Cliffs AP Chemistry, 3rd Edition

Scientific Notation

Try to use scientific notation when writing your answers. For example, instead of writing

1,345,255, write 1.345255 × 106. Remember always to write one digit, a decimal point, the rest

of the digits (making sure to use only the correct number of significant figures), and then times

10 to the proper power. An answer such as 0.000045 should be written 4.5 × 10 –5(2 s.f.). Also,

don’t forget that when you multiply exponents you add them and when you divide exponents

you subtract them. Your chemistry textbook or math book probably has a section that covers

significant figures, logs, antilogs, scientific notation, and the like. If your math background or

algebra skills are weak, you must thoroughly review and polish these skills before attempting

to do the problems in this book.

Accuracy

Absolute error =Experimental value −Accepted value

%%error=actual measuredactual- # 100

Consider the following expression:

.

(... )

4 3422 %

32 56 0 4303 0 08700

100

##

#

The % error for each term is

Term Calculation % Error

32.5 6 ± 0.01 [(32.56 + 0.01) – 32.56/32.56] · 100% 0.0307

0.430 3 ± 0.0001 [(0.4303 + 0.0001) – 0.4303/0.4303] · 100% 0.0232

0.0870 0 ± 0.00001 [(0.08700 + 0.00001) – 0.08700/0.08700] · 100% 0.0115

4.342 2 ± 0.0001 [(4.3422 + 0.0001) – 4.3422/4.3422] · 100% 0.0023

Adding up the % errors: 0.0307 + 0.0232 + 0.0115 + 0.0023 =0.0677% and

.

(... )

4 3422 %

32 56 0 4303 0 08700

100

##

# =28.07147 with 0.0677% error

reported as 28.07 ± 0.01

Use the term with the largest possible error (32.5 6 ± 0.01) for significant numbers.

Two types of errors may affect the accuracy of a measured value:

(a) determinate errors — errors that are instrumental, operative and involved in the methodol-

ogy. These types of errors can be avoided or corrected.

(b) indeterminate errors — accidental and/or random. These types of errors cannot be esti-

mated or predicted except through the use of probability theory and follow a Gaussian

distribution.

Questions Commonly Asked About the AP Chemistry Exam

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