2 Milli m 10-3 Micro  10-6 Nano n 10-9

King Henry Died Unexpectedly Drinking Chocolate Milk K H D U D C M

Metric Conversions g m L 103 102 101 10-1 10-2 10-3 kilo hecto deka Base unit deci centi milli Conversions in the metric system are merely a matter of moving a decimal point. The “base unit” means the you have a quantity (grams, meters, Liters, etc without a prefix.

Metric Conversions g m L 103 102 101 10-1 10-2 10-3 kilo hecto deka Base unit deci centi milli 1 2 3 18. L 18. liters = 18,000. mL Example #1: Convert 18 liters to milliliters

Metric Conversions g m L 103 102 101 10-1 10-2 10-3 kilo hecto deka Base unit deci centi milli 3 2 1 450. mg = 0.450 g 450.mg Example #2: Convert 450 milligrams to grams

Metric Conversions g m L 103 102 101 10-1 10-2 10-3 kilo hecto deka Base unit deci centi milli 1 2 3 4 5 6 20 kg 20 kg = 20,000,000 mg Example #3: Convert 20 kilograms to milligrams

Uncertainty and Significant Figures Cartoon courtesy of Lab-initio.com

Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

Accuracy – how close a measurement is to the true value Precision – A) how close a set of measurements are to each other B) the detail of a number (for example, 3.00 g is more precise than 3 g) accurate & precise precise but not accurate not accurate & not precise 1.8

Chemistry In Action On 9/23/99, $125,000,000 Mars Climate Orbiter entered Mars’ atmosphere 100 km lower than planned and was destroyed by heat. 1 lb = 1 N 1 lb = 4.45 N “This is going to be the cautionary tale that will be embedded into introduction to the metric system in elementary school, high school, and college science courses till the end of time.” One team used English units (e.g., inches, feet and pounds) while the other used metric units for a key spacecraft operation. 1.7

Significant Figures ~Fast fingers~

Rules for Counting Significant Figures (SigFigs)- Details Nonzero integers always count as significant figures. 3456 has 4 significant figures

0.0486 has 3 significant figures 0.00000486 has SigFigs – ZERO Details Leading zeros never count as significant figures. 0.0486 has 3 significant figures 0.00000486 has

16.07 has 4 significant figures SigFigs – ZERO Details Captive zeros always count as significant figures. 16.07 has 4 significant figures

9.300 has 4 significant figures 2500 has 2 significant figures SigFigs – ZERO Details Trailing zeros are significant only if the number has a decimal point 9.300 has 4 significant figures 2500 has 2 significant figures

1 inch = 2.54 cm, exactly SigFigs 8 apples Exact numbers & equivalent statements have an infinite number of significant figures. 8 apples 1 inch = 2.54 cm, exactly

Can you summarize the rules for SigFigs?

Sig Fig Practice #1 How many significant figures are in each of the following measurements? 24 mL 2 significant figures 3001 g 4 significant figures 0.0320 m3 3 significant figures 6.4 x 104 molecules 2 significant figures 560 kg 2 significant figures 1.8

Sig Fig Practice #2 1.0070 m  5 sig figs 17.10 kg  4 sig figs How many significant figures in each of the following? 1.0070 m  5 sig figs 17.10 kg  4 sig figs 100,890 L  5 sig figs 3.29 x 103 s  3 sig figs 0.0054 cm  2 sig figs 3,200,000 ns 2 sig figs

Decimal Places

Significant Figures – Mathematical Operation Rules for Addition or Subtraction The answer cannot have more digits to the right of the decimal point than any of the original numbers. (Answer must match the least precise number in the question.) 89.332 1.1 + 90.432 Shows the thousandths place Only shows the tenth place Answer must match the least precise used, so round off to the tenth place: 90.4 3.70 -2.9133 0.7867 Shows the hundredth place Shows the ten thousandths place Answer must match the least precise used, so round off to the hundredth place: 0.79 1.8

Significant Figures - Mathematical Operation Rules for Multiplication or Division The number of significant figures in the result is set by the original number that has the smallest number of significant figures. (The answer must match the least # of sigfigs in the question.) 4.51 x 3.6666 = 16.536366 = 16.5 3 sig figs round to 3 sig figs 5 sig figs 6.8 ÷ 112.04 = 0.0606926 = 0.061 2 sig figs round to 2 sig figs 5 sig figs 1.8

Rules for Significant Figures in Mathematical Operations Multiplication and Division: Number of sig figs in the result equals the number in the least precise measurement used in the calculation. 6.38 x 2.0 = = 12.76 rounded to correct # of sigfigs: 13 (2 sig figs)

Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m x 7.0 m 100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3 0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2 710 m ÷ 3.0 s 236.6666667 m/s 240 m/s 1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft 1.030 g ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL

Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m 100.0 g - 23.73 g 76.27 g 76.3 g 0.02 cm + 2.371 cm 2.391 cm 2.39 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb 2.030 mL - 1.870 mL 0.16 mL 0.160 mL

Significant Figures Exact Numbers Numbers from definitions or numbers of objects are considered to have an infinite number of significant figures. (They will not Limit the number of sigfigs in our answer.) The average of three measured lengths; 6.64, 6.68 and 6.70? 6.64 + 6.68 + 6.70 3 = 6.67333 = 6.67 = 7 Because 3 is an exact number 1.8

Dimensional Analysis Method of Solving Problems Determine which unit conversion factor(s) are needed Carry units through calculation If all units cancel except for the desired unit(s), then the problem was solved correctly. Round to proper number of sigfigs. How many mL are in 1.632 L? 1 L = 1000 mL (this statement has infinite sigfigs!) 1L 1000 mL 1.632 L x = 1632 mL 1L 1000 mL 1.632 L x = 0.001632 L2 mL 1.9

Dimensional Analysis Method of Solving Problems Determine which unit conversion factor(s) are needed Carry units through calculation If all units cancel except for the desired unit(s), then the problem was solved correctly. Round to proper number of sigfigs. How many g are in 355 kg? 1 kg = 1000 g (this statement has infinite sigfigs!) 1kg 1000 g 355 kg x = 355000 g 1.9

The speed of sound in air is about 343 m/s The speed of sound in air is about 343 m/s. What is this speed in miles per hour? meters to miles seconds to hours 1 mi = 1609 m EXACTLY 1 min = 60 s EXACTLY 1 hour = 60 min EXACTLY 343 m s x 1 mi 1609 m 60 s 1 min x 60 min 1 hour x = 767 mi hour Determine which unit conversion factor(s) are needed Carry units through calculation If all units cancel except for the desired unit(s), then the problem was solved correctly. Round to proper number of sigfigs. 1.9

SCIENTIFIC NOTATION

Scientific Notation In science, we deal with some very LARGE numbers: 1 mole = 602200000000000000000000 atoms In science, we deal with some very SMALL numbers: Mass of an electron = 0.000000000000000000000000000000091 kg

Imagine the difficulty of calculating the mass of 1 mole of electrons! 0.000000000000000000000000000000091 kg x 602200000000000000000000 atoms ???????????????????????????????????

(Positive or negative) Scientific Notation: A method of representing very large or very small numbers in the form: M x 10n n is an integer (Positive or negative) 1  M  10

. 2 500 000 000 9 8 7 6 5 4 3 2 1 Step #1: Insert an understood decimal point Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n

2 500 000 000 2.5 x 109 The exponent is positive because the decimal form of the number we started with was greater than 1.

0.0000579 1 2 3 4 5 Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n

0.0000579 5.79 x 10-5 The exponent is negative because the decimal form of the number we started with was less than 1.

(Positive or negative) Scientific notation expresses a number in the form: M x 10n n is an integer (Positive or negative) 1  M  10

Metric Conversion Practice g m L 103 102 101 10-1 10-2 10-3 kilo hecto deka Base unit deci milli centi Liters 103 102 101 10-1 10-2 10-3 kL hL daL L Base Unit dL mL cL

Problem #1 Convert 400 mL to Liters 400 mL 1 L .400 L = 1 000 mL 10-1 10-2 10-3 101 102 103 Base unit deci centi milli deka hecto kilo = 4x10-1 L

Problem #2 Convert 10 meters to mm 10 m 1 000 mm 10 000 mm = 1 m = 1x104 mm 10-1 10-2 10-3 101 102 103 Base unit deci centi milli deka hecto kilo

Problem #3 Convert 73 grams to kg 73 g 1 kg 0.073 kg = 1 000 g = 7.3x10-2 kg 10-1 10-2 10-3 101 102 103 Base unit deci centi milli deka hecto kilo

Problem #4 Convert 0.02 kilometers to m 0.02 km 1 000 m 20 m = 1 km = 2x101 m 10-1 10-2 10-3 101 102 103 Base unit deci centi milli deka hecto kilo

Problem #5 Convert 20 centimeters to m 20 cm 1 m 0.2 m = 100 cm = 2x10-1 m 10-1 10-2 10-3 101 102 103 Base unit deci centi milli deka hecto kilo

Problem #6 Convert 450 milliliters to dL 450 mL 1 dL 4.5 dL = 100 mL 10-1 10-2 10-3 101 102 103 Base unit deci centi milli deka hecto kilo

Problem #7 Convert 10 kilograms to grams 10 kg 1 000 g 10 000 g = 1 kg = 1x104 g 10-1 10-2 10-3 101 102 103 Base unit deci centi milli deka hecto kilo

Problem #8 Convert 935 mg to cg 1 935 mg cg 93.5 cg = 10 mg 10-1 10-2 10-3 101 102 103 Base unit deci centi milli deka hecto kilo = 9.35x101 cg

Problem #9 Convert 5.2 kg to mg 5.2 kg 1 000 000 mg mg = 1 kg 10-1 10-2 10-3 101 102 103 Base unit deci centi milli deka hecto kilo = 5 200 000 mg = 5.2x106 mg

Problem #10 Convert 175 mL to kL 1 kL 175 mL = kL 1000000 mL 0.000175 = kL 1000000 mL 10-1 10-2 10-3 101 102 103 Base unit deci centi milli deka hecto kilo = 1.75x10-4 kL

Problem #11 Convert 288 g to mg 1000 mg 288 g = mg 1 g = 2.88 x105 mg 288000 = mg 1 g 10-1 10-2 10-3 101 102 103 Base unit deci centi milli deka hecto kilo = 2.88 x105 mg

VI. Derived SI units derived unit--a unit that can be obtained from combinations of fundamental units.

Draw a picture of a cube that is 1 cm x 1 cm x 1 cm below: What is the volume of this box? 1 cm3 If you fill the box with water, what is the volume of the water? 1 mL 1 cm 1 cm 1 cm

Milliliter (mL): 1 mL = 1 cm3 = 1 cc What’s cc mean? Cubic centimeter

Density Density—the ratio that compares the mass of the substance to its volume

Commonly used units are solid: g/cm3 liquid: g/mL gas: g/L d = m/v Commonly used units are solid: g/cm3 liquid: g/mL gas: g/L  

Example 36: Find the density of a piece of Al with a volume of 4 Example 36: Find the density of a piece of Al with a volume of 4.0 cm3 and a mass of 10.8 g.   d = m/v d = 10.8 g/ 4.0 cm3 (yes, you must show units in your work) 2.7 g/cm3

Example 37: A 40. 0 cm3 sample of quartz has a density of 2. 65 g/cm3 Example 37: A 40.0 cm3 sample of quartz has a density of 2.65 g/cm3. What is the mass of the quartz sample?   d = m/v Rearrange your equation first! m = d x v m = 2.65 g/cm3 x 40.0 cm3 m = 106 g

Example 38: The density of a sample of cork is 0. 24 g/cm3 Example 38: The density of a sample of cork is 0.24 g/cm3. What is the volume of this sample if it has a mass of 36.2 g?   d = m/v Rearrange equation! v = m/d v = __36.2 g_ 0.24 g/cm3 V = 150 cm3 (2 sigfigs!)

Diagram: Now, draw that picture of a cube that is 1 cm x 1 cm x 1 cm again. What is the volume of this box? 1 cm3 or 1 mL If you fill the box with water, what is the MASS of the water? 1 g 1 cm 1 cm

What’s it’s mass if it were filled with aluminum. 2. 7 g gold. 19 What’s it’s mass if it were filled with aluminum? 2.7 g gold?? 19.3 g Air? 0.00119 g Wood? 0.9 g 1 cm 1 cm 1 cm

Important fact to memorize! The density of water is 1 g/mL

WATER AND DENSITY 10 g 25 mL Water has a density of ~1 g/mL. 1 mL of water has a mass of 1 gram. Mass of 10 mL of water? 10 g Volume of 25 g of water? 25 mL Water is densest at 4ºC, therefore, ice floats.