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Unit 7 Measurements in Chemistry
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
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.
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
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
Temperature • SI base unit: Kelvin (K) • Lowest temperature is 0 K • Celsius (C) • Fahrenheit (F) • K= C + 273 • F = (1.8xC) + 32
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)
0 Greek Prefixes SI System Table
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
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 = 100000m
Learning Check • Write relationships between the following units: • mm and km • Mg and dg • ks and ms
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
Cw • Metric units conversions
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
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
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
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
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.
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.
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 =
( ) _____ 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…
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
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
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?
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
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.
Classwork dimensional analysis handout
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!
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!
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?
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)
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
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?
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
0 Measurement and Problem SolvingDensity as a Conversion Factor • Solution Map: kg g cm3