Chapter 1 Matter,Measurement, and Problem Solving

Chapter 1 Matter,Measurement, and Problem Solving

Classification of Matter matter is anything that has mass and occupies space we can classify matter based on whether it s solid, liquid, or gas State Shape Volume Compress Flow Solid Fixed Fixed No No Liquid Indef. Fixed No Yes Gas Indef. Indef. Yes Yes Fixed = keeps shape when placed in a container Indefinite = takes the shape of the container

Solids the particles in a solid are packed close together and are fixed in position though they may vibrate incompressible the inability of the particles to move around results in solids retaining their shape and volume when placed in a new container, and prevents the particles from flowing

Crystalline vs. Amorphous solids some solids have their particles arranged in an orderly geometric pattern we call these crystalline solids salt and diamonds some solids have their particles randomly distributed without any long-range pattern we call these amorphous solids plastic glass charcoal

Liquids the particles in a liquid are closely packed, but they have some ability to move around Incompressible take the shape of their container and to flow however, they don t have enough freedom to escape and expand to fill the container

Gases in the gas state, the particles have complete freedom from each other the particles are constantly flying around, bumping into each other and the container Compressible because there is a lot of empty space, the particles can be squeezed closer together therefore gases are compressible because the particles are not held in close contact and are moving freely, gases expand to fill and take the shape of their container, and will flow

Classification of Matter by Composition 1) made of one type of particle 2) all samples show the same intensive properties 1) made of multiple types of particles 2) samples may show different intensive properties 7

Classification of Pure Substances 1) made of one type of atom (some elements found as multiatom molecules in nature) 2) combine together to make compounds 1) made of one type of molecule, or array of ions 2) molecules contain 2 or more different kinds of atoms 8

Classification of Mixtures 1) made of multiple substances, whose presence can be seen 2) portions of a sample have different composition and properties 1) made of multiple substances, but appears to be one substance 2) all portions of a sample have the same composition and properties 9

Separation of Mixtures separate mixtures based on different physical properties of the components Physical change Different Physical Property Technique Boiling Point State of Matter (solid/liquid/gas) Adherence to a Surface Volatility Density Distillation Filtration Chromatography Evaporation Centrifugation & Decanting 10

Changes in Matter Dissolving of Sugar C 12 H 22 O 11 (s) changes that alter the state or appearance of the matter without altering the composition are called physical changes state changes boiling / condensing melting / freezing subliming C 12 H 22 O 11 (aq)

Physical change vs. Chemical change changes that alter the composition of the matter are called chemical changes during the chemical change, the atoms that are present rearrange into new molecules, but all of the original atoms are still present rusting processes that release lots of energy burning C 3 H 8 (g) + 5 O 2 (g) 3 CO 2 (g) + 4 H 2 O(l) Burning propane gas 12

Energy changes in matter, both physical and chemical, result in the matter either gaining or releasing energy energy is the capacity to do work work is the action of a force applied across a distance a force is a push or a pull on an object electrostatic force is the push or pull on objects that have an electrical charge

Energy kinetic energy is energy of motion motion of the atoms, molecules, and subatomic particles potential energy is energy that is stored in the matter due to the composition of the matter and its position in the universe chemical potential energy arises from electrostatic forces between atoms, molecules, and subatomic particles Law of Conservation of Energy energy is neither created nor destroyed. It is converted from one form to another

Temperature measure of the average amount of kinetic energy higher temperature = larger average kinetic energy heat flows from the matter that has high thermal energy into matter that has low thermal energy until they reach the same temperature heat is exchanged through molecular collisions between the two materials

Temperature Scales Fahrenheit Scale, F used in the U.S. Celsius Scale, C used in all other countries Kelvin Scale, K absolute scale no negative numbers directly proportional to average amount of kinetic energy 0 K = absolute zero 16

Fahrenheit vs. Celsius a Celsius degree is 1.8 times larger than a Fahrenheit degree the standard used for 0 on the Fahrenheit scale is a lower temperature than the standard used for 0 on the Celsius scale T C = (T F 32) 1.8 T F = 1.8 T C + 32 the size of a degree on the Kelvin scale is the same as on the Celsius scale so 1 kelvin is 1.8 times larger than 1 F the 0 standard on the Kelvin scale is a much lower temperature than on the Celsius scale K = C + 273.15 17

Example The melting point of gallium is 85.6 o F. What is this temperature on Celsius scale Kelvin scale

The Standard Units Scientists have agreed on a set of international standard units for comparing all our measurements called the SI units Système International = International System Quantity Unit Symbol length meter m mass kilogram kg time second s temperature kelvin K 19

Common Prefix Multipliers in the SI System All units in the SI system are related to the standard unit by a power of 10 The power of 10 is indicated by a prefix multiplier The prefix multipliers are always the same, regardless of the standard unit Report measurements with a unit that is close to the size of the quantity being measured Prefix Symbol Decimal Equivalent Power of 10 mega- M 1,000,000 Base x 10 6 kilo- k 1,000 Base x 10 3 deci- d 0.1 Base x 10-1 centi- c 0.01 Base x 10-2 milli- m 0.001 Base x 10-3 micro- m or mc 0.000 001 Base x 10-6 nano- n 0.000 000 001 Base x 10-9 pico p 0.000 000 000 001 Base x 10-12 20

Common Units and Their Equivalents Mass 1 kilogram (km) = 2.205 pounds (lb) 1 pound (lb) = 453.59 grams (g) 1 ounce (oz) = 28.35 grams (g) Volume 1 liter (L) = 1000 milliliters (ml) 1 liter (L) = 1000 cubic centimeters (cm 3 ) 1 liter (L) = 1.057 quarts (qt) 1 U.S. gallon (gal) = 3.785 liters (L) Length 1 kilometer (km) = 0.6214 mile (mi) 1 meter (m) = 39.37 inches (in.) 1 meter (m) = 1.094 yards (yd) 1 foot (ft) = 30.48 centimeters (cm) 1 inch (in.) = 2.54 centimeters (cm) exactly 21

Volume Derived unit any length unit cubed Measure of the amount of space occupied SI unit = cubic meter (m 3 ) Commonly measure solid volume in cubic centimeters (cm 3 ) Commonly measure liquid or gas volume in milliliters (ml) 22

Mass, g Mass & Volume two main physical properties of matter mass and volume are extensive properties the value depends on the quantity of matter extensive properties cannot be used to identify what type of matter something is Large iceberg and small ice cube even though mass and volume are individual properties, for a given type of matter they are related to each other! 160 140 120 100 80 60 40 20 Volume vs. Mass of Brass y = 8.38x 0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 Volume, cm 3 23

Density Ratio of mass:volume is an intensive property value independent of the quantity of matter Solids = g/cm 3 1 cm 3 = 1 ml Liquids = g/ml Gases = g/l Volume of a solid can be determined by water displacement Archimedes Principle Density : solids > liquids >>> gases except ice is less dense than liquid water! Density Mass Volume For equal volumes, denser object has larger mass For equal masses, denser object has smaller volume Heating an object generally causes it to expand, therefore the density changes with temperature 24

A Measurement the unit tells you what standard you are comparing your object to the number tells you 1. what multiple of the standard the object measures 2. the uncertainty in the measurement scientific measurements are reported so that every digit written is certain, except the last one which is estimated If the length is reported as 3.26 cm, the digits 3 and 2 are certain (known). the final digit, 6, is estimated (uncertain). all three digits (2, 7, and 6) are significant, including the estimated digit. 25

Known & Estimated Digits For the following volume readings, what would be measured values? E.g l 8.... l.... l 9.... l.... l 10.. cm What is the length of the line? 1) 9.2 cm 2) 9.13 cm 3) 9.19 cm 26

Uncertainty in Measured Numbers accuracy is an indication of how close a measurement comes to the actual value of the quantity precision is an indication of how reproducible a measurement is 27

Accuracy, Precision, and Significant Figures Significant figures: The number of meaningful digits in a measured or calculated quantity. They come from uncertainty in any measurement. Generally the last digit in a reported measurement is uncertain (estimated). Exact numbers and relationships (7 days in a week, 30 students in a class, etc.) effectively have an infinite number of significant figures.

Examples Classify each of the following as (1) exact or (2) measured numbers. A. Gold melts at 1064 C. B. 1 yard = 3 feet C. The diameter of a red blood cell is 6 x 10-4 cm. D. There are 6 hats on the shelf. E. A can of soda contains 355 ml of soda. 29

Accuracy, Precision, and Significant Figures Rules for counting significant figures (left-to-right): 1. Zeros in the middle of a number are like any other digit; they are always significant. 4.803 cm 4 sf 2. Rules for counting significant figures (left-to-right): Zero at the beginning of a number are not significant (placeholders). 0.00661 g 3 sf or 6.61 x 10-3 g 3. Zeros at the end of a number and after the decimal point are always significant. 55.220 K 5 sf 4. Zeros at the end of a number without a written decimal point are ambiguous and should be avoided by using scientific notation if 150 has 2 sig. figs. then 1.5 x 10 2 but if 150 has 3 sig. figs. then 1.50 x 10 2

Rounding Numbers If the first digit you remove is 4 or less, it and all following digits are dropped from the number 5.664 425 = 5.664 (4 s.f) If the digit you remove is 5 or greater, the last digit of the number is increases by 1 5.664 525 = 5.665 (4 s.f) Sometimes, a calculator displays a small whole number. To give an answer with the correct number of significant figures, significant zeros may need to be written after the calculator result. E.g 8.00 2.00 = 4 4.00 3 s.f 3 s.f calculator 2 zeros are needed result to give 3 s.f

Significant figures in calculation When multiplying or dividing the final answer must have the same number of significant figures as the measurement with the fewest significant figures. Example: 110.5 x 0.048 = 5.304 = 5.3 (rounded) 4 SF 2 SF calculator 2 SF When adding or subtracting the final answer must have the same number of decimal places as the measurement with the fewest decimal places. 25.2 one decimal place + 1.34 two decimal places 26.54 calculated answer 26.5 final answer with one decimal place 32

Both Multiplication/Division and Addition/Subtraction with Significant Figures when doing different kinds of operations with measurements with significant figures, do whatever is in parentheses first, evaluate the significant figures in the intermediate answer, then do the remaining steps 3.489 (5.67 2.3) = 2 dp 1 dp 3.489 3.37 = 12 4 sf 1 dp & 2 sf 2 sf 33

Metric Equalities An equality states the same measurement in two different units. can be written using the relationships between two metric units. Example: 1 meter is the same as 100 cm and 1000 mm. 1 m = 100 cm 10-2 m = 1cm 1 m = 1000 mm 10-3 m = 1 mm 34

Conversion Factors A conversion factor is obtained from an equality. E.g Metric U.S system Equality: 1 in. = 2.54 cm written as a fraction (ratio) with a numerator and denominator. inverted to give two conversion factors for every equality. 1 in. = 1 = 2.54 cm 2.54 cm 1 in. Arrange conversion factors so given unit cancels Arrange conversion factor so given unit is on the bottom of the conversion factor given unit desired unit given unit desired unit 35

Using Two or More Factors Often, two or more conversion factors are required to obtain the unit needed for the answer. Unit 1 Unit 2 Unit 3 Additional conversion factors are placed in the setup problem to cancel each preceding unit. Given unit x factor 1 x factor 2 = needed unit Unit 1 x Unit 2 x Unit 3 = Unit 3 Unit 1 Unit 2 36

Example If a ski pole is 3.0 feet in length, how long is the ski pole in m? Convert 288.0 cm to yard Convert 9255 cm 3 to gallons

1.8 Density Density compares the mass of an object to its volume. is the mass of a substance divided by its volume. Density Expression Density = mass = g or g = g/cm 3 volume ml cm 3 Note: 1 ml = 1 cm 3 Can we use density as a conversion factor to calculate mass or volume? 38

Examples What is the density (g/cm 3 ) of 48.0 g of a metal if the level of water in a graduated cylinder rises from 25.0 ml to 33.0 ml after the metal is added? 25.0 ml 33.0 ml object A drop of gasoline has a mass of 22.0 mg and a density of 0.754 g/cm 3. What is its volume in Liters? 39