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1. Unit 7 Measurements in Chemistry

2. 0 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

3. 0 Length • SI unit = meter • A meter is the distance that light travels in a vacuum (space with no matter) in 1/299,792,458 second • Commonly use centimeters (cm) • 1 m = 100 cm • 1 cm = 10 mm • 1 inch = 2.54 cm (exactly) Time • SI base unit: second (s) • A second is the frequency of the radiation given off by a cesium-133 atom.

4. 0 Mass • Measure of the amount of matter present in an object • A kilogram is defined by a platinum-iridium cylinder kept at Sèvres, France. • SI unit = kilogram (kg) • 1 kg = 2.2046 pounds • 1 kg = 1000 g • 1 g = 1000 mg

5. 0 Volume (V) • Measure of the amount of space occupied • SI unit = cubic meter (m3) • a Derived Unit • Commonly measure solid volume in cubic centimeters (cm3) • 1 m3 = 1x106 cm3 • Commonly measure liquid or gas volume in milliliters (mL) • 1 L = 1000 mL 1L=1 dm3 1 mL = 1 cm3 • Volume for geometric figures: • Rectangle: V =Length x width x height • Cylinder : V= r2h h: height r: radius

6. Temperature • SI base unit: Kelvin (K) • Lowest temperature is 0 K • Celsius (C) • Fahrenheit (F) • K= C + 273 • F = (1.8xC) + 32

7. 0 Related Units in the SI System • All units in the SI system are related to the standard (base) unit by a power of 10 • The power of 10 is indicated by a prefix • The prefixes are always the same, regardless of the standard unit Ex. cm (centimeter), cg (centigram), cL (centiliter)

8. 0 Greek Prefixes SI System Table

9. Writing relationships between units. • Write down the relationship between meters ,m (base unit) and kilometers, km. • Km are greater than m • 1km = • 1km= 1000 m

10. Relationship between mL and cL? • cL is greater than mL • 1cL= • 1cL = 10mL • Relationship between m and dm. • dm is greater than m • 1dm= • 1dm = 100000m

11. Learning Check • Write relationships between the following units: • mm and km • Mg and dg • ks and ms

12. Learning Check • Write relationships between the following units: • mm and km 1km = 1,000,000 mm • Mg and dg 1 Mg= 10,000,000 dg • ks and ms 1ks = 1,000, 000 ms

13. Cw • Metric units conversions

14. 0 Dimensional Analysis (factor labeled method): • Always write every measurement with its number and with its associated unit • Always include units in your calculations • you can do the same kind of operations on units as you can with numbers • cm × cm = cm2 • cm + cm = cm • cm ÷ cm = 1 • using units as a guide to problem solving is called dimensional analysis

15. 0 Problem Solving and Dimensional Analysis • Many problems in Chemistry involve using relationships to convert one unit of measurement to another • Conversion Factors are ratios between two units • May be exact or measured • Both parts of the conversion factor have the same number of significant figures • Conversion factors generated from equivalence statements • Ex. 1 inch = 2.54 cm can give or

16. 0 Using Dimensional Analysis • Write down Given Amount and Unit • Write down what you want to Find and Unit • Write down needed Conversion Factors or Equations • Write down equivalence statements for each relationship • Change equivalence statements to Conversion Factors

17. 0 Dimensional Analysis • Plan a Solution for the Problem • order conversions to cancel previous units or • arrange Equation to solve for the variable wanted • Apply the Steps in the Plan • check that units cancel properly • multiply terms across the top and divide by each bottom term • Check the Answer to see if its Reasonable • correct size and unit

18. 100 cm ______ 100 cm 1 m ______ 1 m 1 m 100 cm ______ 132 cm ( ) equality: 1 m = 100 cm Ex. 1 How many cm are in 1.32 meters? applicable conversion factors: or ? cm = 1.32 m = We use the idea of unit cancellation to decide upon which one of the two conversion factors we choose.

19. 0.0872 m 100 cm ______ 1 m ______ 1 m 100 cm ______ ( ) 1 m 100 cm equality: 1 m = 100 cm Ex. 2 How many meters is 8.72 cm? applicable conversion factors: or ? m = 8.72 cm = Again, the units must cancel.

20. 1 km 1,000 m ( ) ______ ( ) ____ 1 m 10 dm 1.5 km How many kilometers is 15,000 decimeters? 1m = 10 dm 1km=1000m ? km = 15,000 dm =

21. ( ) _____ 60 min 1 h 378,432 s ( ) ( ) ____ 60 s 3.78 x 105 s ____ 24 h 1 min 1 d How many seconds is 4.38 days? ? s = 4.38 d = accounting for significant figures, change this to…

22. Learning Check • An object has a mass of 0. 125kg. How many grams is this? 1kg= 1000g 0.125 kg 1000g 1kg = 125g How many km are in 5.78x108 mm? 1km = 1x106 mm 5.78x10 8mm 1km 1x106 mm = 578 km

23. 0 Conversion Factors (units with a power) • Convert Cubic Inches (in3) into Cubic Centimeters (cm3) • Find Relationship : 1 in = 2.54 cm • Plan a solution in3 cm3 Change Relationship into Conversion Factors with Starting Units on the Bottom

24. Write down the given quantity and its units. Given: 2,659 cm2 Write down the quantity to find and/or its units. Find: ? M2 Collect Needed Conversion Factors: 1 00cm = 1m 0 Example:A circle has an area of 2,659 cm2. What is the area in square meters?

25. Write a Solution Map for converting the units : Information Given: 2,659 cm2 Find: ? m2 Conv. Fact.: 100 cm = 1 m 0 Example:A circle has an area of 2,659 cm2. What is the area in square meters? cm2 m2

26. Apply the Solution Map: Information Given: 2,659 cm2 Find: ? m2 Conv. Fact. 1 cm = 0.01 m Sol’n Map: cm2 m2 0 Example:A circle has an area of 2,659 cm2. What is the area in square meters? = 0.2659 m2 • Sig. Figs. & Round: = 0.2659 m2 The units of the answer, m2, are correct. The magnitude of the answer makes sense since square centimeters are smaller than square meters.

27. Classwork dimensional analysis handout

28. 0 Density Relation of Mass & Volume • two main characteristics of matter • cannot be used to identify what type of matter something is • if you are given a large glass containing 100 g of a clear, colorless liquid and a small glass containing 25 g of a clear, colorless liquid - are both liquids the same stuff? • even though mass and volume are individual properties - for a given type of matter they are related to each other!

29. 0 Density • Ratio of mass:volume • Solids = g/cm3 • 1 cm3 = 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!

30. 0 Density • For equal volumes, denser object has larger mass • For equal masses, denser object has smaller volume • Heating objects causes objects to expand • does not effect their mass!! • How would heating an object effect its density? • In a heterogeneous mixture, the denser object sinks • Why do hot air balloons rise?

31. 0 Platinum has become a popular metal for fine jewelry. A man gives a woman an engagement ring and tells her that it is made of platinum. Noting that the ring felt a little light, the woman decides to perform a test to determine the ring’s density before giving him an answer about marriage. She places the ring on a balance and finds it has a mass of 5.84 grams. She then finds that the ring displaces 0.556 cm3 of water. Is the ring made of platinum? (Density Pt = 21.4 g/cm3)

32. 0 She places the ring on a balance and finds it has a mass of 5.84 grams. She then finds that the ring displaces 0.556 cm3 of water. Is the ring made of platinum? (Density Pt = 21.4 g/cm3) Given: Mass = 5.84 grams Volume = 0.556 cm3 Since 10.5 g/cm3 21.4 g/cm3 the ring cannot be platinum

33. 11.3 g Pb 1 cm3 Pb x = 4.0 cm3 Pb 45 g Pb 0 Density as a Conversion Factor • can use density as a conversion factor between mass and volume!! • density of H2O = 1 g/mL \ 1 g H2O = 1 mL H2O • density of Pb = 11.3 g/cm3\ 11.3 g Pb = 1 cm3 Pb • How much does 4.0 cm3 of Lead weigh?

34. 0 Measurement and Problem SolvingDensity as a Conversion Factor • The gasoline in an automobile gas tank has a mass of 60.0 kg and a density of 0.752 g/cm3. What is the volume? • Given: 60.0 kg • Find: Volume in L • Conversion Factors: • 0.752 grams/cm3 • 1000 grams = 1 kg

35. 0 Measurement and Problem SolvingDensity as a Conversion Factor • Solution Map: kg  g  cm3

36. Classwork: Density handout