Chapter 2

Measurements and Calculations Notes

I. SI (System of International) Units of Measurements

A. Metric System

Mass is measured in kilograms (other mass units: grams, milligrams)

Volume in liters Length in meters Time in seconds Chemical quantity in moles Temperature in Celsius

B. Prefixes Prefix Value Abbreviation Example  

Pico l x l0-12 ppm, pgNano l x l0-9 n nmMicro l x l0-6 gMilli l x l0-3 m mm, mgCenti l x l0-2 c cl, cgDeci l x l0-1 d dl, dg(stem: liter, meter, gram)Deka l x l01 da dag, dalHecto l x l02 hhl,hmKilo l x l03 k kl, kgMega l x l06 M Mg, MmGiga 1 X 109 G GgTera 1 X 1012T Tg

C. Derived Units C. Derived Units: combinations of

quantities: area (m2), Density (g/cm3), Volume (cm3 or mL) 1cm3 = 1mL

D. Temperature- Be able to convert between degrees Celcius and Kelvin.

Absolute zero is 0 K, a temperature where all molecular motion ceases to exist. Has not yet been attained, but scientists are within thousandths of a degree of 0 K. No degree sign is used for Kelvin temperatures.

Celcius to Kelvin: K = C + 273

Convert 98 ° C to Kelvin: 98° C + 273 = 371 K

II. Density – relationship of mass to volume D = M/V Density is a derived unit (from both mass and volume)

For solids: D = grams/cm3

Liquids: D = grams/mL Gases: D = grams/liter

Know these units

D = M V

Density (cont.)

Example Problems: 1. An unknown metal having a mass of

287.8 g was added to a graduated cylinder that contained 31.47 ml of water. After the addition of the metal, the water level rose to 58.85 ml. Calculate the density of the metal.

Density (cont.)

2. The density of mercury is 13.6 g/mL. How many grams would l.00 liter of mercury weigh?

3. A solid with a density of 11.3 g/ml has a mass of 5.00g. What is its volume?

IV. Using Scientific Measurements

A. Precision and Accuracy1. Precision – the closeness of a set of

measurements of the same quantities made in the same way (how well repeated measurements of a value agree with one another).

2. Accuracy – is determined by the agreement between the measured quantity and the correct value.

Ex: Throwing Darts

ACCURATE = CORRECT

PRECISE = CONSISTENT

B. Counting Significant Figures

When you report a measured value, it is assumed that all the figures are correct except for the last one, where there is an uncertainty of ±1. If your value is expressed in proper exponential notation, all of the figures in the pre-exponential value are significant, with the last digit being the least significant figure (LSF).

“7.143 grams” contains 4 significant figures

B. Counting Significant FiguresIf that value is expressed as 0.007143, it still has 4

significant figures. Zeros, in this case, are placeholders. If you are ever in doubt about the number of significant figures in a value, write it in exponential notation.

Example of nail on page 46: the nail is 6.36cm long. The 6.3 are certain values and the final 6 is uncertain! There are 3 significant figures in 6.36cm (2 certain and 1 uncertain). The reader can see that the 6.3 are certain values because they appear on the ruler, but the reader has to estimate the final 6.

Significant Figures Indicate precision of a measurement. Recording Significant Figures (sig figs)

Sig figs in a measurement include the known digits plus a final estimated digit

2.35 cm

The rules for counting significant figures are:

1. Leading zeros do not count. Ex: 0.0005 cm2. Captive zeros always count. Ex: 505 cm3. Trailing zeros count only if there is a

decimal.Ex: 5,000 vs 5,000.

Give the number of significant figures in the following values:

a. 38.4703 mL b. 0.00052 g c. 0.05700 s d. 6.19 x 101 years

Helpful Hint :Convert to exponential form if you are not certain as to the proper number of significant figures.

A very important idea is that you DO NOT ROUND OFF YOUR ANSWER UNTIL THE VERY END OF THE PROBLEM.

Significant Figures FlowchartMeasurement

What is the number?

No- not significant

Ex: 0.05

Yes, the zero is significant

Ex: 0.50

All the numbers are significant

Ex: 5.0

Trailing zeros are not significant

Ex: 50

Where are the zeros? Is there a decimal?

<1 >1

Before the # After the # Yes No

C. Significant Figures in Calculations

In addition and subtraction, your answer should have the same number of decimal places as the measurement with the least number of decimal places.

EX: find the answer for 12.734 -3.0

Solution: 12.734 has 3 figures past the decimal point. 3.0 has only 1 figure past the decimal point. Therefore, your final result, where only addition or subtraction is involved, should round off to one figure past the decimal point.

12.734- 3.0 9.734 -------- 9.7

Add/Subtract – additional example

3.75 mL+ 4.1 mL 7.85 mL

224 g+ 130 g 354 g 7.9 mL 350 g

3.75 mL+ 4.1 mL 7.85 mL

224 g+ 130 g 354 g

Multiplication & Division with Significant Figures

2. In multiplication and division, your answer should have the same number of significant figures as the least precise measurement.

61 x 0.00745 = 0.45445 = 0.45 2SF a. 32 x 0.00003987 b.   5 x 1.882 c.   47. 8823 X 9.322

Multiplication & Division with Significant Figures

3. There is no uncertainty in a conversion factor; therefore they do not affect the degree of certainty of your answer. The answer should have the same number of SF as the initial value.

a. Convert 25. meters to millimeters.

b. Convert 0.12 L to mL.

E. Scientific Notation Converting into Sci. Notation:

Move decimal until there’s 1 digit to its left. Places moved = exponent.

Large # (>1) positive exponentSmall # (<1) negative exponent

Only include sig figs.

E. Scientific Notation

-used to express very large or very small numbers 1 X 10-2

Convert to scientific notation:a. 1760 b. 0.00135c. 10.2 d. –0.00000673 e. 301.0 f. 0.000000532

Practice ProblemsExpand each number (or convert to regular

notation):a. 4.78 x l02 b. 5.50 x l04

c. –9.3 x l03 d. 8.31 x l0-1

e. 7.01 x l0-2 f. 8.5 x l0-6

E. Scientific Notation Calculating with Sci. Notation

(5.44 × 107 ) ÷ (8.10 × 104) =

5.44EXPEE

÷EXPEE ENTER

EXE7 8.10 4

= 671.6049383 = 672 g/mol = 6.72 × 102 g/mol

Type on your calculator: