Plan for Mon, 22 Sept 08

• Sign-in sheet…make sure to write your email extra legibly

• Introduction to the course, syllabus• Today’s Lecture:

– Uncertainty in measurement and sig figs (1.4-5)– Density (1.8)– Classification of matter (1.9)

• Other sections you should review:– 1.3 (units of measurement), 1.6 (dimensional

analysis), 1.7 (temperature conversions)

Uncertainty in Measurement

The accuracy of a measurement depends on the device.

Imagine measuring ~40-50 mL of water using a…100-mL beaker

100-mL graduated cylinder

or, The Reason You Have to Learn Sig Fig Rules

2 sig figs: one certain digit, one estimated digit

3 sig figs: two certain digits, one estimated digit

45 mL46.3 mL

Significant Figure Rules1. All nonzero digits are significant.

3.45 3 significant figures

2. Zeros.a. Leading Zeros appear before nonzero digits. These are not significant figures.

0.00040 2 significant figuresb. Captive Zeros appear between nonzero digits. These are always significant.

3.05 3 significant figuresc. Trailing Zeros appear at the right end of a number. These are significant only if

the number contains a decimal point.0.400 3 significant figures4.0 2 significant figures40,000 1 significant figure40,000. 5 significant figures4.00 x 104 3 significant figures

3. Exact Numbers that are determined by counting or by definition are considered to have infinite significant figures.

Sig Figs in Calculated Values• Since there is a limit to the accuracy of measured values,

there must also be a limit to the accuracy of calculations performed using measured values.

• In general, we can say that a calculated value can be no more accurate than the least accurate measurement used in the calculation.

• However, exactly how the least-accurate measurement determines the number of significant figures in the calculated result depends on the operation performed.

Sig Figs in Calculated Values (cont)• Multiplication/Division: The result of a multiplication or division must

have the same number of significant figures as the measurement with the fewest number of significant figures.

• For example, let's say you want to determine the area of a rectangular room using the lengths of two walls, 3.55 m and 11.65 m:

• Reporting 41.3575 m2 implies that the calculated area was more accurate than either of the wall measurements, which is impossible.

• Since your least accurate value has two certain digits and one estimated digit, your calculated digit simply can't do any better, so it cannot have more than three significant figures.

2 2

measured value measured value correct answercalculator answer 3 sig figs 4 sig figs 3 sig figs 6 digits

3.55 m 11.65 m 41.3575 m 41.4 m

• Addition/Subtraction: The result of an addition or subtraction must have the same number of decimal places as the measurement with the fewest number of decimal places.

• Let's say that in addition to the area, you were also interested in determining the perimeter of the room:

• Reporting 30.4 m would imply that this calculated value is somehow less accurate than either of the wall measurements.

• We have an estimate for the hundredths place in our measured values. We can include information about the hundredths place in our calculated value by adding a zero to the end, to give two decimal places and four significant figures.

measured values measured valuescalculator answer2 decimal places each 2 decimal places each 1 d 4 sig figs each 3 sig figs each

11.65 m + 11.65 m + 3.55 m + 3.55 m = 30.4 m correct answertwo decimal places

ecimal place 4 sig figs 3 digits

= 30.40 m

Sig Figs in Calculated Values (cont)

• Now, consider the difference between two masses, weighed on scales with different accuracy:

• Reporting 77.15 kg implies that the second scale is more accurate than it really is.

• The result is limited by the accuracy of the second scale.

measured value measured value correct answecalculator answer2 decimal places 1 decimal place 2 decimal places 4 sig figs 2 sig figs 4 digits

81.65 kg 4.5 kg = 77.15 kg = 77.2 kg r

1 decimal place 3 sig figs

Sig Figs in Calculated Values (cont)

Mass from first scale

Mass from second scale

Sig Fig Examples

0.004708 x 0.050 = 0.0002354 = 0.00024

15.004 – 0.0009 = 15.0031 = 15.003

2.0270/10.3333 = 0.19616192 = 0.19616

(3.40 + 1.1)/0.00874 = 4.5/0.00874 = 514.87414

= 510

Density: how much mass can we cram into a given volume?

Fig. 3-9, p. 81

For solids and liquids, the volume of a sample is directly proportional to the mass of the sample. (For gases the situation is a little more complicated).

We can define a proportionality constant called “density” and write a expression for this relationship...

m = d * v

Density and Phase

water

ice

liquid paraffin

solid paraffin

Petrucci, Fig. 13.30

In most compounds, the density of the solid is greater than that of the liquid.

But solid water is actually less dense than liquid water...this is why any of us are ALIVE.

Why does ice float in water?

Density Examples

1. A block has a volume of 25.3 cm3. Its mass is 21.7 g. What is the density of the block?

2. A cube of magnesium (Mg) is needed that has the mass 60.5 g. What must be the length of the cube’s edge in cm? The density of Mg is 1.74 g/cm3.

0.858 g/cm3

3.26 cm

Chemistry involves the study of matter on the molecular/atomic scale

http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

Just how small are we talking?

Matter has mass and takes up space.

Matter can exist in three different states, or phases.

Chemical vs. Physical Properties of Matter

• All substances have physical properties such as odor, color, shape, density, boiling point, melting point, electrical conductivity, etc.

• A physical change in a substance involves a change in one or more of these physical properties, but the chemical composition remains the same.– e.g., density of liquid vs solid water

• A chemical change in a substance means the chemical composition is altered (new substances are formed), which can be accompanied by changes in physical properties.– e.g., color change, temperature change, odor (think rotten milk)

ice water steam

During a physical change, the composition of the molecules stays the same, but one or more physical properties change.

When the state of matter changes, the association between neighboring molecules changes.

Physical Change

Chemical Changeliquid water

hydrogen gasoxygen gas

Applying an electrical current to a sample of liquid water causes the water molecules to break apart and form hydrogen gas and oxygen gas.

This is a chemical change, the composition of the molecules changes.

Example of a Chemical Change: Spontaneous Combustion

http://genchem.chem.wisc.edu/demonstrations/Gen_Chem_Pages/06thermopage/spontaneous_combustion_of_.htm

White Phosphorus, P4

A suspension of P4 in alcohol, a solvent that evaporates quickly.

When P4 is exposed to O2, it undergoes spontaneous combustion.

Chemical of Physical Change?

1. Baking bread

2. Grinding sugar into powder

3. Burning wood

4. Evaporation of water

5. Dissolving sugar in warm water

C

C

C

P

P

P

P

Classification of MatterThere are 3 broad classes of matter:

• Element: – composed entirely of atoms (all identical)– cannot be decomposed into other pure, stable substances

• Compound: – composed entirely of molecules (all identical)– can be decomposed into constituent elements or other compounds

• Mixture: – composed of different kinds of atoms or molecules, mixed together.– can be separated into constituent elements and/or compounds

Some pictures of elements

Fluorine (F2): gas at rm. temp.

Chlorine (Cl2): gas at rm. temp. Bromine (Br2): liq/gas

at rm. temp.

Iodine (I2): solid/gas at rm. temp.

Sulfur, S8Carbon (C) nanotubes

Osmium (Os) metal.

The densest element!!

d = 22.61 g/cm3

Carbon dioxide (CO2)

Copper sulfate, CuSO4

crystalline solid

Potassium bromide, KBr

Obsidian, volcanic glass.

70–75% SiO2, plus MgO, Fe3O4

amorphous solid

Some pictures of compounds

Gallium metal, an element

Alloy (a mixture) of gallium, indium, and tin...three different elements

Target Check 2.5: Elements or Compounds?

• Na2S

• Br2

• Potassium Hydroxide

• Fluorine

compound

compound

compound

element

element

element