Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 107	Fundamentals of Chemistry	Fall 2008
Lecture Notes: 9 September	© R. Paselk 2005
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Memorize: 1 mL = 1 cm³; 1 inch = 2.54 cm; 1 liter is about 1 quart; density of water = 1 g/mL; 0° C = 32 °F, 100°C = 212 °F, -40 °C = -40 °F

Dimensional (Unit) Analysis and Problem Solving

A convenient check on your work, or even a way to determine the best approach to a problem, is to use dimensional analysis. This simply means to include all of the units for each factor in an equation, and then to check to see that the units on both sides of the equation are equal.

For example, how long is a one foot ruler? Know conversion for cm to inches: 2.54 cm = 1 inch (no sig figs, defined ) [ans. = 30.48 cm]

Let's try some density problems. First recall that the units of density are g/cm³ or g^.cm^-3.

• A student found that 20.0 mL of a liquid weighed 35.987 g. What is its density?
  
• Using a jewelers balance a student found that a coin weighed 2.34 carats in air. By weighing it again submerged in water she found it had a volume of 0.034 mL. What is its density? (1 carat = 200 mg, defined)

Heat and Specific Heat: Earlier we spoke of heat as a measure of energy transferred between objects of different temperatures. We are already familiar with the units of temperature, what are the units of heat?

• joule (SI unit): It takes 4.184 J to raise 1 g of water at 20 °C 1 °C.
• calorie (metric, non-SI unit): It takes 1 cal to raise 1 g of water at 20 °C 1°C. Thus 1 cal = 4.184 J (defined).
• Calorie (large Calorie = nutritional Calorie): 1 Calorie = kilocalorie.

Let's look at a specific heat problem. Specific heat is the amount of heat it takes to raise 1 g of a specific substance 1 °C. Specific heats for other substances are relative to water, so no units (comparing results in canceling out units).

The heat transferred in a process (q) is summarized in the equation:

Heat = q = mC_spT

Example: 750 calories of heat is transferred to 100.0 g of water at 20.00 °C. What will the new temperature of the water be assuming no heat is lost to the container of the surroundings?

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Last modified 9 September 2008