MEASUREMENT

AND

PROBLEM SOLVING

Chapter 3 & 4

Importance of Measurements

1. Fundamental to all sciences

2. In chemistry you use the

International System of

Measurements (SI units).

Qualitative vs. Quantitative

Measurements

Qualitative -- descriptive,

nonnumeric

Quantitative -- results in a definite

form, usually as numbers and

units.

Scientific Notation

• 3.6 x 10 4 = 36,000

• 8.1 x 10 –3 = 0.0081

• Numbers less than 1 the exponent is

negative and represents the number of

places the decimal has been moved to

the right.

• Numbers greater than 1, the

exponent is positive and represents the

number of places the decimal is moved

to the left.

Manipulation of Exponents:

Multiply -- multiply the

coefficients and add the

exponents.

Ex: (3.0 x 10 4 ) (2.0 x 102 ) =

6.0 x 10 4 + 2 = 6.0 x 10 6

Division -- Divide coefficients and

subtract denominators from the

numerator.

Example:

3.0 x 104 = 3.0 X 10 4 – 2= 1.5x 102

2.0 x 102 2.0

Addition & Subtraction – make exponents the same, by moving the decimal

Example:

5.4 x 103 + 6.0 x 102 = 5.4 x 103

+ 0.60 x103

6.0 x 103

Accuracy – How close a

measurement comes to the

actual or true value. To

evaluate the accuracy of a

measurement, it must be

compared with the correct

value.

Precision -- A measure of how

close a series of measurements

are to one another. Depends

on more than one

measurement.

Error – the difference between what you get and the actual value.

1. Actual (True) Value – The correct value based on reliable references.

2. Experimental value –measured in the lab.

Error = Actual – Experimental

a.Can be positive or negative

b. Percent error is the absolute

value divided by the accepted

value, multiplied by 100%.

SIGNIFICANT DIGITS

To determine the number of

significant digits in a written

number complete one of

the following:

1. Qualifying statement: The numerical value has no decimal place written.

Action to take: Count from the first non-zero digit to the last non-zero digit.

Examples:

18,004 - 5 significant digits

10,040,000– 4 sig digs

10 – 1 sig dig

2. Qualifying statement: The numerical

value contains a decimal place.

Action to take: Count from the first non-

zero digit to the end of the number.

Examples:

100.00 – 5 sig digs

1,050. – 4 sig digs

0.000 145 00 – 5 sig digs

Using Significant Digits in problems:

Addition and Subtraction – Answer the

problem then round to the same

number of decimal places as the

measurement with the least number

of sig digs.

Example: 14.05 + 21.3 = 35.35 = 35.4

Multiplication and Division --

answer the problem and round

the answer to the same number

of sig. digs. As the measurement

with the least number of sig.

digs.

Example : 24.55 x 52.3 x 14.235 =

18277.24178 = 18300

Units :

1. All measurements depend on

units

2. Science uses the metric

system.

3. Each type of measurement has

a base unit.

• Length (distance) = meter

• Volume (the amount of

space occupied by matter) =

liter

• Mass (weight) = gram

Prefixes are added to the

base unit in order to

measure in different

amounts.

Common prefixes

1. Kilo ( K ) = 1000

2. Hecta ( H ) = 100

3. Deka ( D ) = 10

4. deci ( d ) = 1 /10

5. centi ( c ) = 1 / 100

6. milli ( m ) = 1/ 1000

7. micro (μ ) =

1 / 1x10-6

8. nano ( n ) =

1 / 1x 10-9

Density – the relationship between

an objects mass and its volume.

Density = Mass / Volume (D = M / V)

Example: D = ? If the mass of an

object is 114 g and takes up a

volume of 10.0 ml.

D = 11.4 g/ml.

If the mass of an object stays the

same, but the volume changes

then the density will change.

Typically as the volume gets smaller

the density gets larger. Water is

an exception to this.

Temperature – of an object

determines the direction of heat

transfer.

- Heat moves from the object of

higher temperature to the object

of lower temperature.

- Almost all substances expand

with an increase in

temperature

(thermal expansion).

Scales

Celsius -- uses two reference

points to set it, the freezing

point ( 0º C ) and the boiling

point of water ( 100 º C ).

Kelvin – ( absolute scale ) the

freezing point of water is

273.15 K and the boiling point

is 373.15 K.

-No degree sign is used.

-The zero point is equal to

–273.15 º C , and is called

absolute zero.

Conversion Formulas:

•K = º C + 273.15

K = 20°C + 273.15 = 293.15K

•º C = K – 273.15

°C = 118K – 273.15 = -155.15°C

Problem SolvingThree steps to solving problems

1. Analyze

a. Identify the known ( what is

given ).

b. Identify the unknown

c. Plan a solution ( choose

appropriate equation )

2. Calculate

a. Substituting known quantities

b. Arithmetic manipulation

c. Convert the units

3. Evaluate

Does the answer make sense?

Is it written in the correct units?

Conversion Factors – a ratio of equivalent measurements.

Example: 100cm = 1 m

1m 100cm

The numerator (top) is equal to

the denominator (bottom).

Dimensional Analysis – a way to

analyze and solve problems

using the units, or dimensions, of

the measurements.

Multistep Problems

1. Solve by breaking the solution

into steps.

2. Convert complex units, using

dimensional analysis.

Practice Problems on board.