section 1.4—converting units

Section 1.4—Converting Units

Converting Units

Often, a measurement is more convenient in one unit but is needed in another unit for calculations.

Dimensional Analysis is a method for converting units

You may have learned another method of converting units in math or previous science classes…trust me…learn this one now!

It will help you solve many other chemistry problems later in the class!

Equivalents

Dimensional Analysis uses equivalents…what are they?

1 foot = 12 inches

What happens if you put one on top of the other?

1 foot 12 inches

Equivalents

Dimensional Analysis uses equivalents…what are they?

1 foot = 12 inches

What happens if you put one on top of the other?

1 foot 12 inches

When you put two things that are equal on top & on bottom, they cancel out and equal 1

= 1

Dimensional Analysis

Dimensional analysis is based on the idea that you can multiply anything by 1 as many times as you want and you won’t change the physical meaning of the measurement!

27 inches 1 = 27 inches



1 foot 12 inches

= 2.25 feet27 inches

27 inches 1 = 27 inches



1 foot 12 inches

= 2.25 feet27 inches

Remember…this equals “1”

27 inches 1 = 27 inches Same physical meaning…it’s the same length either way!

1 foot 12 inches

12 inches

Canceling

Anything that is on the top and the bottom of an expression will cancel

When canceling units…just cancel the units…

1 foot 12 inches

27 inches

Unless the numbers cancel as well!

Steps for using Dimensional Analysis

1 Write down your given information

2Write down an answer blank and the desired unit on the right side of the problem space

3 Use equivalents to cancel unwanted unit and get desired unit.

4Calculate the answer…multiply across the top & divide across the bottom of the expression

Common Equivalents

1 ft 12 in

1 in 2.54 cm

1 min 60 s

1 hr 3600 s

1 quart (qt) 0.946 L

4 pints 1 quart

1 pound (lb) 454 g

=

=

=

=

=

=

=

Example #1

Example:How many grams are equal to

1.25 pounds?

1.25 lb

1 Write down your given information

Example #1


1.25 pounds?

1.25 lb

2Write down an answer blank and the desired unit on the right side of the problem space

= ________ g

Example #1


1.25 pounds?

1.25 lb = ________ g

3 Use equivalents to cancel unwanted unit and get desired unit.

The equivalent with these 2 units is: 1 lb = 454 gA tip is to arrange the units first and then fill in numbers later!

lb

g

Put the unit on bottom that you want to cancel out!

1

454

Example #1


1.25 pounds?

1.25 lb = ________ glb

g

1

454

4Calculate the answer…multiply across the top & divide across the bottom of the expression

Enter into the calculator: 1.25 454 1

568

Metric Prefixes

Metric prefixes can be used to form equivalents as wellFirst, you must know the common metric prefixes used in chemistry

kilo- (k) 1000

deci- (d) 0.1

centi- (c) 0.01

milli- (m) 0.001

micro- (μ) 0.000001

nano (n) 0.000000001

=

=

=

=

=

=

These prefixes work with any base unit, such as grams (g), liters (L), meters (m), seconds (s), etc.

Metric Equivalents

Many students confuse where to put the number shown in the previous chart…it always goes with the base unit (the one without a prefix)

kilo = 1000

There are two options:1 kg = 1000 g1000 kg = 1 g

Example:Write a correct

equivalent between

“kg” and “g”To help you write correct equivalents, read the number that equals the prefix as the prefix itself in a “sentence”

Metric Equivalents

Many students confuse where to put the number shown in the previous chart…it always goes with the base unit (the one without a prefix)

kilo = 1000

There are two options:1 kg = 1000 g1000 kg = 1 g


equivalent between

“kg” and “g”

“1 kg is kilo-gram”…correct“kilo- kg is 1 gram”…incorrect

To help you write correct equivalents, read the number that equals the prefix as the prefix itself in a “sentence”

Try More Metric Equivalents

milli = 0.001

There are two options:1 L = 0.001 mL0.001 L = 1 mL


equivalent between “mL” and

“L”

centi = 0.01

There are two options:1 cm = 0.01 m0.01 cm = 1 m


equivalent between “cm” and

“m”

Try More Metric Equivalents

milli = 0.001

There are two options:1 L = 0.001 mL0.001 L = 1 mL


equivalent between “mL” and

“L”

“1 L is milli-mL”…incorrect“milli-liter is 1 mL”…correct

centi = 0.01

There are two options:1 cm = 0.01 m0.01 cm = 1 m


equivalent between “cm” and

“m”

“1 cm is centi-meter”…correct“centi-cm is 1 m”…incorrect

Metric Volume Units

To find the volume of a cube, measure each side and calculate: length width height

length

heig

ht

width

But most chemicals aren’t nice, neat cubes!Therefore, they defined 1 milliliter as equal to

1 cm3 (the volume of a cube with 1 cm as each side measurement)

1 cm3 1 mL=

Example #2


127.0 mg?

127.0 mg = ________ g

You want to convert between mg & g“1 mg is 1 milli-g”1 mg = 0.001 g

Example #2


127.0 mg?

127.0 mg = ________ gmg

g

1

0.001

Enter into the calculator: 127.0 0.001 1

0.1270

You want to convert between mg & g“1 mg is 1 milli-g”1 mg = 0.001 g

You may be able to do this in your head…but practice the technique on the more simple problems so that you’ll be a dimensional analysis pro for the more difficult problems (like stoichiometry)!

Multi-step problems

There isn’t always an equivalent that goes directly from where you are to where you want to go!

Rather than trying to determine a new equivalent, it’s faster to use more than one step in dimensional analysis!

This way you have fewer equivalents to remember and you’ll make mistakes less often

With multi-step problems, it’s often best to plug in units first, then go back and do numbers.

Example #3

Example:How many kilograms

are equal to 345 cg?

345 cg = _______ kg

There is no equivalent between cg & kgWith metric units, you can always get to the base unit from any prefix!And you can always get to any prefix from the base unit!

You can go from “cg” to “g”Then you can go from “g” to “kg”

345 cg = _______ kg

Example #3



cg

g

Go to the base unit

g

kg

Go from the base unit

= _______ kg

Example #3



cg

g

1

0.01345 cg

g

kg

1000

1

1 cg = 0.01 g1000 g = 1 kg

Remember—the # goes with the base unit & the “1” with the prefix!

= _______ kg

Example #3



cg

g

1

0.01

Enter into the calculator: 345 0.01 1 1 1000

0.00345345 cg g

kg

1000

1

Whenever dividing by more than 1 number, hit the divide key before EACH number!

It doesn’t matter what order you type this in…you could multiply, divide, multiply divide if you wanted to!

Let’s Practice #1

Example:0.250 kg is

equal to how many

grams?

10000.250 kg

Let’s Practice #1

Example:0.250 kg is

equal to how many

grams?

= ______ gkg

g

1

1 kg = 1000 g

Enter into the calculator: 0.250 1000 1

250.

Let’s Practice #2

Example:How many mL is equal to 2.78 L?

12.78 L

Let’s Practice #2

Example:How many mL is equal to 2.78 L?

= ______ mLL

mL

.001

1 mL = 0.001 L

Enter into the calculator: 2.78 1 0.001

2780

Let’s Practice #3

Example:147 cm3 is equal to

how many liters?

Let’s Practice #3

Example:147 cm3 is equal to

how many liters?

Remember—cm3 is a volume unit, not a length like meters!

= _______ Lcm3

mL

1

1147 cm3

mL

L

1

0.001

There isn’t one direct equivalent1 cm3 = 1 mL1 mL = 0.001 L

Enter into the calculator: 147 1 0.001 1 1

0.147

Let’s Practice #4

Example:How many milligrams

are equal to 0.275 kg?

Let’s Practice #4

Example:How many milligrams

are equal to 0.275 kg?

= _______ mgkg

g

1

10000.275 kg

g

mg

0.001

1

There isn’t one direct equivalent1 kg = 1000 g1 mg = 0.001 g

Enter into the calculator: 0.275 1000 1 1 0.001

275,000

section 1.4—converting units

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