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? When you put two things that are equal on top & on bottom, they cancel out and equal 1 1 foot 12 inches = 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

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 27 inches  = 2.25 feet

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! Same physical meaning…it’s the same length either way! 27 inches  1 = 27 inches 1 foot 12 inches 27 inches  = 2.25 feet Remember…this equals “1”

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! 1 foot 12 inches 

Steps for using Dimensional Analysis 1 Write down your given information Write down an answer blank and the desired unit on the right side of the problem space 2 Use equivalents to cancel unwanted unit and get desired unit. 3 Calculate the answer…multiply across the top & divide across the bottom of the expression 4

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

How many grams are equal to 1.25 pounds? Example #1 1 Write down your given information Example: How many grams are equal to 1.25 pounds? 1.25 lb

How many grams are equal to 1.25 pounds? Example #1 Write down an answer blank and the desired unit on the right side of the problem space 2 Example: How many grams are equal to 1.25 pounds? 1.25 lb = ________ g

How many grams are equal to 1.25 pounds? Example #1 Use equivalents to cancel unwanted unit and get desired unit. 3 Example: How many grams are equal to 1.25 pounds? 454 g 1.25 lb  = ________ g 1 lb Put the unit on bottom that you want to cancel out! The equivalent with these 2 units is: 1 lb = 454 g A tip is to arrange the units first and then fill in numbers later!

How many grams are equal to 1.25 pounds? Example #1 Calculate the answer…multiply across the top & divide across the bottom of the expression 4 Example: How many grams are equal to 1.25 pounds? 454 g  568 1.25 lb = ________ g 1 lb Enter into the calculator: 1.25  454  1

Metric Prefixes Metric prefixes can be used to form equivalents as well First, you must know the common metric prefixes used in chemistry kilo- (k) = 1000 These prefixes work with any base unit, such as grams (g), liters (L), meters (m), seconds (s), etc. deci- (d) = 0.1 centi- (c) = 0.01 milli- (m) = 0.001 micro- (μ) = 0.000001 = nano (n) 0.000000001

Write a correct equivalent between “kg” and “g” 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 Example: Write a correct equivalent between “kg” and “g” There are two options: 1 kg = 1000 g 1000 kg = 1 g To help you write correct equivalents, read the number that equals the prefix as the prefix itself in a “sentence”

Write a correct equivalent between “kg” and “g” 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 Example: Write a correct equivalent between “kg” and “g” There are two options: 1 kg = 1000 g 1000 kg = 1 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 Example: Write a correct equivalent between “mL” and “L” milli = 0.001 There are two options: 1 L = 0.001 mL 0.001 L = 1 mL Example: Write a correct equivalent between “cm” and “m” centi = 0.01 There are two options: 1 cm = 0.01 m 0.01 cm = 1 m

Try More Metric Equivalents Example: Write a correct equivalent between “mL” and “L” milli = 0.001 There are two options: 1 L = 0.001 mL 0.001 L = 1 mL “1 L is milli-mL”…incorrect “milli-liter is 1 mL”…correct Example: Write a correct equivalent between “cm” and “m” centi = 0.01 There are two options: 1 cm = 0.01 m 0.01 cm = 1 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 height width length 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

How many grams are equal to 127.0 mg? Example #2 Example: How many grams are equal to 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

How many grams are equal to 127.0 mg? Example #2 Example: How many grams are equal to 127.0 mg? 0.001 g 0.1270 127.0 mg  = ________ g 1 mg You want to convert between mg & g “1 mg is 1 milli-g” 1 mg = 0.001 g Enter into the calculator: 127.0  0.001  1 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.

How many kilograms are equal to 345 cg? Example #3 Example: How many kilograms are equal to 345 cg? 345 cg = _______ kg There is no equivalent between cg & kg With 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”

How many kilograms are equal to 345 cg? Example #3 Example: How many kilograms are equal to 345 cg? g kg 345 cg   = _______ kg cg g Go to the base unit Go from the base unit

How many kilograms are equal to 345 cg? Example #3 Example: How many kilograms are equal to 345 cg? 0.01 g 1 kg 345 cg   = _______ kg 1 cg 1000 g 1 cg = 0.01 g 1000 g = 1 kg Remember—the # goes with the base unit & the “1” with the prefix!

How many kilograms are equal to 345 cg? Example #3 Example: How many kilograms are equal to 345 cg? 0.01 g 1 kg 345 cg   = _______ kg 0.00345 1 cg 1000 g Enter into the calculator: 345  0.01  1  1  1000 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!

0.250 kg is equal to how many grams? Let’s Practice #1 Example: 0.250 kg is equal to how many grams?

0.250 kg is equal to how many grams? Let’s Practice #1 Example: 0.250 kg is equal to how many grams? 1000 g 0.250 kg  = ______ g 250. 1 kg 1 kg = 1000 g Enter into the calculator: 0.250  1000  1

Let’s Practice #2 Example: How many mL is equal to 2.78 L?

Let’s Practice #2  1 mL 2.78 L = ______ mL .001 L 2780 1 mL = 0.001 L Example: How many mL is equal to 2.78 L? 1 mL 2.78 L  = ______ mL 2780 .001 L 1 mL = 0.001 L Enter into the calculator: 2.78  1  0.001

147 cm3 is equal to how many liters? Let’s Practice #3 Example: 147 cm3 is equal to how many liters?

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! 1 mL 0.001 L 147 cm3   = _______ L 0.147 1 cm3 1 mL There isn’t one direct equivalent 1 cm3 = 1 mL 1 mL = 0.001 L Enter into the calculator: 147  1  0.001  1  1

How many milligrams are equal to 0.275 kg? Let’s Practice #4 Example: How many milligrams are equal to 0.275 kg?

How many milligrams are equal to 0.275 kg? Let’s Practice #4 Example: How many milligrams are equal to 0.275 kg? 1000 g 1 mg 0.275 kg   = _______ mg 275,000 1 kg 0.001 g There isn’t one direct equivalent 1 kg = 1000 g 1 mg = 0.001 g Enter into the calculator: 0.275  1000  1  1  0.001