Chemistry 1 – McGill Chapter 3 Scientific Measurement

3.1 Qualitative measurements –measurements that give results in a descriptive, non-numerical form. Examples: He is tall Electrons are tiny

Quantitative measurements –measurement that gives results in a definite form, usually as numbers and units. Examples: He is 2.2 m tall Electrons are 1/1840 times the mass of a proton

What is Scientific Notation? Scientific notation is a way of expressing really big numbers or really small numbers. Scientific notation is a way of expressing really big numbers or really small numbers. It is most often used in “scientific” calculations where the analysis must be very precise. It is most often used in “scientific” calculations where the analysis must be very precise. For very large and very small numbers, scientific notation is more concise. For very large and very small numbers, scientific notation is more concise.

Scientific notation consists of two parts: A number between 1 and 10 A number between 1 and 10 A power of 10 A power of 10 N x 10 x

To change standard form to scientific notation… Place the decimal point so that there is one non- zero digit to the left of the decimal point. Place the decimal point so that there is one non- zero digit to the left of the decimal point. Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive. If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

Scientific Notation –a number is written as the product of two numbers: a coefficient and 10 raised to a power. Examples: = 5.67 X = 2.31 X 10 -3

Examples: Convert to or from Scientific Notation: 241 = 6015=.0162=.512= 6.62 x 10 2 = 3.4 x = 2.41 x x x x

Learning Check Express these numbers in Scientific Notation: Express these numbers in Scientific Notation: 1) ) ) ) 2 5) X X X X X 10 -1

Scientific Notation Cont. (This is important to master!!!) 6.25 x x 10 2 = (2.15 x 10 3 )(6.1 x 10 5 )(5.0 x ) = 3.25 x 10 8 = 3.6 x x x 10 3 FYI: “EE” button on calc= typing “X10^”

Accuracy Vs. Precision What do you think the differences are? Ideas anyone???

3.2Accuracy –the measure of how close a measurement comes to the actual or true value of whatever is measured. –how close a measured value is to the accepted value. Precision –the measure of how close a series of measurements are to one another.

Three targets with three arrows each to shoot. Can you hit the bull's-eye? Both accurate and precise Precise but not accurate Neither accurate nor precise How do they compare? Can you define accuracy and precision?

Let’s use a golf analogy

Accurate?No Precise? Yes 10

Accurate?Yes Precise?Yes 12

Precise?No Accurate?Maybe? 13

Accurate?Yes Precise?We cant say! 18

In terms of measurement Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across. Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across. Were they precise? Were they precise? Were they accurate? Were they accurate?

Percent Error Formula: % Error = accepted value- experimental value x 100 accepted value- experimental value x 100 accepted value accepted value *always a positive number- indicated by the absolute value sign* You will use this formula when checking the accuracy of your experiment.

Significant Figures – includes all of the digits that are known plus a last digit that is estimated. FYI: These rules are not fun, but they will save you many points in the future if you learn them NOW! !

Rules for determining Significant Figures 1. All non-zero digits are significant. 1, 2, 3, 4, 5, 6, 7, 8, 9

2. Zeros between non-zero digits are significant. (AKA captive zeros)

3. Leading zeros (zeros at the beginning of a measurement) are NEVER significant

4. Trailing zeros (zeros after last integer) are significant only if the number contains a decimal point

5. All digits are significant in scientific notation. 2.1 x x 10 23

Exact numbers have unlimited Significant Figures Examples: 1 dozen = exactly people in this room Do not use these when you are figuring out sig figs…

Examples: How many significant digits do each of the following numbers contain: a) 1.2d) 4600 b) 2.0e) c) 3.002f) 6.02 x

Learning Check A. Which answers contain 3 significant figures? 1) ) ) 4760 B. All the zeros are significant in 1) ) ) x 10 3 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x ) 535 2) 535,000 3) 5.35 x 10 5

Solution A. Which answers contain 3 significant figures? 1) ) ) 4760 B. All the zeros are significant in 1) ) ) x 10 3 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x ) 535 2) 535,000 3) 5.35 x 10 5

Learning Check In which set(s) do both numbers contain the same number of significant figures? 1 ) 22.0 and ) 22.0 and ) and 40 3) and 150,000

Solution In which set(s) do both numbers contain the same number of significant figures? 3) and 150,000

State the number of significant figures in each of the following: A m B L C g D m E. 2,080,000 bees Learning Check

State the number of significant figures in each of the following: A m B L C g D m E. 2,080,000 bees Learning Check

Rounding Rules:  5 round up < 5 round down (don’t change) Examples: Round to 1 significant digit = Round to 3 sig. digs. = Round to 2 = Round 65,002 to 2 sig. digs. = ,000

Addition and Subtraction The measurement with the fewest significant figures to the right of the decimal point determines the number of significant figures in the answer.

Examples: Solve using correct significant figures m m = m m =

Multiplying and Dividing Measurements The measurement with the fewest significant figures determines the number of significant figures in the answer.

Examples: Solve using correct significant figures: 3.43 m X m = m X 1.2 m = m / 2.2 m = 22.0 m 2 55 m Notice the decimal! ***Why did the “m” unit go away on the last example?***

Uncertainty In lab, you record all numbers you know for sure plus the first uncertain digit. The last digit is estimated and is said to be uncertain but still considered significant.  Graduated cylinders have markings to the nearest mL (milliliter) and you will determine volume to the nearest 0.1 mL… because that is ONE DIGIT OF UNCERTAINTY.

International System of Units revised version of the metric system revised version of the metric system abbreviated SI abbreviated SI All units, their meanings and values can be found on pgs. 63,64,65. Meter (m) – Liter (L) – Gram (g) – SI unit for length SI unit for volume SI unit for mass

Some Tools for Measurement Which tool(s) would you use to measure: A. temperature B. volume C. time D. weight

Solution A. temperaturethermometer B. volume measuring cup, graduated cylinder C. timewatch D. weightscale

Learning Check Match L) length M) mass V) volume ____ A. A bag of tomatoes is 4.6 kg. ____ B. A person is 2.0 m tall. ____ C. A medication contains 0.50 g Aspirin. ____ D. A bottle contains 1.5 L of water. M L M V

Learning Check What are some U.S. units that are used to measure each of the following? A. length B. volume C. weight D. temperature

Solution Some possible answers are A. length inch, foot, yard, mile B. volume cup, teaspoon, gallon, pint, quart C. weight ounce, pound (lb), ton D. temperature  F

Metric Prefixes Kilo- means 1000 of that unit Kilo- means 1000 of that unit –1 kilometer (km) = 1000 meters (m) Centi- means 1/100 of that unit Centi- means 1/100 of that unit –1 meter (m) = 100 centimeters (cm) –1 dollar = 100 cents Milli- means 1/1000 of that unit Milli- means 1/1000 of that unit –1 Liter (L) = 1000 milliliters (mL)

Metric Prefixes

Learning Check Select the unit you would use to measure 1. Your height a) millimeters b) meters c) kilometers 2. Your mass a) milligramsb) grams c) kilograms 3. The distance between two cities a) millimetersb) meters c) kilometers 4. The width of an artery a) millimetersb) meters c) kilometers

Solution 1. Your height b) meters 2. Your mass c) kilograms 3. The distance between two cities c) kilometers 4. The width of an artery a) millimeters

Equalities State the same measurement in two different units length 10.0 in cm

m = 1 ___a) mm b) km c) dm g = 1 ___ a) mg b) kg c) dg L = 1 ___a) mL b) cL c) dL m = 1 ___ a) mm b) cm c) dm Learning Check

m = 1 ___a) mm b) km c) dm g = 1 ___ a) mg b) kg c) dg L = 1 ___a) mL b) cL c) dL m = 1 ___ a) mm b) cm c) dm Learning Check

Instruments for Measuring Volume Graduated cylinder SyringeVolumetric flask BuretPipet

Units of Measuring Volume 1 L = 1000 mL 1 qt = 946 mL Timberlake, Chemistry 7 th Edition, page 3

Reading a Meniscus

Units for Measuring Mass 1 kg = 2.20 lb Timberlake, Chemistry 7 th Edition, page 3

Quantities of Mass Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25 Earth’s atmosphere to 2500 km Ocean liner Indian elephant Average human 1.0 liter of water Grain of table salt Typical protein Uranium atom Water molecule g g g g g 10 9 g 10 6 g 10 3 g 10 0 g g g g g g g g g Giga- Mega- Kilo- base milli- micro- nano- pico- femto- atomo-

LAB TIME!! Metric Lab Metric Lab

Dimensional Analysis (Conversion Factors) Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: 1 in. = 2.54 cm Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

How many minutes are in 2.5 hours ? Conversion factor Conversion factor 2.5 hr x 60 min = 150 min 2.5 hr x 60 min = 150 min 1 hr 1 hrcancel By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

Sample Problem You have $7.25 in your pocket in quarters. How many quarters do you have? You have $7.25 in your pocket in quarters. How many quarters do you have? 7.25 dollars 4 quarters 7.25 dollars 4 quarters 1 dollar 1 dollar X = 29 quarters

Learning Check Write conversion factors that relate each of the following pairs of units: 1. Liters and mL 2. Hours and minutes 3. Meters and kilometers

Learning Check A rattlesnake is 2.44 m long. How long is the snake in cm? a) 2440 cm b)244 cm c)24.4 cm

Learning Check How many seconds are in 1.4 days? Unit plan: days hr min seconds 1.4 days x 24 hr x ?? 1 day 1 day

Wait a minute! What is wrong with the following setup? 1.4 day x 1 day x 60 min x 60sec 24 hr 1 hr 1 min 24 hr 1 hr 1 min

Learning Check Learning Check An adult human has 4.65 L of blood. How many gallons of blood is that? Unit plan: L qt gallon Unit plan: L qt gallon Equalities:1 quart = L 1 gallon = 4 quarts 1 gallon = 4 quarts Your Setup:

Solution Unit plan: L qt gallon Setup: 4.65 L x 1 qt x 1 gal = 1.23 gal L 4 qt L 4 qt

Dealing with Two Units – Pre- AP Only If your pace on a treadmill is 65 meters per minute, how many seconds will it take for you to walk a distance of 8450 feet? If your pace on a treadmill is 65 meters per minute, how many seconds will it take for you to walk a distance of 8450 feet? 8450 ft 1m 1 min60 sec ft65m1 min

The Mole A counting unit A counting unit Similar to a dozen, except instead of 12, it’s 602 billion trillion 602,000,000,000,000,000,000,000 Similar to a dozen, except instead of 12, it’s 602 billion trillion 602,000,000,000,000,000,000, X (in scientific notation) 6.02 X (in scientific notation) This number is named in honor of Amedeo Avogadro (1776 – 1856), who studied quantities of gases and discovered that no matter what the gas was, there were the same number of molecules present This number is named in honor of Amedeo Avogadro (1776 – 1856), who studied quantities of gases and discovered that no matter what the gas was, there were the same number of molecules present

Just How Big is a Mole? Enough soft drink cans to cover the surface of the earth to a depth of over 200 miles. Enough soft drink cans to cover the surface of the earth to a depth of over 200 miles. If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles. If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles. If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole. If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole.

The Mole 1 dozen cookies = 12 cookies 1 mole of cookies = 6.02 X 1023 cookies 1 dozen cars = 12 cars 1 mole of cars = 6.02 X 1023 cars 1 dozen Al atoms = 12 Al atoms 1 mole of Al atoms = 6.02 X 1023 atoms Note that the NUMBER is always the same, but the MASS is very different! Mole is abbreviated mol (gee, that’s a lot quicker to write, huh?)

6.02 x particles 6.02 x particles 1 mole 1 mole or or 1 mole 1 mole 6.02 x particles Note that a particle could be an atom OR a molecule! Avogadro’s Number as Conversion Factor

1. Number of atoms in mole of Al a) 500 Al atoms b) 6.02 x Al atoms b) 6.02 x Al atoms c) 3.01 x Al atoms 2.Number of moles of S in 1.8 x S atoms a) 1.0 mole S atoms b) 3.0 mole S atoms c) 1.1 x mole S atoms` Learning Check

DENSITY - an important and useful physical property Mercury 13.6 g/cm g/cm 3 Aluminum 2.7 g/cm 3 Platinum

-Mass – (g) amount of matter in an object -Volume – (mL) amount of space occupied by an object -Density – (g/mL) a ratio of mass to volume

Formula: D = m vm v Rewrite this formula to solve for m & v! What is the unit for Density???? Remember: A material has the same density no matter how big or small it is!

Example: A piece of metal has a volume of 4.70 mL and a mass of 57.3 g. What is the density? A piece of metal has a volume of 4.70 mL and a mass of 57.3 g. What is the density? M = 57.3 g V = 4.70 mL D = M / V D = 57.3 g / 4.70 mL D = g/mL D = 12.2 g/mL

Problem A piece of copper has a mass of g. It is 9.36 cm long, 7.23 cm wide, and 0.95 mm thick. Calculate density (g/cm 3 ). D M V

Strategy 1. Get dimensions in common units. 2. Calculate volume in cubic centimeters. 3. Calculate the density.

Learning Check Osmium is a very dense metal. What is its density in g/cm 3 if g of the metal occupies a volume of 2.22cm 3 ? 1) 2.25 g/cm 3 2)22.5 g/cm 3 3)111 g/cm 3

Volume Displacement A solid displaces a matching volume of water when the solid is placed in water. 33 mL 33 mL 25 mL

Learning Check What is the density (g/cm 3 ) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? 1) 0.2 g/ cm 3 2) 6 g/mL 3 3) 252 g/cm 3 33 mL 33 mL 25 mL 25 mL

Learning Check Which diagram represents the liquid layers in the cylinder? (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL) 1) 2) 3) K K W W W V V V K

Solution (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL) 1) K W V

Learning Check The density of octane, a component of gasoline, is g/mL. What is the mass, in kg, of 875 mL of octane? 1) kg 2) 614 kg 3) 1.25 kg

Learning Check If blood has a density of 1.05 g/mL, how many liters of blood are donated if 575 g of blood are given? 1) L 2) 1.25 L 3) 1.83 L

Graphs of density and volume can be used to find the density of a substance. The slope of the line formed when mass and volume are plotted is the density. Remember “rise over run”. Graphs of density and volume can be used to find the density of a substance. The slope of the line formed when mass and volume are plotted is the density. Remember “rise over run”.

Buoyancy Buoyancy – The upward force extended on an object by a liquid or a gas. Buoyancy – The upward force extended on an object by a liquid or a gas. Buoyant force is equal to the weight of the fluid displaced. Buoyant force is equal to the weight of the fluid displaced. In gases as Temperature increases, volume increases In gases as pressure increases, volume decreases.

Viscosity Viscosity – the resistance to flow Viscosity – the resistance to flow Two factors that effect viscosity are Temperature and friction.

Temperature – measurement of the average kinetic energy of a system.

Temperature Scales Celsius Sets the freezing point of water at 0  C and the boiling point at 100  C Sets the freezing point of water at 0  C and the boiling point at 100  C Kelvin Absolute zero is set as the zero on the Kelvin scale. It is the temperature at which all motion theoretically ceases.

Temperature Scales Fahrenheit Fahrenheit Celsius Celsius Kelvin Kelvin Anders Celsius Lord Kelvin (William Thomson)

To convert: K = ºC (Kelvin does not use “degrees”.) -273 º C = 0 K = absolute zero

Examples: Convert 25 º C to Kelvin. K = ºC K = 25 º C = 298 K

Learning Check The normal temperature of a chickadee is 105.8°F. What is that temperature in °C? The normal temperature of a chickadee is 105.8°F. What is that temperature in °C? 1) 73.8 °C 2) 58.8 °C 3) 41.0 °C

Solution 3) 41.0 °C 3) 41.0 °CSolution: °C = 5/9 (°F - 32) = 5/9 ( ) =5/9 * 73.8°F = 41.0°C

Learning Check – Pizza is baked at 455°F. What is that in °C? 1) 437 °C 2) 235°C 3) 221°C

Solution Pizza is baked at 455°F. What is that in °C? 2) 235°C 5/9 ( ) = 235°C