Lecture 3

A. States of Matter: Summary  

Matter may be heterogeneous or homogeneous

Homogeneous matter may be a pure substance or a solution

Pure substances may be elements or compounds

Pure solids may have network structures or molecular structures

See Lecture 1, Lecture 2, and Figure 1.1 in the 4th edition of Kotz and Treichel

B. Why Pay Attention to Units?

Read "The Gimli Glider", p. 42 in the 4th edition of Kotz and Treichel

C. Percentages

Percent: from the Latin per centum, "per hundred"

For example, assume that the Chemistry Club orders 20 pizzas and 6 are pepperoni. Let's calculate the percentage of pepperoni pizzas, which is the number of pizzas that would be pepperoni IF the Chemistry Club had ordered 100 pizzas.

Note that 6 pepperoni pizzas/20 pizzas represents the fraction of the pizzas that are pepperoni. Thus,

% pepperoni pizzas = (fraction of pepperoni pizzas) * 100

Percentage is used in many contexts, e.g.,

• % right on an exam (score out of 100 possible marks = fraction correct * 100)
• % composition (how many jellybeans in 100 are black?) = fraction black * 100
• % error = 100*(accepted value-your value)/accepted value
• mass % of X = (grams of X/100 grams of sample) = fraction of X by mass * 100
• volume % of X = (mL of X in 100 mL of sample) = fraction of X by volume * 100

D. Example: Mass % and its use in calculations

A sample of iron ore contains 32.5 mass % of the iron mineral Fe₂O₃. Fe₂O₃ is 69.9 mass % iron. How much iron ore must be processed in order to produce 10.0 kg of metallic iron?

32.5 mass % Fe₂O₃ = 32.5 kg Fe₂O₃/100 kg iron ore

69.9 mass % iron = 69.9 kg Fe/100 kg Fe₂O₃

Therefore,

= 44.0 kg iron ore must be processed to yield 10.0 kg of metallic iron

 

E. Example: Volume % and its use in calculations

U. S. beer is typically 3.8 mass % alcohol, whereas Canadian beer is usually 5.0 volume % alcohol. Convert 3.8 mass % alcohol to volume % alcohol. The density of beer is 1.010 g/mL; the density of pure alcohol is 0.7893 g/mL.

3.8 mass % means that there is 3.8 g alcohol in 100 g beer

Volume % is the volume of alcohol in 100 mL of beer

So convert the masses to volumes.

3.8 g alcohol * (1 mL alcohol/0.7893 g) = 4.81 mL alcohol

100 g beer * (1 mL beer/1.010 g beer) = 99.0 mL beer

Thus, the volume % alcohol is the volume fraction of alcohol * 100

= (4.81 mL alcohol/99.0 mL beer) * 100

= 4.86% alcohol. (Round to 4.9% since there are 2 s.f. in 3.8 mass %)

Hence, Canadian beer and American beer have about the same alcoholic strength.

 

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Last modified September 19, 2000 by M. F. Richardson
© Brock University, 2000