Unit 2. Measurement

Do Now  In your own words, what do you think is the difference between:  Accuracy and Precision?

A. Accuracy vs. Precision  Accuracy - how close a measurement is to the accepted value  Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT

ACCURATE = CORRECT PRECISE = CONSISTENT

 B. Percent Error  The accuracy of an individual value can be compared with the correct or accepted value by calculating the percent error.  Percent error is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100.

B. Percent Error  Indicates accuracy of a measurement your value accepted value

B. Percent Error  A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.90 %

 Describe the difference between a qualitative and a quantitative measurement.  Describe the difference between accuracy and precision.  Write a number in scientific notation.  State the appropriate units for measuring length, volume, mass, density, temperature and time in the metric system..  Calculate the percent error in a measurement.  Calculate density given the mass and volume, the mass given the density and volume, and the volume given the density and mass. Objectives:

 Chapter 2  Section 1  Scientific Method

 Scientific Method is a logical approach to solving problems by observing and collecting data, formulating hypotheses, testing hypotheses and formulating theories that are supported by data.  Observations Hypothesis Experimentation Theory

Observations Collecting data Measuring Communicating with other scientists

Measurements  Measurements are divided into two sets:  Qualitative – a descriptive measurement. Color, hardness, shininess, physical state. (non-numerical)  Quantitative – a numerical measurement. Mass in grams, volume in milliliters, length in meters.

Hypothesis  A tentative explanation that is consistent with the observations (educated guess).  An experiment is then designed to test the hypothesis.  Predict the outcome from the experiments

Theory  Attempts to explain why something happens.  Has experimental evidence to support the hypothesis.  Observations, data and facts.

Classwork  What is the scientific theory?  What is the difference between qualitative and quantitative measurements?  Which of the following are quantitative? a. The liquid floats on water? b. The metal is malleable? c. A liquid has a temperature of 55.6 o C?  How do hypothesis and theories differ?

Units of Measurement

 Measurements represent quantities.  A quantity is something that has magnitude, size or amount.  All measurements are a number plus a unit (grams, teaspoon, liters).

A. Number vs. Quantity  Quantity - number + unit UNITS MATTER!!

B. SI Units QuantityBase Unit Abbrev. Length Mass Time Temp meter kilogram second kelvin m kg s K Amountmolemol Symbo l l m t T n

B. SI Units mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro-  nano-n10 -9 pico-p kilo-k10 3 BASE UNIT

SI Prefix Conversions 1) 20 cm = ______________ m 2) L = ______________ mL 3) 45  m = ______________ m

Derived SI Units  Many SI units are combinations of the quantities shown earlier.  Combinations of SI units form derived units.  Derived units are produced by multiplying or dividing standard units.

C. Derived Units cont…  Combination of base units.  Volume (m 3 or cm 3 )  length  length  length D = MVMV 1 cm 3 = 1 mL 1 dm 3 = 1 L  Density  (kg/m 3 or g/mL or g/cm 3 )  mass per volume

Volume  Volume (m 3 ) is the amount of space occupied by an object.  length x width x height  Also expressed as cubic centimeter (cm 3 ).  When measuring volumes in the laboratory a chemist typically uses milliliters (mL).  1 mL =1 dm 3 = 1 cm 3

Density  Density is a characteristic physical property of a substance.  It does not depend on the size of the sample.  As the sample’s mass increases, its volume increases proportionally.  The ratio of mass to volume is constant.

Density…  Calculating density is pretty straight forward  You need the measure Mass and Volume  Mass- Obtain by weighing the mass of an object by using a balance and then determine the volume.

Volume  Solids - the volume can be a little difficult.  If the object is a regular solid, like a cube, you can measure its three dimensions and calculate the volume.  Volume = length x width x height

Volume Cont…. If the object is an irregular solid, like a rock, determining the volume is more difficult. Archimedes’ Principle – states that the volume of a solid is equal to the volume of water it displaces. Put some water in a graduated cylinder and read the volume. Next, put the object in the graduated cylinder and read the volume again. The difference in volume of the graduated cylinder is the volume of the object.

Volume Displacement A solid displaces a matching volume of water when the solid is placed in water. 35mL 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/cm 3 3) 252 g/cm 3

PROBLEM: Mercury (Hg) has a density of 13.6 g/cm 3. What is the mass of 95 mL of Hg in grams?

PROBLEM: Mercury (Hg) has a density of 13.6 g/cm 3. What is the mass of 95 mL of Hg?  First, note that 1 cm 3 = 1 mL Strategy Use density to calc. mass (g) from volume.  Density = Mass Volume

PROBLEM: Mercury (Hg) has a density of 13.6 g/cm 3. What is the mass of 95 mL of Hg?  Density = Mass Volume 13.6g/cmMass (g) = 95 mL 3

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

Solution Placing the mass and volume of the osmium metal into the density setup, we obtain D = mass = g = volume2.22 cm 3 = g/cm 3 = 22.5 g/cm 3

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 The density of octane, a component of gasoline, is g/mL. What is the mass, in kg, of 875 mL of octane? 1) kg

D. Density Mass (g) Volume (cm 3 )

Problem-Solving Steps 1. Analyze 2. Plan 3. Compute 4. Evaluate

D. Density  An object has a volume of 825 cm 3 and a density of 13.6 g/cm 3. Find its mass. GIVEN: V = 825 cm 3 D = 13.6 g/cm 3 M = ? WORK :

D. Density  An object has a volume of 825 cm 3 and a density of 13.6 g/cm 3. Find its mass. GIVEN: V = 825 cm 3 D = 13.6 g/cm 3 M = ? WORK : M = DV M = (13.6 g/cm 3 )(825cm 3 ) M = 11,200 g

D. Density  A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g WORK :

D. Density  A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g WORK : V = M D V = 25 g 0.87 g/mL V = 29 mL

III. Unit Conversions

A. SI Prefix Conversions 1.Find the difference between the exponents of the two prefixes. 2.Move the decimal that many places. To the left or right?

A. SI Prefix Conversions mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro-  nano-n10 -9 pico-p kilo-k10 3 move left move right BASE UNIT

A. SI Prefix Conversions 1) 20 cm = ______________ m 2) L = _____________ mL 3) 45  m = ______________ nm 4) 805 dm = ______________ km

C. Johannesson A. SI Prefix Conversions 1) 20 cm = ______________ m 2) L = ______________ mL 3) 45  m = ______________ nm 4) 805 dm = ______________ km ,000 32

Conversion Factors  Conversion factor – a ratio derived from the equality between two different units that can be used to convert from one unit to the other.  Example: the conversion between quarters and dollars:  4 quarters 1 dollar  1 dollar or 4 quarters

Conversion Factors  Example:  Determine the number of quarters in 12 dollars?  Number of quarters = 12 dollars x conversion factor  ? Quarters = 12 dollars x 4 quarters = 48 quarters 1 dollar

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

B. Dimensional Analysis  The “Factor-Label” Method  Units, or “labels” are canceled, or “factored” out to make your calculations easiers

B. Dimensional Analysis  Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

Learning Check 1) A rattlesnake is 2.44 m long. How long is the snake in cm? a) 2440 cm b)244 cm c)24.4 cm 2.44 m x 100 cm = 244 cm (b) 1 m

B. Dimensional Analysis 2) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? 8.0 cm1 in 2.54 cm = 3.2 in cmin

B. Dimensional Analysis 3) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire? 1.3 m 100 cm 1 m = 86 pieces cmpieces 1 piece 1.5 cm

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