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The Mathematics of ChemistryPowerPoint Presentation

The Mathematics of Chemistry

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The Mathematics of Chemistry

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The Mathematics of Chemistry

4

5

2

8

Significant Figures

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

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

- 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.

- Rules for Significant Figures (cont.):
- For values written in scientific notation, the digits in the coefficient are significant.
- In a common logarithm, there are as many digits after the decimal point as there are significant figures in the original number.

Rule #1- Non-zero digits….. are always significant.

00340.003210

Rule #1- …zeros between non-zero digits are always significant.

00340.003210

Rule # 2 – Leading zeros are not significant.

00340.003210

Rule #3 - Zeros to the right of all non-zero digits are only significant if a decimal point is shown.

00340.003210

00340.0

4

Rules #1, 2, and 3

800.1

4

Rule #1

0800.10

5

Rules # 1, 2, and 3

800

1

Rules # 1 and 3

800.

3

Rules # 1 and 3

0.008

1

Rules # 1 and 2

0.180

3

Rules # 1, 2, and 3

- 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.

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.

892.542g

20.629g

0.18g

4.20g

3

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

- 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.

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

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.

Expanded Notation

Scientific Notation

2.63 X 10- 3 moles

1.90 X 10-7moles

2.593516 X 105 grams

1 X 105 milliliters

A. 0.00263 moles

- .000000190 moles
- 259, 351.6 grams
- 100,000 milliliters