Dimensional Analysis Worksheet

This worksheet is designed to give you practice using dimensional analysis as a problem solving tool. For this reason it is very important to show your work. In each problem write the equality statement if you are confused, if not then just write out the string of calculations with the correct conversion factor, including the units. Show how the units cancel to give the final answer with the correct units. GOOD LUCK!!!

PART 1 Dimensional Analysis and the metric system. Memorize the prefixes of the metric system so you can write the correct equivalence statements without assistance.

Prefix	Kilo	Base unit (grams, liters, meters)	deci	centi	milli	micro	nano
Prefix Abbreviation	K		d	c	m	µ	n
Value (Standard Notation)	1000	1	1/10	1/100	1/1000	1/1,000,000	1/1,000,000,000
Value (Scientific Notation)	10^3	10^0	10^-1	10^-2	10^-3	10^-6	10^-9

1) Write an equivalence statement between the two given measurements.

A) 1 Km = ___________ m or 1 m = _____________ Km

B) 1 µm = ___________m or 1 m = _____________ µm

C) 1 nL = ____________l or 1 l = ______________ nL

D) 1 ft = _____________ in or 1 yard = ___________ ft

E) 1 cm = .39370 in and 1 in = 2.54________cm

F) 1 km = .62137 mi and 1 mi = 3.1117______ km

You are NOT required to memorize the conversion factors between the metric and English systems of measurement.

2) Perform the following conversions using the equivalence statements you wrote in #1. SHOW YOUR WORK IN THE SPACE PROVIDED UNDER EACH LETTER. WRITE SMALL!!

A) 75 Km = ? m

? =

= ________________

B) 2.68 E-6 µm = ? m

? =

= ________________

C) 11.2 nL = ? L

? =

= ________________

D) 37.687 yds = ? in

? =

= ________________

E) .00898 km = ? in

? =

= ________________

F) 8.98 E15 nm = ? mi

? =

= ________________

Part 2 Varied Applications

3) You visit the store and find a banana sale. On average 8 bananas weigh one pound. The sale price for bananas is four pounds for $5.00. You decide to treat your advising group to 25 banana splits, 1 banana per split.

A) Write the equivalence statements.

________________bananas = 1 lb _______________lbs = _________________ dollars

B) How much will it cost you to buy 25 bananas?

? =

= ________________

4) The average length of a hotdog is 12.0 cm. The distance to the moon is 3.84 E8 meters. How many hotdogs must you line up to reach the moon?

A) Write the equivalence statements

________ hot dog = _______ cm __________ m = __________cm

distance to moon = __________________ m

B) How many hotdogs must you line up to reach the moon?

? =

= ________________

5) The distance to the sun is 1.496 E11 meters. The speed of light is 3.00 E8 m/s. A minute is defined to be 60 seconds.

A Write the equivalence statements

Distance to sun = ________________ m Speed of light = ____________________m/s

______________minute = _____________seconds

B) How long does it take for light to get from the sun to the earth?

? =

= ________________

6) If the density of mercury is 13.6 g/ml, find the A) mass of 43.0 ml of mercury, B) volume of 43.0 grams of mercury. (Hint: use the density of mercury to write an equivalence statement between mass and volume.)

________________= ________________

A) Mass of 43.0 mL of mercury

? =

= ________________

B) Volume of 43.0 grams of mercury

? =

= ________________

7) You exhale about .0800 liters of CO₂ (carbon dioxide) gas in a single breath. 22.4 liters of CO₂ contain 6.022 x 10²³ molecules. 6,022 x 10²³ CO₂ molecules have a mass of 44.0 grams. Find the A) number of carbon dioxide molecules you exhale in each breath. Find the mass of the CO₂ you exhale in a single breath.

________________= ________________ ________________= ________________

? =

= ________________

Chemistry Students in 2007

Do NOT complete any of the problems below!!!!!

Part 3 Counting by weighing and dozen mass.

Data Table for part 3

Quantity Measured	Mass of Sample	Dozen Mass (Based on 8B)
One Cat	15.0 lbs
20 chicken eggs	1.00 Kg
14 pugs	76.37 Kg
19 marbles	52.25 grams
Mass of John	81.89 Kg

8) Be sure you can write equivalence statements based on the data in the table above. Write the equivalence statement for cats, eggs, and pugs.

A)

________________= _________________

________________= _________________

________________= _________________

B)

Find the dozen mass for each quantity using dimensional analysis. After completing the problem fill in the third column of the data table above.

CATS

? =

= ________________

EGGS

? =

= ________________

PUGS

? =

= ________________

MARBLES

? =

= ________________

JOHN

? =

= ________________

C) A sample of cats has a mass of 13,905 lbs. How many dozens of cats are in the sample? How many cats are in the sample? (For extra credit draw a picture of every cat in this sample and give it a nice name. NO, NO, NO, I WAS JUST KIDDING)

? =

= ________________

D) How many dozens of eggs would it take to have a mass of 13,905 lbs? ( 1 Kg = 2.200 lbs) Why is this number larger than your answer to part C?

? =

= ________________

E) A sample of marbles has a mass of 1000. Kg.

How many dozens of marbles are in this sample?

? =

= ________________

How many marbles are in the sample?

? =

= ________________

F) Find the mass and number of pugs in a sample that contains 897.6 dozen pugs.

? =

= ________________

? =

= ________________

G) How many Johns would it take to have the same mass as the pug sample?

? =

= ________________

Part 4 Counting by Weighing – Moles, Molar Mass and Avagadro’s Number

Remember 1 dozen is defined to be 12 things and 1 mole is defined to be 6.022 E23 things.

Remember Dozen Mass is the mass of 1 dozen things measured in grams/dozen and Molar Mass is the mass of 1 mole of things measured in grams.

Number of Particles

Mass in Grams

Moles

Molar Mass Avagadro’s #

grams/mol 6.022 E23 cule/mole

1. Find the molar mass of each of the following substances in grams/mole

A) Ne

B) NaF

C) H₂SO₄

D) B₂(SO₄)₃

2. Find the number of moles in each sample.

A) Moles of Ne in 10.0 grams of Ne atoms?

? =

= ________________

B) Moles NaF in 10.0 grams of NaF

? =

= ________________

C) Moles of H₂SO₄ in 150.0 grams of H₂SO₄

? =

= ________________

D) Moles of B₂(SO₄)₃ in 85.00 grams B₂(SO₄)₃

? =

= ________________

3. Find the mass of each sample in grams.

A) Mass of 1.00 moles of Ne

? =

= ________________

B) Mass of 2.50 moles of NaF

? =

= ________________

C) Mass of 3.25 x 10^-8 moles of H₂SO₄

? =

= ________________

D) Mass of 673 kilomoles of B₂(SO₄)₃

? =

= ________________

4. Find the number of particles in each sample.

A) How many Ne atoms are there in 2.00 moles of Ne?

? =

= ________________

B)How many sulfuric acid molecules in 6.48 mole of H₂SO₄ ?

? =

= ________________

5. Find the number of moles in each sample.

A) How many moles of Ne in 6.89 x 10⁹ Ne atoms

? =

= ________________

B) How many moles of sulfuric acid molecules in 1.78 x 10²⁵ molecules of H₂SO₄ ?

? =

= ________________

6. Find the number of particles in each sample

A) How many Ne atoms are there in10.0 grams of Ne?

? =

= ________________

B) How many NaF formula units are there in 10.0 grams of NaF?

? =

= ________________

C) How many sulfuric acid molecules are there in 150.0 grams of H₂SO₄ ?

? =

= ________________

D) How many B₂(SO₄)₃ are there in 85.00 grams B₂(SO₄)₃ ?

? =

= ________________