Unit 1 Math & Measurement - Mr Palermo

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UNIT 1 MATH AND MEASUREMENT

MR. PALERMO

LESSON 1: METRIC CONVERSIONS

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OBJECTIVE: BY THE END OF THIS VIDEO

YOU WILL BE ABLE TO:

ü  Identify base units of measurement. ü Convert between units of

measurement.

WHAT IS CHEMISTRY?

•  The study of Matter and the changes it undergoes…..

•  What is Matter? -  Matter is anything that has mass and

takes up space.

MATTER CAN BE DESCRIBED AS:

•  Qualitative measurements: descriptive, non-numerical observations

•  Quantitative Measurements: are in the

form of NUMBERS and UNITS.

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QUANTITATIVE MEASUREMENTS:

•  The METRIC SYSTEM (SI): System of measurement used in science and in most countries

•  The BASE UNITS of measurement: (Found on Reference Table D)

TABLE D (BASE UNITS)

PREFIXES:

•  Used to modify base units of measurement. (Found on Reference Table C)

Example: gram (g)

CHECK YOUR UNDERSTANDING:

ü Can you identify the base unit of measurement?

CONVERTING UNITS USING TABLE C

1. Find the difference between the exponents of the two prefixes on Table C.

2. Move the decimal that many places.

To the left or right?

WHERE ARE THE BASE UNITS?

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TRICK: TURN THE TABLE ON ITS SIDE

EXAMPLE 1: CONVERT 5.2 CM = ____ MM

•  The difference between the two factors (-‐2 and -‐3) is 1.

•  Since you are moving from a larger prefix to a smaller prefix you move the decimal one place to the right.

EXAMPLE 2: CONVERT 45.5 MM = ____ M

•  The difference between the two factors (-‐3 and 0) is 3.

•  Since you are moving from a smaller prefix to a larger prefix you move the decimal three places to the leH.

EXAMPLE 3

Convert the following: 20 cm = ____________ m


ü Can you convert between units of measurement?

YOU SHOULD BE ABLE TO:

ü  Identify base units of measurement. ü Convert between units of

measurement.

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LESSON 2: DENSITY

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ü Determine the volume of a substance ü Calculate density/mass/volume

QUANTITATIVE CALCULATIONS:

•  Mass: the amount of matter an object contains. (This is different than weight, which is mass plus gravity)

•  Volume: The amount of space a substance occupies

HOW DO WE MEASURE MASS IN THE LAB?

•  Electronic Balance

HOW CAN WE MEASURE VOLUME?

•  l x w x h (regular solid) -  ex. V = 1cm3

•  Graduated cylinder (liquids) -  Read bottom of MENISCUS -  ex. V = 27.5 mL

READING A MENISCUS

10

8

6

line of sight too high

reading too low

reading too high

line of sight too low proper line of sight

reading correct

graduated cylinder

10 mL

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MEASURING VOLUME: IRREGULAR SOLID

Water displacement method

1. Measure initial volume

2.  Measure final volume with object

3.  The Difference is the volume of the object

EXAMPLE: WHAT IS THE VOLUME OF THE SOLID?


ü Can you Determine the volume of a substance?

DENSITY

•  Ratio of mass of an object to its volume

•  Use density formula •  Located on Table T

VMD =

EXAMPLE 1

What is the density of an object with a mass of 60 g and a volume of 2 cm3?

VMD =


ü Can you calculate density/mass/volume

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EXAMPLE 2

An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.

VMD =



HOW TO SOLVE FOR MASS OR VOLUME IF DENSITY IS NOT GIVEN:

USE TABLE S Example: The volume of an aluminum sample is 251 cm3. What is the mass of the sample?

The density of aluminum on table S is 2.70g/cm3




•  Determine the volume of a substance •  Calculate density/mass/volume

LESSON 3: TEMPERATURE

CONVERSIONS WWW.MRPALERMO.COM

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ü Differentiate between Kelvin and Celsius Scales

ü Convert between Celsius and Kelvin temperature

TEMPERATURE:

•  Measure of average kinetic Energy

TEMPERATURE SCALES CELSIUS SCALE

•  Freezing point of water at 0°C. •  Boiling for water at 100°C. •  Below 0 is NEGATIVE.

KELVIN SCALE

•  Water freezes at 273K and boils at 373K •  Theoretical point of ABSOLUTE ZERO is when

all molecular motion stops

•  NO NEGATIVE NUMBERS

•  Divisions (degrees) are the same as in Celsius

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ü Can you differentiate between Kelvin and Celsius Scales

CONVERTING BETWEEN TEMPERATURE SCALES

•  Formula: K = °C + 273 •  Located on Table T

EXAMPLE 1:

What is the temperature in Kelvin of an object that is 55°C ?

EXAMPLE 2:

What is the temperature in Celsius of an object that is 150 K?


ü Can you convert between Celsius and Kelvin temperature

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ü Differentiate between Kelvin and Celsius Scales

ü Convert between Celsius and Kelvin temperature

LESSON 4: PERCENT ERROR

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ü Differentiate between accuracy and precision

ü Calculate percent error

OBJECTIVE: BY THE END OF THIS VIDEO YOU WILL BE ABLE TO: ACCURACY VS. PRECISION

•  Accuracy - how close a measurement is to the accepted or true value

•  Precision - how close a series of measurements are to each other

EXAMPLE EXAMPLE:

Student A (g/cm3)

Student B (g/cm3)

Student C (g/cm3)

Trial 1 1.54 1.40 1.70

Trial 2 1.60 1.68 1.69

Trial 3 1.57 1.45 1.71

Avg. 1.57 1.51 1.70

Range 0.06 0.28 0.02

These students were asked to determine the density of sucrose. Sucrose has a density of 1.59 g/cm3. Which student is more accurate?

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ü Can you differentiate between accuracy and precision


PERCENT ERROR

•  Measurement of ACCURACY -  the % that the measured value is “off”

from accepted value

•  Measured value = value you “get” •  Accepted value = value you “should

get”

Formula is found on Table in your Reference Table:

•  If answer is negative, your measured value is LESS THAN the accepted value

•  If answer is positive, your measured value is GREATER THAN the accepted value

EXAMPLE

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.


ü Can you calculate percent error


ü Differentiate between accuracy and precision

ü Calculate percent error

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LESSON 5: PRECISION & SIGNIFICANT FIGURES

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ü  Identify the precision of a measuring device

ü  Identify the amount of significant figures in a number

OBJECTIVE: BY THE END OF THIS VIDEO YOU WILL BE ABLE TO:

SIGNIFICANT FIGURES

•  Indicate PRECISION of a measurement.

•  Recording Sig Figs -  Sig figs in a measurement include the known

digits plus a final estimated digit (precision of instrument)

2.38 cm

EXAMPLE MEASURING LENGTH:

•  We know for sure that the object is

more than ____, but less than ____ •  We know for sure that the object is

more than ____, but less than ____ •  This ruler allows us to estimate the

length to ______

2 RUNNERS FINISH THE RACE IN 8 SECONDS. WHO WON?

1

2

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Runner 1

Runner 2

EXAMPLE: WHAT IS THE LENGTH OF THE RED LINE?

cm 0 1 2 3 4 5

ü Can you identify the precision of a measuring device

CHECK YOUR UNDERSTANDING: RULES FOR COUNTING SIG FIGS

1. All non-‐zero digits are significant. 2. Leading zeros are never significant.

ex. 0.421 (3 sig figs) 3. All capTve zeros are significant. (Cap+ve is a zero between 2 other non-‐zero digits.) ex. 4012 (4 sig figs) 4. For Trailing zeros: (zeros aHer last non-‐zero digit)

-‐ Decimal point → significant -‐No decimal point → not significant

ex. 114.20 (5 sig figs) ex. 11,420 (4 sig figs)

HOW TO COUNT SIG FIGS

1.  Start counTng from LEFT to RIGHT at first NONZERO number.

2.  If decimal point is present then count any trailing zeros

3.  If decimal is not present don’t count trailing zeros

EXAMPLE

1) 2545.300 g (7 sig figs) 2) 4530 km (3 sig figs) 3) 0.00453 m (3 sig figs)

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ü Can you identify the amount of sig figs in a number

ü  Identify the precision of a measuring device

ü  Identify the amount of significant figures in a number


LESSON 6: ROUNDING SIG

FIGS IN CALCULATIONS WWW.MRPALERMO.COM

ü  Round answers to proper sig figs in calculations


WHAT DO I ROUND MY ANSWER TO?

•  Every measurement has some error in it. When performing calculations AN ANSWER CAN NEVER BE MORE PRECISE THAN YOUR LEAST PRECISE MEASUREMENT

ROUNDING: SIG FIG IN CALCULATIONS

•  MulTply/Divide -‐ Round answer to the least number of significant figures.

Example:

(13.91g/cm3)(23.3cm3) = 324.103g

324 g

4 SF 3 SF 3 SF

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ü Can you round answers to proper sig figs in calculations

CALCULATING SIG FIGS (CON’T)

•  Add/Subtract – Round to the least place value Example:

3.75 mL + 4.1 mL 7.85 mL

224 g + 130 g 354 g → 7.9 mL → 350 g

3.75 mL + 4.1 mL 7.85 mL

224 g + 130 g 354 g

ü  Round answers to proper sig figs in calculations


LESSON 7: SCIENTIFIC

NOTATION WWW.MRPALERMO.COM

ü Convert numbers into scientific notation and standard notation

ü Calculate mathematical operations using scientific notation


SCIENTIFIC NOTATION

•  A way to represent large or small numbers

For example: •  The mass of a hydrogen atom is

0.00000000000000000000000167g. •  2 g of H2 contains

602,000,000,000,000,000,000,000 molecules.

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SCIENTIFIC NOTATION IS WRITTEN AS:

• The product of two numbers: a coefficient and a 10 raised to a power. • The coefficient (number written first) is always a number from 1 to 9 Example: 1.67 x 10-24 g 2 g of H2 is composed of 6.02 x 1023

molecules.

CONVERTING FROM EXPANDED FORM INTO SCIENTIFIC NOTATION

1.  For #’s greater than 1 move decimal to the LEFT until there’s 1 digit to its left. The number of places moved = exponent number

Example: 45,450 g =

2. For #’s less than 1 move decimal to RIGHT stopping after the first non zero number. The number of places moved = negative exponent number

Example: 0.00453 ml = 4.53 x 10-3 ml

ü Can you convert numbers into scientific notation and standard notation


CONVERTING FROM SCIENTIFIC NOTATION TO STANDARD NOTATION

1.  Move the decimal place the number of times indicated by the exponent.

2.  To the right if it is positive. 3.  To the left if it is negative. Example:

4.5 x 10-2 = 0.045

ü Can you convert numbers into scientific notation and standard notation


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CALCULATING WITH SCI NOTATION USING A CALCULATOR

Ex. (5.44 × 107 g) ÷ (8.10 × 104 mol) =

5.44 EXP

EE ÷

EXP

EE ENTER

EXE 7 8.10 4

= 671.60493 = 672 g/mol = 6.72 × 102 g/mol

Type on your calculator:


ü Can you calculate mathematical operations using scientific notation

ü Convert numbers into scientific notation and standard notation

ü Calculate mathematical operations using scientific notation


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Unit 1 Math & Measurement - Mr Palermo