### Use Your Knowledge of English:

1. Analyze the Units of the Answer. How many dimensions?

Most chemistry problems (stoichiometry) deal with questions asking for a only one dimensional unit. Sometimes a compound unit, two dimensions, is requested and this is usually a single unit in the numerator and a single unit in the denominator. Examples of single and compound dimensional unit answers are:

 One Dimensional Units: Length Mass Count Time Volume* Two Dimensional Units: Velocity:         Length/Time Density:          Mass/Volume Molecular Mass:    Mass/Count Concentration:      Count/Volume % :    Parts pure/100 Parts Mixture * Volume is actually three dimensional (Length3), but chemistry problems will be easier if we treat it as one.

2. The Number of dimensions of the answer must MATCH the number of dimensions of the Given!

• If the answer has only 1 dimension, then given must have only 1 dimension.

• If the answer has two dimensions, a numerator and a denominator, then the given must a numerator with one dimension and the denominator a unit with one dimension

• If the numerator of the answer has two dimensions (i.e. area yd2), the Given must have two dimensions in the numerator: (i.e.: 30 ft x 40ft or 1200 ft2)

### __???__unit (unknown's number of dimensions) = __###__ unit (given's number of dimensions)

3. Extract the Number with the Unit in the problem that does not appear to be a Unit Factor (Section 2.8), which also matches the dimensions of the Unit of the Answer.

(Do Not worry if the Given Unit is not in the same catagory (Length, Mass, Count, Time) such as the catagory of the units of answer, such as a lone number in the problem which is Time, but the given Unit is Length.)
• Unit conversion factors are equivalent relationships

• An equivalent relationship is a relationship between two quantities that are equal

• For example: 60 seconds = 1 minute is an equivalent relationship

• A unit conversion factor, or Unit Factor, is a ratio of two equivalent quantities

• For example: 60 seconds/1 minute is a unit factor. Write it in fraction form:

• 60 seconds

1 minute

• Since the numerator and the denominator are equal, the reciprocal ratio: 1 minute/60 seconds is also a valid unit factor. Write it in fractional form:

• 1 minute

60 seconds

S

ome Two Dimensional Unit Definitions: (Mixed Dimensional Categories)

Density Connects Mass to Volume (or Volume to Mass)
 7.43 gSn Density:   Mass/unit Volume Density tin = 7.43 gSn / 1 cm3Sn

Velocity Connects Length to Time (or Time to Length)
 55 miles Velocity:   Length/unit Time 'Speed' = 55 miles / 1 hour

Molecular Mass   Connects Mass to Count (or Count to Mass)
 18 g H2O Molecular Mass:   Mass/unit Count Mol Mass = 18 g H2O / 1 moleH2O

Mole Ratio Connects CountA to CountB (or CountB to CountA)
 2 molesA Balanced Equation:    2A + 3B ---> 4C + 1D   2 molecules A react with 3 molecules B Mole Ratio:   2 molesA = 3 molesB Mole Ratio:   2 molesA / 3 molesB

Molarity   Connects Count to Volume (or Volume to Count)
 16 molesHCl Solute Molarity:   Moles/unit Volume Molarity    =   16 MolarHCl   or 16 molesHCl Solute / 1 literHCl Solution

% by Mass   Connects Masspure to Massmixture (or Mixture to Pure)
 6 gpure NaClO % by Mass: Masspure/100 units Massmixture 6%NaClO = 6 gpure NaClO / 100 gBleach Solution

• Note the labels (subscripts) placed on each unit. Labels must also match before connecting units.

• Link to: Sample Test     Steps 1 and 2 Sample Test     Setup and Answer Sample Test

# Sample Problems

Problem 1
If the sun is 93,000,000 miles from the Earth, how many kilometers is the distance?
(Given: One mile equals 1.61 kilometers.)

Problem 2
If the sun is 93,000,000 miles from the Earth, how many minutes does it take for sunlight to reach the Earth? (Given: The velocity of light is 186,000 miles per second.)

Problem 3
Find the mass in grains of a 325 milligram aspirin tablet.
(Given: 1.00 g = 15.4 grains)

Problem 4
Insurance statistics state that a person loses 8 minutes of average life for each cigarette smoked. If there are 20 cigarettes in a pack and the average cost of cigarette is \$5.00 per pack over the next 25 years, how many years of average life would a person lose for smoking 1.5 packs a day for 25 years?

Problem 5
What is the density of water in lb/ft3, if the density of water at 25oC is 1.00 g/ml?
[Hint: There are 2.54 cm = 1 in (or 16.48 cm3 = 1 in3); 454 g = 1 lb ]

Problem 6
Calculate the velocity of a car traveling car traveling 65 miles/hr in ft/sec.

Problem 7
How many milligrams does a 0.750 carat diamond weigh?
(Hint: 1 carat = 0.200 g)

Problem 8
Diamond has a density of 3.513 g/cm3. The mass of a diamond is often measured in carats, 1 carat equaling 0.200 g. What is the volume of a 1.50 carat diamond?

Problem 9
Liquor used to be sold in fifths. A fifth is one fifth of a gallon. A gallon is 128 fluid ounces. Today liquor is sold in bottle sizes of 750 ml to equate to the old fifth. If there are 946 ml in a quart, calculate the number of milliliters in a fifth. How many milliliters difference is there in the bottling?

The True Story
On July 23, 1983, Air Canada Flight 143 was flying at an altitude of 26,000 ft from Montreal to Edmonton. Warning buzzers sounded in the cockpit of the Boeing 767. One of the world's larger planes was now a glider-the plane had ran out of fuel! Like all Boeing 767s, the plane had a sophisticated fuel gauge, but it was not working properly. However, the plane was still allowed to fly, because there is an alternate method for determining fuel. The Mechanics have a dip stick, calibrated in centimeters, and translated into volume in liters. The Mechanics calculated the three tanks had a total of 7682L of fuel. Pilots always calculate fuel quantities in mass, because they need to know the total mass of the plane before takeoff. Air Canada pilots had always calculated the mass in pounds, but the new 767s fuel consumption was given in kilograms. This involved using the fuel's density to convert 7682 L to a mass in kilograms, so that the pilot could calculate the mass of fuel that had to be added. The First Officer of the plane asked the Mechanic for the conversion factor to calculate volume-to-mass conversion, and the Mechanic replied "1.77". Using that number, the officer and the Mechanic calculated that 4917 L of fuel should be added. The required amount for the trip was 22,300 kg. The mechanic never gave the First Officer the conversion units which was for pounds per liter, not kg/liter as the First Officer assumed. The rest of the story is that the Pilot could not make it to the nearest airport, Winnipeg, but to a little town Gimli which had a former Royal Canadian Air Force runway converted to a race track. For 30 minutes the plane glided to Gimil and managed to land.

Now The Problem 10
The Gimli Glider was a Boeing 767 that ran out of fuel. Read the story above, then verify that the ground crew should have added 20,163 L of fuel instead 4916. The crucial piece of information is the density of the fuel. The crew used 1.77, but did not recognize the units were pounds per liter. To solve the problem you need first to find the density in units of kilograms per liter (Hint: 1 lb = 453.6 grams).

Link to: Sample Test     Steps 1 and 2 Sample Test     Setup and Answer Sample Test