**DIMENSIONAL ANALYSIS**Dimensional analysis is a critical problem solving technique utilized throughout chemistry. It is a mathematical approach that allows one to convert from one unit to another unit using conversion factors.

Below are some examples of basic dimensional analysis:

__Example 1:__**Convert 45.3 cm to its equivalent measurement in mm.**

Select a conversion factor which will convert the unit "cm" to the unit "mm". The appropriate conversion

factor is: 10 mm / 1 cm. Arrange the problem so that the given measurement, when multiplied by the

correct unit factor, will yield an answer with the proper label:

45.3

Select a conversion factor which will convert the unit "cm" to the unit "mm". The appropriate conversion

factor is: 10 mm / 1 cm. Arrange the problem so that the given measurement, when multiplied by the

correct unit factor, will yield an answer with the proper label:

45.3

**cm X**

1 cm

__10 mm__= 453 mm1 cm

__Example 2:__**Change a speed of 72.4 miles per hour to its equvalent in meters per second.**

**In this example, several conversion factors are needed. One to change the miles into meters and the other**

to change hours into seconds?

to change hours into seconds?

__72.4 mi__X__1760 yd__X__36 inches__X__1 meter__**X**

1 hr 1 mi 1 yd 39 inches 3600 s s

__1 hr__= 32.7__m__1 hr 1 mi 1 yd 39 inches 3600 s s

__Example 3:__**The density of mercury is 13.6 g/mL. What is the mass in kilograms of a 2 L commercial**flask

**of mercury?**

Set up the problem so that the calculation will yield a result with a mass in grams.

1 mL 1 L 1000 g

Set up the problem so that the calculation will yield a result with a mass in grams.

__13.6 g__X__1000 mL__X 2 L X__1 kg__= 27.2 kg1 mL 1 L 1000 g

**EXCELLENT PRACTICE PROBLEMS:****Use dimensional analysis in solving each of the following problems.**

1. Convert 32.5 oz to its equivalent in cg.

2. Convert 3.55 yd to its equivalent in cm.

3. Convert 143.55 mL to its equivalent in pints.

4. Convert a speed of 35.8 mi/hr to its equivalent in m/s.

5. Convert a density of 13.6 g/mL to its equivalent in lb/ft3.

6. A mole of hydrogen atoms contains 6.02 X 1023 atoms and occupies 22.4 L. How many hydrogen atoms are contained in 25.00 mL of this gas?

7. What volume of hydrogen would contain 4.5 X 1018 hydrogen atoms? How many moles of hydrogen would this be?

8. A

1. Convert 32.5 oz to its equivalent in cg.

2. Convert 3.55 yd to its equivalent in cm.

3. Convert 143.55 mL to its equivalent in pints.

4. Convert a speed of 35.8 mi/hr to its equivalent in m/s.

5. Convert a density of 13.6 g/mL to its equivalent in lb/ft3.

6. A mole of hydrogen atoms contains 6.02 X 1023 atoms and occupies 22.4 L. How many hydrogen atoms are contained in 25.00 mL of this gas?

7. What volume of hydrogen would contain 4.5 X 1018 hydrogen atoms? How many moles of hydrogen would this be?

8. A

**molecule**

**of hydrogen moves at a speed of 115 cm/s. How long will it take to travel the length of a football field (100 yd long)?**

9. The speed of light is 3.0 X 1010 cm/s. Express this in mi/hr.

10. A sample of sea water contains 0.075 g of sodium chloride per mL of solution. How many moles of sodium chloride are there per L of this solution? A mole of sodium chloride is equivalent to 58.5 g of sodium chloride.

11. A doctor orders that a patient recieve 1.5 X 10-3 mole of sodium chloride. The only solution available contains 1.00 g per 100 mL of solution. A mole of sodium chloride is equivalent to 58.5 g of sodium chloride. How much of this solution should the nurse give the patient?

12. A sample of air contains 2.33 X 10-4 mg of lead per mL of gas. This air passes through an office, the volume of which is 3.25 X 104 L. Seven people normally work in this office. How many μg of lead will each person in the office receive from this sample of air?

ANSWERS

9. The speed of light is 3.0 X 1010 cm/s. Express this in mi/hr.

10. A sample of sea water contains 0.075 g of sodium chloride per mL of solution. How many moles of sodium chloride are there per L of this solution? A mole of sodium chloride is equivalent to 58.5 g of sodium chloride.

11. A doctor orders that a patient recieve 1.5 X 10-3 mole of sodium chloride. The only solution available contains 1.00 g per 100 mL of solution. A mole of sodium chloride is equivalent to 58.5 g of sodium chloride. How much of this solution should the nurse give the patient?

12. A sample of air contains 2.33 X 10-4 mg of lead per mL of gas. This air passes through an office, the volume of which is 3.25 X 104 L. Seven people normally work in this office. How many μg of lead will each person in the office receive from this sample of air?

ANSWERS

ANSWER KEY (with work shown)

**BELOW ARE TUTORIALS CREATED TO ASSIST WITH DIMENSIONAL ANALYSIS (includes problem solving tips, comments on sig. figs., etc.):**