Problem Solving in ChemistryDimensional Analysis

• Used in _______________ problems.

*Example: How many seconds are there in 3 weeks?

• A method of keeping track of the_____________.

Conversion Factor

• A ________ of units that are _________________ to one another.

*Examples: 1 min/ ___ sec (or ___ sec/ 1 min)

___ days/ 1 week (or 1 week/ ___ days)

1000 m/ ___ km (or ___ km/ 1000 m)

• Conversion factors need to be set up so that when multiplied, the unit of the “Given” cancel out and you are left with the “Unknown” unit.

• In other words, the “Unknown” unit will go on _____ and the “Given” unit will go on the ___________ of the ratio.

conversion

units

ratio equivalent

60 607 7

1 1

topbottom

How to Use Dimensional Analysis to Solve Conversion Problems

• Step 1: Identify the “________”. This is typically the only number given in the problem. This is your starting point. Write it down! Then write “x _________”. This will be the first conversion factor ratio.

• Step 2: Identify the “____________”. This is what are you trying to figure out.

• Step 3: Identify the ____________ _________. Sometimes you will simply be given them in the problem ahead of time.

• Step 4: By using these conversion factors, begin planning a solution to convert from the given to the unknown.

• Step 5: When your conversion factors are set up, __________ all the numbers on top of your ratios, and ____________ by all the numbers on bottom.

If your units did not ________ ______ correctly, you’ve messed up!

Given

Unknown

conversion factors

multiplydivide

cancel out

Practice Problems: (1)How many hours are there in 3.25 days?

(2) How many yards are there in 504 inches?

(3) How many days are there in 26,748 seconds?

24 hrs1 day

3.25 days

x = 78 hrs

1 ft 12 in.

1 yard 504 in. x x = 14 yards

60 sec1 hr 1 min26,748 sec

x x = 0.30958 days

3 ft

60 minx

24 hrs1 day

Scientific Measurement Qualitative vs. Quantitative

• Qualitative measurements give results in a descriptive nonnumeric form. (The result of a measurement is an _____________ describing the object.)

*Examples: ___________, ___________, long, __________...

• Quantitative measurements give results in numeric form. (The results of a measurement contain a _____________.)

*Examples: 4’6”, __________, 22 meters, __________...

Accuracy vs. Precision

• Accuracy is how close a ___________ measurement is to the ________ __________ of whatever is being measured.

• Precision is how close ___________ measurements are to _________ ___________.

adjective

short heavy cold

number

600 lbs. 5 ºC

singlevaluetrue

severalothereach

Practice Problem: Describe the shots for the targets.

Bad Accuracy & Bad Precision

Good Accuracy & Bad Precision

Bad Accuracy & Good Precision

Good Accuracy & Good Precision

Significant Figures

• Significant figures are used to determine the ______________ of a measurement. (It is a way of indicating how __________ a measurement is.)

*Example: A scale may read a person’s weight as 135 lbs. Another scale may read the person’s weight as 135.13 lbs. The ___________ scale is more precise. It also has ______ significant figures in the measurement.

• Whenever you are measuring a value, (such as the length of an object with a ruler), it must be recorded with the correct number of sig. figs.

• Record ______ the numbers of the measurement known for sure.

• Record one last digit for the measurement that is estimated. (This means that you will be ________________________________ __________ of the device and taking a __________ at what the next number is.)

more

marksreading in between the

guess

precise

ALL

second

precision

Significant Figures

• Practice Problems: What is the length recorded to the correct number of significant figures?

(cm) 10 20 30 40 50 60 70 80 90 100

length = ________cm

length = ________cm11.65

58

The SI System (The Metric System)

• Here is a list of common units of measure used in science:

Standard Metric Unit Quantity Measured

kilogram, (gram) ______________

meter ______________

cubic meter, (liter) ______________

seconds ______________

Kelvin, (˚Celsius) _____________

• The following are common approximations used to convert from our English system of units to the metric system:

1 m ≈ _________ 1 kg ≈ _______ 1 L ≈ 1.06 quarts

1.609 km ≈ 1 mile 1 gram ≈ ______________________

1mL ≈ _____________ volume 1mm ≈ thickness of a _______

mass

length

volume

timetemperature

1 yard

sugar cube’s

2.2 lbs.

mass of a small paper clip

dime

The SI System (The Metric System)

Metric Conversions• The metric system prefixes are based on factors of _______.

Here is a list of the common prefixes used in chemistry:

kilo- hecto- deka- deci- centi- milli-

• The box in the middle represents the standard unit of measure such as grams, liters, or meters.

• Moving from one prefix to another involves a factor of 10.

*Example: 1000 millimeters = 100 ____ = 10 _____ = 1 _____

• The prefixes are abbreviated as follows:

k h da g, L, m d c m

*Examples of measurements: 5 km 2 dL 27 dag 3 m 45 mm

grams Liters meters

mass

cm dm m

Metric Conversions

• To convert from one prefix to another, simply count how many places you move on the scale above, and that is the same # of places the decimal point will move in the same direction.

Practice Problems:

380 km = ______________m 1.45 mm = _________m

461 mL = ____________dL 0.4 cg = ____________ dag

0.26 g =_____________ mg 230,000 m = _______km

Other Metric Equivalents

1 mL = 1 cm3 1 L = 1 dm3

For water only:

1 L = 1 dm3 = 1 kg of water or 1 mL = 1 cm3 = 1 g of water

Practice Problems:

(1) How many liters of water are there in 300 dm3 ? ___________

(2) How many kg of water are there in 500 mL? _____________

380,000

4.61260

0.001450.0004

230

300 L0.5 kg

grams Liters meters

Area and Volume Conversions

• If you see an exponent in the unit, that means when converting you will move the decimal point that many times more on the metric conversion scale.

*Examples: cm2 to m2 ......move ___________ as many places

m3 to km3 ......move _____ times as many places

Practice Problems: 380 km2 = _________________m2

4.61 mm3 = _______________cm3

k h da g, L, m d c m

twice

3

380,000,000

0.00461

Scientific Notation• Scientific notation is a way of representing really large or small

numbers using powers of 10.

*Examples: 5,203,000,000,000 miles = 5.203 x 1012 miles

0.000 000 042 mm = 4.2 x 10−8 mm

Steps for Writing Numbers in Scientific Notation

(1) Write down all the sig. figs.

(2) Put the decimal point between the first and second digit.

(3) Write “x 10”

(4) Count how many places the decimal point has moved from its original location. This will be the exponent...either + or −.

(5) If the original # was greater than 1, the exponent is (__), and if the original # was less than 1, the exponent is (__)....(In other words, large numbers have (__) exponents, and small numbers have (_) exponents.

+

+−

−

477,000,000 miles = _______________miles

0.000 910 m = _________________ m

6.30 x 109 miles = ___________________ miles

3.88 x 10−6 kg = __________________ kg

Scientific Notation

• Practice Problems: Write the following measurements in scientific notation or back to their expanded form.

4.77 x 108

9.10 x 10−4

6,300,000,000

0.00000388

−

Evaluating the Accuracy of a Measurement

• The “Percent Error ” of a measurement is a way of representing the accuracy of the value. (Remember what accuracy tells us?)

% Error = (Accepted Value) − (Experimentally Measured Value) x 100 (Accepted Value)

Practice Problem:

A student measures the density of a block of aluminum to be approximately 2.96 g/mL. The value found in our textbook tells us that the density was supposed to be 2.70 g/mL. What is the accuracy of the student’s measurement?

(Absolute Value)

% Error = |2.70−2.96| ÷ 2.70 = 0.096296…x 100 = 9.63% error