The%20Mathematics%20of%20Chemistry

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The Mathematics of Chemistry
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• Significant Figures

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Uncertainty in Measurement

• Measurements always have uncertainty.
• Significant figures are the number of digits that
  are certain (can be measured) and the first
  uncertain digit.

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Accuracy and Precision

• Accuracy refers to how closely a measurement
  agrees with the accepted or true value.
• Precision refers to reproducibility of
  measurements.
• Chemistry calculations utilize significant
  figures to communicate uncertainty.

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• Rules for Significant Figures
• Non-zero digits and zeros between
• non-zero digits are always significant.
• 2. Leading zeros are not significant.
• 3. Zeros to the right of all non-zero digits
• are only significant if a decimal point
• is shown.

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• Rules for Significant Figures
• For values written in scientific notation, the
  digits are only significant if a decimal point is
  shown.
• In a common logarithm, there are as many digits
  after the decimal point as there are significant
  figures in the original number.

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Rules for Finding Significant Figures

• Rule 1- Non-zero digits and zeros between
  non-zero digits are always significant.

00340.003210
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Rules for Finding Significant Figures

• Rule 1- Non-zero digits and zeros between
  non-zero digits are always significant.

00340.003210
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Rules for Finding Significant Figures

• Rule 2 - Zeros to the right of all non-zero
  digits are only significant if a decimal point is
  shown.

00340.003210
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Rules for Finding Significant Figures

• These zeros are not significant. There is not a
  rule that supports counting them.

00340.003210
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How many significant figures?

• 00340.0
• 4
• Rule 3

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How many significant figures?

• 800.1
• 4
• Rule 1

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How many significant figures?

• 0800.10
• 5
• Rules 1 and 3

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How many significant figures?

• 800
• 1
• Rule 3

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How many significant figures?

• 800.
• 3
• Rule 3

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How many significant figures?

• 0.008
• 1
• Rule 2

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How many significant figures?

• 0.180
• 3
• Rule 3

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Using Significant Figures when Adding and
Subtracting in Calculations

• Determine the number of significant figures in
• the decimal portion of each of the numbers
  in
• the problem.
• 2. Add or subtract the numbers.
• Round the answer to match the least number of
• places in the decimal portion of any number
  in
• the problem.

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Using Significant Figures when Adding and
Subtracting

• Give it a try!
• Add 0.03 g of NaCl to 155 g of water. What is
  the total mass?
• Answer 155 g because the mass of water has no
  decimal places, so the final answer must be
  written with no decimal places.

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Using Significant Figures when Adding and
Subtracting

• 892.542g
• 20.629g
• 0.18g
• 4.20g

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3
2
2

917.551
The least amount of significant figures to the
right of the decimal in the numbers is 2
therefore, the answer should only have 2
significant figures to the right of the decimal.
917.55 g
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Using Significant Figures when Multiplying and
Dividing

• Determine how many significant figures each
  numbers being multiplied or divided has, and note
  which number has the fewest.
• Complete the calculation.
• Write the answer using the same number of
  significant figures as the least number of
  significant figures found in the numbers used in
  the calculation.

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Using Significant Figures when Multiplying and
Dividing

• 28.3 cm X 5.0 cm ____cm2
• 28.3 has 3 significant figures, and 5.0 has 2
  significant figures therefore, the answer 141.5
  should be written 140, so that it only has 2
  significant figures.
• 140 cm2

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Try it!

• 454.02 g of aluminum hydroxide multiplied by 5.2
  g equals how many grams?
• 454.02 g X 5.2 g _____ g
• Rule Write the answer using the same number of
• significant figures as the least number of
• significant figures found in the numbers used in
  the
• calculation.

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Scientific Notation

• Expanded Notation

• Scientific Notation

1. 2.63 X 10- 3 moles
2. 1.90 X 10-7 moles
3. 2.593516 X 105 grams
4. 1 X 105 milliliters

• A. 0.00263 moles
• .000000190 moles
• 259, 351.6 grams
• 100,000 milliliters