Measurements in Chemistry

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 QuantityUnitSymbol Length (L)meterm Mass (m)kilogramkg Time (t)seconds Temperature (T)kelvinK Mole (mol)Molemol

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.

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 = pounds 1 kg = 1000 g 1 g = 1000 mg

Volume (V) Measure of the amount of space occupied SI unit = cubic meter (m 3 ) a Derived Unit Commonly measure solid volume in cubic centimeters (cm 3 ) 1 m 3 = 1x10 6 cm 3 Commonly measure liquid or gas volume in milliliters (mL) 1 L = 1000 mL 1L=1 dm 3 1 mL = 1 cm 3 Volume for geometric figures: Rectangle: V =Length x width x height Cylinder : V=  r 2 h h: height r: radius

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

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)

Greek Prefixes SI System Table PrefixSymbol Decimal Equivalent Power of 10 Giga-G1000,000,0001 x 10 9 mega-M1,000,0001 x 10 6 kilo-k 1,0001 x 10 3 BASE UNIT (Ex. m, g) deci-d 0.11 x centi-c x milli-m x micro-  x nano-n x 10 -9

Writing relationships between units. Write down the relationship between meters,m (base unit) and kilometers, km. 1. Km are greater than m 2. 1km = 3. 1km= 1000 m

Relationship between mL and cL? 1. cL is greater than mL 2. 1cL= 3. 1cL = 10mL Relationship between  m and dm. 1. dm is greater than  m 2. 1dm= 3. 1dm =  m

Learning Check Write relationships between the following units: 1. mm and km 2. Mg and dg 3. ks and ms

Learning Check Write relationships between the following units: 1. mm and km 1km = 1,000,000 mm 2. Mg and dg 1 Mg= 10,000,000 dg 3. ks and ms 1ks = 1,000, 000 ms

Cw Metric units conversions

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 = cm 2 cm + cm = cm cm ÷ cm = 1 using units as a guide to problem solving is called dimensional analysis

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

Using Dimensional Analysis 1) Write down Given Amount and Unit 2) Write down what you want to Find and Unit 3) Write down needed Conversion Factors or Equations a) Write down equivalence statements for each relationship b) Change equivalence statements to Conversion Factors

Dimensional Analysis 4) Plan a Solution for the Problem order conversions to cancel previous units or arrange Equation to solve for the variable wanted 5) Apply the Steps in the Plan check that units cancel properly multiply terms across the top and divide by each bottom term 6) Check the Answer to see if its Reasonable correct size and unit

Ex. 1 How many cm are in 1.32 meters? applicable conversion factors: equality: or ? cm = 1.32 m= 1 m = 100 cm ______1 m 100 cm We use the idea of unit cancellation to decide upon which one of the two conversion factors we choose. ______ 1 m 100 cm () ______ 1 m 100 cm 132 cm

Ex. 2 How many meters is 8.72 cm? applicable conversion factors: equality: or ? m = 8.72 cm= 1 m = 100 cm ______1 m 100 cm Again, the units must cancel. ______ 1 m 100 cm () ______ m 1 m 100 cm

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

How many seconds is 4.38 days? = 1 h 60 min24 h 1 d1 min 60 s ____ ()() () _____ ? s = 4.38 d 378,432 s3.78 x 10 5 s accounting for significant figures, change this to…

Learning Check a) An object has a mass of kg. How many grams is this? 1kg= 1000g kg 1000g 1kg = 125g 1km = 1x10 6 mm 5.78x10 8 mm 1km 1x10 6 mm = 578 km b)How many km are in 5.78x10 8 mm?

Conversion Factors (units with a power) Convert Cubic Inches (in 3 ) into Cubic Centimeters (cm 3 ) 1) Find Relationship : 1 in = 2.54 cm 2) Plan a solution in 3 cm 3 3)Change Relationship into Conversion Factors with Starting Units on the Bottom

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

Write a Solution Map for converting the units : cm 2 m2m2 Information Given:2,659 cm 2 Find:? m 2 Conv. Fact.:100 cm = 1 m Example: A circle has an area of 2,659 cm 2. What is the area in square meters?

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

Classwork dimensional analysis handout

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!

Density Ratio of mass:volume 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 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?

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 cm 3 of water. Is the ring made of platinum? (Density Pt = 21.4 g/cm 3 )

She places the ring on a balance and finds it has a mass of 5.84 grams. She then finds that the ring displaces cm 3 of water. Is the ring made of platinum? (Density Pt = 21.4 g/cm 3 ) Given: Mass = 5.84 grams Volume = cm 3 Since 10.5 g/cm 3  21.4 g/cm 3 the ring cannot be platinum

Density as a Conversion Factor can use density as a conversion factor between mass and volume!! density of H 2 O = 1 g/mL  1 g H 2 O = 1 mL H 2 O density of Pb = 11.3 g/cm 3  11.3 g Pb = 1 cm 3 Pb How much does 4.0 cm 3 of Lead weigh? = 4.0 cm 3 Pb 11.3 g Pb 1 cm 3 Pb 45 g Pb x

Measurement and Problem Solving Density as a Conversion Factor The gasoline in an automobile gas tank has a mass of 60.0 kg and a density of g/cm 3. What is the volume? Given: 60.0 kg Find: Volume in L Conversion Factors: grams/cm grams = 1 kg

Measurement and Problem Solving Density as a Conversion Factor Solution Map: kg  g  cm 3

Classwork: Density handout