Unit 1 Math and Measurement

Mr. Palermo

LESSON 1:

Metric Conversions

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.

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)

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?

Move the decimal to the:

LEFT when going from a smaller prefix to

a larger prefix

RIGHT when going from a larger prefix to

a smaller prefix 52.010

52.010

Where are the base units?

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 left.

Example 3

Convert the following:

20 cm = _________________ m

LESSON 2:

Density

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

proper line of sight reading correct

graduated

cylinder

10 mL

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?

Density

Ratio of mass of an object to its volume

Use density formula

Located on Table T

V

MD

Example 1

What is the density of an object with a

mass of 60 g and a volume of 2 cm3?

V

MD

Example 2

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

V

MD

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

LESSON 3:

Temperature Conversions

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

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?

LESSON 4:

Percent Error

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?

STOP AND THINK

Which student is more precise in the

previous 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

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.

Stop and Think

What is the percent error if a student measures an object to be 56.2 cm and the actual length is 56.9 cm?

Stop and Think

In a lab experiment, you are told by your teacher that the actual amount of sugar in a can of Coke is 39 g. You experimentally determine it to be 37 g based on your own data and calculations. What is your percent error?

LESSON 5:

Precision & Sig Figs

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 3

2.8 2.9

2.85 cm

2 Runners finish the race in 8

seconds. Who won?

1

2

Runner 1

Runner 2

Stop and Think:

What is the length of the red line?

cm 0 1 2 3 4 5

Stop and Think:

What is the length of the red line?

cm 0 1 2 3 4 5

Stop and Think:

What is the volume of the liquid?

LESSON 6:

Counting Sig Figs

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 captive zeros are significant. (Captive is a zero between 2 other non-zero digits.) ex. 4012 (4 sig figs)

4. For Trailing zeros: (zeros after 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 counting 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)

Stop and Think:

How many sig figs in 23.500 m?

Stop and Think:

How many sig figs in 53,000 km?

Stop and Think:

How many sig figs in 0.0800 g?

Lesson 7: Rounding Sig Figs

in Calculations

LESSON 7:

Rounding 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

Multiply/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

Stop and Think

Round answer to proper # of sig figs

15.30 g ÷ 6.4 mL =

Stop and Think

Round answer to proper # of sig figs

18.9 g x 0.84 g =

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

Stop and Think

Round answer to proper # of sig figs

28.9 g - 0.85 g =

Stop and Think

Round answer to proper # of sig figs

80.4 mm – 16.532 mm =

LESSON 8:

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.

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

Stop and Think

Convert to Scientific Notation

45,700 m =

Stop and Think

Convert to Scientific Notation

0.00009 cm =

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

Stop and Think

Convert to Standard Notation

9.6 x 103 m =

Stop and Think

Convert to Standard Notation

1.2 x 10-4 g =

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:

Stop and Think

3.95 x 102 ÷ 1.5 x 106 =

Stop and Think

3.5 x 102 x 6.45 x 1010 =