Units and Measurement

Chemistry

Science 3rdESO

A) SI Units, Scientific Notation, Measurement, Accuracy, Precision,

Error

Math and UnitsMath- the language of ScienceSI Units – International System

MKSMeter mMass kgTime s

National Bureau of StandardsPrefixes

SI Unit PrefixesName Symbol

giga- G 109

mega- M 106

kilo- k 103

deci- d 10-1

centi- c 10-2

milli- m 10-3

micro- μ 10-6

nano- n 10-9

pico- p 10-12

Length

Metric Units

The basic unit of length in the metric system in the meter and is represented by a lowercase m.

Standard: The distance traveled by light in absolute vacuum in 1⁄299.792.458 of a second.

Metric Units

1 Kilometer (km) = 1000 meters

1 Meter = 100 Centimeters (cm)

1 Meter = 1000 Millimeters (mm)

Which is larger?

A. 1 meter or 105 centimeters

B. 4 kilometers or 4400 meters

C. 12 centimeters or 102 millimeters

D. 1200 millimeters or 1 meter

Click the image to watch a short video

about the meter.

Measuring Length

Ruler: http://www.k12math.com/math-concepts/measurement/ruler-cm.jpg

How many millimeters are in 1 centimeter?

What is the length of the line in centimeters? _______cm

What is the length of the line in millimeters? _______mm

What is the length of the line to the nearest centimeter? ________cm

HINT: Round to the nearest centimeter – no decimals.

1 centimeter = 10 millimeters

Measuring Tapes:Long distance (up to 1metre) are available in closed and open reel configurations.  The open reel is good for outside or dirty environments. Calibrations are in centimetres or in millimetres.

Straight Rules:Straight rules available in a large variety of materials, scales and graduations.  Lengths typically don't exceed 1m. It is used to

measure in centimetres of length.

Calliper ruleA variation to the more traditional caliper is the inclusion of a vernier scale; this makes it possible to directly obtain a more precise measurement.

Vernier calipers can measure internal dimensions (using the uppermost jaws in the picture at right), external dimensions using the pictured lower jaws, and depending on the manufacturer, depth measurements by the use of a probe that is attached to the movable head and slides along the centre of the body. The vernier scales may include both metric and inch measurements on the upper and lower part of the scale.Vernier calipers commonly used in industry provide a precision to a hundredth of a millimetre (10 micrometres), or one thousandth of an inch.

Measuring Instruments

Mass

Metric UnitsMass refers to the amount of matter in an object.

The base unit of mass in the metric system in the kilogram and is represented by kg.

Standard: 1 kilogram is equal to the mass of the International Prototype Kilogram (IPK), a platinum-iridium cylinder kept by the BIPM at Sèvres, France.

Metric Units

1 Kilogram (kg) = 1000 Grams (g)

1 Gram (g) = 1000 Milligrams (mg)

Which is larger?

A. 1 kilogram or 1500 grams

B. 1200 milligrams or 1 gram

C. 12 milligrams or 12 kilograms

D. 4 kilograms or 4500 grams

Click the image to watch a short video

about mass.

Kilogram Prototype

Measuring Mass

We will be using triple-beam balances to find the mass of various objects.

The objects are placed on the scale and then you move the weights on the beams until you get the lines on the right-side of the scale to match up.

Once you have balanced the scale, you add up the amounts on each beam to find the total mass.

What would be the mass of the object measured in the picture?

_______ + ______ + _______ = ________ g

Measuring Mass – Triple-Beam Balance

Click here to try an online activity.

1st – Place the film canister on the scale.2nd – Slide the large weight to the right until the arm drops below the line. Move the rider back one groove. Make sure it “locks” into place.

3rd – Repeat this process with the top weight. When the arm moves below the line, back it up one groove.

4th – Slide the small weight on the front beam until the lines match up.

5th – Add the amounts on each beam to find the total mass to the nearest tenth of a gram.

Volume

Metric Units

Volume is the amount of space an object takes up.

The base unit of volume in the metric system in the liter and is represented by L or l.

Standard: 1 liter is equal to one cubic decimeter Metric Units

1 liter (L) = 1000 milliliters (mL)

1 milliliter (mL) = 1 cm3 (or cc) = 1 gram*

Which is larger?

A. 1 liter or 1500 milliliters

B. 200 milliliters or 1.2 liters

C. 12 cm3 or 1.2 milliliters*

Click the image to watch a short video

about volume.

Measuring Instruments

Differentiate volume-capacity

Volume and capacity are sometimes distinguished, with capacity being used for how much a container can hold (with contents measured commonly in litres or its derived units), and volume being how much space an object displaces (commonly measured in cubic metres or its derived units).

Measuring Volume

We will be using graduated cylinders to find the volume of liquids and other objects.

Read the measurement based on the bottom of the meniscus or curve. When using a real cylinder, make sure you are eye-level with the level of the water.

What is the volume of water in the cylinder? _____ml

What causes the meniscus?

A concave meniscus occurs when the molecules of the liquid attract those of the container. The glass attracts the water on the sides.

Parallax error

If you are measuring the volume of liquid in a measuring cylinder for example, make sure you positioned your eye to take readings at the bottom of menicus for water and top of menicus for mercury.

Parallax is a deceptive change of the position of an object which is observed while the position of the observer changes. Position of eye at all volumetric vessels must be at the same level as the meniscus. If not, the parallax will cause an error while reading the position of the meniscus of a liquid in a burette. It will be a positive mistake if the eye is lower, and negative if the eye is higher than the meniscus plane.

Parallax Error

Measuring Liquid Volume

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Pay attention to the scales for each cylinder.

Measuring Solid Volume

Click here for an online activity about volume. Choose Lessons Volume & Displacement

10 cm

9 cm

8 cm

We can measure the volume of regular object using the formula length x width x

height.

_____ X _____ X _____ = _____

We can measure the volume of irregular object using water

displacement.

Amount of H2O with object = ______

About of H2O without object = ______

Difference = Volume = ______

Scientific Notation

M x 10n

M is the coefficient 1<M<1010 is the basen is the exponent or power of 10

Other Examples:

5,45E+6

5,45 x 10^6

Numbers less than 1 will have a negative exponent.

A millionth of a second is:

0,000001 sec 1x10-6

1,0E-6 1,0x10^-6

Limits of Measurement

Accuracy and Precision

Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.

Example: AccuracyWho is more accurate when

measuring a book that has a true length of 17,0cm?

Susan: 17,0cm; 16,0cm; 18,0cm; 15,0cm

Amy: 15,5cm; 15,0cm; 15,2cm; 15,3cm

Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.

Example: Precision

Who is more precise when measuring the same 17,0cm book?

Susan: 17,0cm; 16,0cm; 18,0cm; 15,0cm

Amy: 15,5cm; 15,0cm; 15,2cm; 15,3cm

Example: Evaluate whether the following are precise, accurate or both.

Accurate

Not Precise

Not Accurate

Precise

Accurate

Precise

Accurancy

Absolute error Relative error

Precision= Significant Figures

Absolute ErrorError= experimental –accepted value

It is the amount of physical error in a measurement. It uses the same units than the measurement.

Relative error (Percent Error)% Error= |experimental –accepted| x100

accepted value

(value of thing measured)

Relative error gives an indication of how good a measurement is relative to the thing being measured.

If a have two students measuring two objects with a metre stick the comparative accurancy of these measurements can be determined by looking at their relative error.

Absolute- relative errorStudents measured time in an experiment. These measurements are: 3,01 s; 3,11 s; 3,20 s;

3,15 s True value? (Valor que se considera exacto)

Absolute and relative error for each measurement?

Measurement Absolute Error Relative Error

3,01 s 3,01 - 3,12 = - 0,11 s -0,11 / 3,12 = - 0,036    (- 3,6%)

3,11 s 3,11 -3,12 = - 0,01 s -0,01 / 3,12 = - 0,003    (- 0,3%)

3,20 s 3,20 -3,12 = + 0,08 s +0,08 / 3,12 = + 0,026    (+ 2,6%)

3,15 s 3,15 - 3,12 = + 0,03 s +0,03 / 3,12 = + 0,010    (+ 1,0%)

B) Significant Figures= Precision

Significant Figures= Precision

The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated.

Centimeters and Millimeters

Graduated Cylinder - Meniscus

B) International System of Unitsand

Prefixes

Base SI Units

Quantity Unit Symbol

Length meter m

Mass kilogram kg

Temperature kelvin K

Time second s

Amount of Substance

mole mol

Luminous Intensity candela cd

Electric Current ampere a

Derived SI Units (examples)Quantity unit Symbol

Volume cubic meter m3

Density kilograms per cubic meter

kg/m3

Speed meter per second m/s

Newton kg m/ s2 N

Energy Joule (kg m2/s2) J

Pressure Pascal (kg/(ms2) Pa

Units for Volume

m3

cm3

dm3

L Liter

mL

1 dm3 = 1L

1cm3= 1mL

Temperature

A measure of how hot or how cold an object is.

SI Unit: the kelvin ( K )

Note: not a degree Absolute Zero= 0 K

Temperature Scales

Celsius and Kelvin

K= oC + 273

Farenheit and Celsius

oF= (1,8 oC ) +32

Unit for Weight

1 Newton

1 N= kg m/s2

Units for Energy Joule J

calorie 1 cal= 4,184 J

1 cal = quantity of heat needed to raise the temp of 1g of water by 1 oC.

Note:

1 Cal = 1kcal =1000cal

SI Unit PrefixesName Symbol

giga- G 109

mega- M 106

kilo- k 103

deci- d 10-1

centi- c 10-2

milli- m 10-3

micro- μ 10-6

nano- n 10-9

pico- p 10-12

SI Unit Prefixes for LengthName Symbol Analogy

gigameter Gm 109

megameter Mm 106

kilometer km 103

decimeter dm 10-1

centimeter cm 10-2

millimeter mm 10-3

micrometer μm 10-6

nanometer nm 10-9

picometer pm 10-12

C) Factor Label Method of Unit Conversion- Dimensional Analysis

Factor-Label Method

Example: Convert 5km to m:

NEW UNIT

5km x 1000m =5000m

km

OLD UNIT

Convert 7000m to km

7000m x 1 km = 7 km

1000m

Convert 2,45cs to s

2,45cs x 1 s = 0,0245s

100cs

Convert 55,00 km/h to m/s

55,00 km x 1000 m x 1 h___ = 15,28m/s

h 1 km 3600 s