CHEMISTRY CHAPTER 2. MEASUREMENTS AND CALCULATIONS SECTION 1. SCIENTIFIC METHOD The scientific method is a logical approach to solving problems by observing and collecting data, formulating hypotheses, testing hypotheses, and formulating theories that are supported by data.

qualitative (descriptive, without numbers) quantitative (numerical) Observing and Collecting Data Observing is the use of the senses to obtain information. Includes the aid of scientific instruments. Data may be qualitative (descriptive, without numbers) quantitative (numerical)

A system is a specific portion of matter in a given region of space that has been selected for study during an experiment or observation. Example – the contents of a flask.

Hypotheses are often “if-then” statements. Formulating Hypotheses Scientists use generalizations about the data to formulate a hypothesis, or testable statement. Hypotheses are often “if-then” statements. A hypothesis is not just a guess – it has scientific reasoning behind it.

What hypothesis was being tested?

Controls are the experimental conditions that remain constant. Testing Hypotheses Testing a hypothesis requires experimentation (or other types of observation) that provides data to support or refute a hypothesis or theory. Controls are the experimental conditions that remain constant. Variables are any experimental conditions that change.

Independent variable: what the researcher changes (or is changed by nature, such as time). Usually plotted on the x-axis. Dependent variable – this changes as a result of changes in the independent variable. Usually plotted on the y-axis.

What are the independent variables? What is the dependent variable? What do you think was controlled?

Depending on the results of testing, a hypothesis may be: confirmed (supported) revised rejected

example: atomic theory Theorizing One or more hypotheses that are confirmed may lead to a theory: a broad generalization that explains a body of facts or phenomena. example: atomic theory Theories are not proved, but may become more and more established. Successful theories predict results of new investigations.

Example – Bohr model of atom Models A theory may contain a model, a representation that helps us understand a complex set of information (but is simplified). Example – Bohr model of atom www.umich.edu/~radinfo/images/atom.gif

A law describes a pattern in nature but does not explain it. Ex. – Laws A law describes a pattern in nature but does not explain it. Ex. – law of gravitation: force = G • m1 • m2 / r2 law of multiple proportions (p. 168)

Scientific Method

Notice that the text does not use commas in writing numbers: SECTION 2. UNITS OF MEASUREMENT Note on commas in numbers Notice that the text does not use commas in writing numbers: 7 000 000 instead of 7,000,000 This is because in other countries commas are used instead of the decimal point: 2,14 instead of 2.14

We need to have standard measures that everyone agrees on. SI Measurement We need to have standard measures that everyone agrees on. Scientists all over the world have agreed on a single measurement system called Le Système International d’Unités, abbreviated SI. SI has seven base units. Most other units are derived from these seven.

SI (Le Systéme International d´Unités) Base units in bold

SI Base Units * not used in this course * *

tera T 1012 giga G 109 mega M 106 kilo k 103 deci d 10-1 centi c 10-2 Metric Prefixes (p. 35) Learn these! tera T 1012 giga G 109 mega M 106 kilo k 103 deci d 10-1 centi c 10-2

milli m 10-3 micro μ 10-6 nano n 10-9 pico p 10-12 femto f 10-15 Metric Prefixes (p. 35) Learn these! milli m 10-3 micro μ 10-6 nano n 10-9 pico p 10-12 femto f 10-15 atto a 10-18

American Scientist, Sept.-Oct. 2010

If the unit gets smaller, the number gets larger. Changing metric units by moving the decimal point If the unit gets smaller, the number gets larger. Move the decimal point to the right according to the power of ten. Example 1: change 50 MW (megawatts) to W mega means 106 move the decimal point six places to the right: 50 MW = 50 000 000 W

Example 2: change 3.25 kg (kilograms) to g kilo means 103 move the decimal point 3 places to the right: 3.25 kg = 3 250 g

If the unit gets larger, the number gets smaller. Move the decimal point to the left according to the power of ten. Example 1: change 3 000 mm (millimeters) to m milli means 10-3 move the decimal point 3 places to the left: 3 000 mm = 3 m

Example 2: change 68 μmol (micromoles) to mol micro means 10-6 move the decimal point 6 places to the left: 68 μmol = 0.000 068 mol

Mass is a measure of the quantity of matter. SI Base Units Mass Mass is a measure of the quantity of matter. The SI standard unit for mass is the kilogram. However, we will normally be using g or mg.

Scientists prefer to define base units using fundamental constants of nature. However, the kilogram is still defined by the mass of a solid piece of platinum and iridium in a vault in France.

http://www.npr.org/templates/story/story.php?storyId=112003322

Some scientists wish to replace the standard kilogram with a new standard (for example, based on the mass of a particular number of atoms in a crystal of silicon).

Weight is a measure of the gravitational pull on matter. Mass does not depend on gravity. Your weight will be smaller on the Moon, but your mass will be the same as on Earth. Conversion factors 1 kg = 2.2 lb (learn this) 1 lb = 454 g 16 oz = 1 lb 1 oz = 28 g

Length is a measure of distance. The SI standard for length is the meter. The meter is defined as the distance that light travels in 1/299 792 485 s in a vacuum.

1 m = 3.281 ft = 39.37 in (so a meter is about a yard) Conversion factors 1 m = 3.281 ft = 39.37 in (so a meter is about a yard) 2.54 cm = 1 in (learn) 0.62 miles = 1 km A non-SI unit used by chemists is the Angstrom (Å). 1 Å = 10-10 m = ____ nm

1 m = 3.281 ft = 39.37 in (so a meter is about a yard) Conversion factors 1 m = 3.281 ft = 39.37 in (so a meter is about a yard) 2.54 cm = 1 in (learn) 0.62 miles = 1 km A non-SI unit used by chemists is the Angstrom (Å). 1 Å = 10-10 m = 0.1 nm

Combinations of SI base units form derived units (see Table 3, p. 36). Derived SI Units Combinations of SI base units form derived units (see Table 3, p. 36). Ex.: pressure is measured in kg/(m•s2), or pascals

Derived SI Units 1 joule = 1 kg•m2/s2

Area is the amount of surface. The derived SI unit is square meters, m2 Area of a rectangle = length x width (A = l • w) Area of a circle: A = π r2 (r = radius) Volume is the amount of space occupied by an object. The derived SI unit is cubic meters, m3 The cubic centimeter, cm3, is often used

The liter, L, is a non-SI unit of volume. 1 mL = 1 cm3 How many cm3 in 1 L? 1 gal = 3.785 L 1 dm3 = ? L

1000 cm3 = 1 L 1 dm3 = (10 cm)3 = 1000 cm3 = 1 L

Density is the ratio of mass to volume, or mass divided by volume.

The derived SI unit is kilograms per cubic meter, kg/m3 g/cm3 or g/mL are also used Density is a characteristic physical property of a substance. (Extensive or intensive?)

Density can be used as one property to help identify a substance

The density of water at 20° C is almost exactly 1 g/cm3 If the density of something is less than this it will float in water; if greater, it will sink.

Problem solving – general guidelines Write the equation Substitute what you know (including units) Do the calculation Check that the number and units make sense

Sample Problem A A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm3. Calculate the density of aluminum. Given: mass (m) = 8.4 g volume (V) = 3.1 cm3 Unknown: density (D) Solution:

When solving for mass or volume, you can use two different approaches: Substitute what you know in the equation for density, and use algebra to calculate the unknown. Rearrange the equation to solve for m or V, then substitute. Sample Problem B – solve for mass What is the mass of a sample having a volume of 2 cm3 and a density of 6 g/mL?

Using the approach of substituting in the density equation: D = m/V Substitute: 6 g/ml = m / 2 mL (note that V = 2 cm3 = 2 mL) Solve: m = (6 g/mL) (2 mL) = 12 g

Sample Problem C – solve for volume What is the volume of a sample with a density of 18 g/cm3 and a mass of 9 g? Using the approach of rearranging the density equation before substituting: D = m/V DV = (m/V)V = m V = m/D Substitute: V = 9 g / (18 g/cm3) Solve: V = 0.5 cm3

Conversion Factors A conversion factor is a ratio (or fraction), equal to 1, derived from the equality between two different units that can be used to convert from one unit to the other. Examples: 60 s / 1 min = 1 1 m / 100 cm = 1 4 quarters / 1 dollar = 1

Dimensional analysis (or the factor-label method) is a mathematical technique that allows you to use units to solve problems involving measurements. In dimensional analysis, quantities in one unit are changed to the desired unit by multiplying by one or more conversion factors.

You will write the conversion factor so that the unit you want to remove will cancel out when you multiply. For example, to change a unit in the numerator, put it in the denominator of the conversion factor.

Example: find the number of quarters in 12 dollars 12 dollars × conversion factor

example: conversion factors for meters and decimeters Deriving Conversion Factors You can derive conversion factors if you know the relationship between the unit you have and the unit you want. example: conversion factors for meters and decimeters

Express a mass of 5.712 grams in kilograms. Sample Problem Express a mass of 5.712 grams in kilograms. 1 000 g = 1 kg Possible conversion factors: Which one should be used?

Use the one that cancels out the unit you want to change (g):