Re: Conversion Factors are killing my grade, can you help?

Dear Sarah,

Sorry for the late response. I usually try to respond within a week, but I have been away on a trip.

It seems that you are having difficulties using dimensional analysis, which tells you how to manipulate units. This concept is crucial in helping you solve your problems. The equations are also important, but they depend on the problem and is where the real chemistry is found. So, I'll explain how to work with units and demonstrate the principles using the problem you gave.

Most things that we measure have units. For example, a person can be 5.5 feet tall, a piece of paper can weigh 1.0 grams, or a phone call can last 2 minutes. In each, there is a value (5.5, 1.0, 2) and a unit (feet, grams, minutes). A value without a unit is meaningless. For example, what is a book which is 10 heavy? Is it 10 grams, 10 kilograms, 10 pounds, etc.?

When we do calculations on numbers, we do it on both the value and the unit. For example, speed is defined as distance divided by time. So, a person that moves 10 meters in 5 sec has a speed of (10 m)/(5 sec) = 1 m/sec. Note that we divided both the values (10/5 = 2) and the units (m/sec). From this example, you can see that units can be handled algebraically, which allows you to keep track of units in calculations.

Dimensional analysis is also very useful when converting units. For example, suppose you wanted to convert 3.50 inches into centimeters. There are 2.54 centimeters per inch. Another way of saying this is to equate them: 2.54 cm = 1 inch. If we divide both sides by 1 inch, we have 2.54 cm / 1 inch = 1. Note that the 1 on the right hand side has no units! Since multiplying by 1 (no units) doesn't change a number, we can multiply by (2.54 cm / 1 inch). So,

                                        2.54 cm
3.50 inch = 3.50 inch x 1 = 3.5 inch x --------- = 8.89 cm
                                        1 inch

Above, the values multiple normally: 3.50 x 2.54 = 8.89. For the units, the inches cancel each other out and all you're left with is cm. Both cm and inches are units of length, so you've successfully converted units!

Now, let's look at how dimensional analysis is used in your problem. First, start with the definition of density: density = mass / volume Since you are given a mass and a density, solve for volume: volume = mass / density. Now, we know mass is 50.0 g and density is 0.950 g/cm³, so

             50.0 g
volume = -------------- = 52.6 cm^3
          0.950 g/cm^3

Above, the grams cancel each other, and algebraically cm³ comes to the numerator. The division of the values is 50.0/.950 = 52.6, so the final answer is 52.6 cm³. As practice, to convert to liters, use the fact that 1000 cm³ = 1 L, so

                            1 L
52.6 cm^3 = 52.6 cm^3 x ----------- = 0.0526 L
                         1000 cm^3

I hope that clarifies how to use units and dimensional analysis. If you have any more questions, feel free to post them to MadSci. Good luck with your classes!

Your MAD Scientist,
Raymond Cheong

References

http://www.chemistrycoach.com/math_skills_for_chemistry_tutori.htm