CHEMISTRY

Chapter 2Measurements &

Calculations

Review of Physical Science….

Classification of Matter

Classifying Matter

Properties of Matter

Evidence of Chemical Change

Comparison of Physical and Chemical Properties

Chemistry—The science that seeks to understand

what matter does by studying

what atoms and molecules do.Virtually everything around you is composed of

chemicals.

• The Scientific Method is an organized, logical approach to solving scientific problems

• There are 6 steps to this process

1: State The Problem

• In order to solve a problem, you must first State the Problem

• This is done through observation. Observation leads to questioning.

• What is the question you are trying to answer?

2: Gather Information

• To investigate a problem, you must first gather information. Do your background research.– Technology is the workhorse used in this step It is

actually an extension of our senses

3: Form A Hypothesis

• A Hypothesis is simply an educated guess or a best explanation– It is based on the information you gathered in the

previous step and your observations

4: Test the Hypothesis• You must test your hypothesis and be able

to support it with facts.• This can be done through measurements of

with a standard unit (ie. meters, inches, degrees, etc.) or simply observations.– Quantitative Observations – measurements

Quantitative data contains a number– Qualitative Observations – all others

4: Testing/ExperimentationVariables

• Variables are factors that affect the result of an experiment

• Manipulated (Independent) Variable – manipulated by the experimenter and causes change in the Dependent Variable.

• Responding (Dependent) Variable – Results that DEPEND on changes to the Independent Variable

4: Testing/Experimentation Control Group/Variable

• In an experiment, the term control refers to the test subject that cannot be altered or changed.

• For instance, when a drug is being tested on a group of people, one person is the control and they will get a placebo (a pill without the drug). This allows a comparison.

For example, a scientist wants to see if the brightness of light has any effect on a moth

being attracted to the light.

• How bright the light is, is controlled by the scientist. This would be the manipulated (independent) variable.

• How the moth reacts to the different light levels would be the responding, (dependent) variable.

Mr. S. wanted to test the effect of magnesium on the

growth of bean plants.

•The manipulated variable that he manipulated is ______.•The responding variable that he could measure is __________.•How would the control variable be set up? ________

Mrs. C. wanted to test the effect of different food

coloring on food chosen by students.

•The manipulated variable that she manipulated is ______.•The responding variable that she could observe is___.•How would the control variable be set up?

4: Testing/ExperimentationControlled Variable

• Controlled Variables - is the same throughout the experiment.

• Why is it important to have a “control” variable in your experiment?– What would be the controlled variable for Mr. S.

experiment?– What would be the controlled variable for Mrs. C.

experiment?

5: Analyze the Data

• This is where you try to make sense of all the data you gathered from your experiment

• Technology is useful here as well because it is in this step that you do the math and make the graph…

5: Analyze the DataGraphing:

0102030405060708090

100

1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

RespondingVariable

Manipulated Variable

6: State the Conclusion

• After completing several tests and observations, you may then state your findings or conclusion.

A _____ states a summary of a repeated observation about nature.

LAW

What is difference between Scientific Law and Scientific Theory?

What is the difference between Accuracy and Precision?

Chapter 2

Accuracy and Precision continued

Percentage Error

Percentage error is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100.

Percentage error = Value

experimental-Value

accepted

Valueaccepted

100

Chapter 2

DENSITY

𝐃𝐞𝐧𝐬𝐢𝐭𝐲=𝐌𝐚𝐬𝐬

𝐕𝐨𝐥𝐮𝐦𝐞

You should be able to algebraically solve for any of the variable….

Density is a ratio of mass to volume for an object/fluid.

Density Problems:• A piece of tin has a mass of 16.52 g and has

the density of 7.31 g/cm3. What is the volume?

• A man has a 50.0 cm3 bottle completely filled with 163 g of a slimy green liquid. What is the density?

• A piece of metal has a density of 11.3 g/cm3 and a volume of 6.7 cm3. What is the mass of this piece of metal?

Scientific Notation: Writing Large and Small Numbers

• A number written in scientific notation has two parts.• A decimal part: a number that is between 1 and 10. • An exponential part: 10 raised to an exponent, n.

• A positive exponent means 1 multiplied by 10 n times.• A negative exponent (–n) means 1 divided by 10 n times.

Converting….

• If the decimal point is moved to the left, the exponent is positive.

• If the decimal is moved to the right, the exponent is negative.

• Move the decimal point to obtain a number between 1 and 10.

• Multiply that number (the decimal part) by 10 raised to the power that reflects the movement of the decimal point.

Try These….• The radius of a dust speck is 4.5 × 10–3 mm.

What is the correct value of this number in decimal notation (i.e., express the number without using scientific notation)?

• Convert 0.000459 to scientific notation.

Significant Figures: Writing Numbers to Reflect Precision

Pennies come in whole numbers, and a count of seven pennies means seven whole pennies.

Our knowledge of the amount of gold in a 10-g gold bar depends on how precisely it was measured.

The first four digits are certain; the last digit is estimated.

The greater the precision of the measurement, the greater the number of significant figures.

Scientific numbers are reported so that every digit is certain except the last, which is estimated.

• This balance has markings every 1 g.

• We estimate to the tenths place.

• To estimate between markings, mentally divide the space into 10 equal spaces and estimate the last digit.

• This reading is 1.2 g.

Estimating tenths of a gram

Estimating hundredths of a gram

• This scale has markings every 0.1 g.

• We estimate to the hundredths place.

• The correct reading is 1.26 g.

Exact Numbers Exact numbers have an unlimited number

of significant figures.

• Exact counting of discrete objects • Integral numbers that are part of an equation• Defined quantities – 12 inches/foot, 2.54cm/in,….• Some conversion factors are defined quantities while others

are not.

Counting significant figures in a correctly reported measurement

1. All nonzero digits are significant.2. Interior zeros (zeros between two numbers) are significant.3. Trailing zeros (zeros to the right of a nonzero number) that fall

after a decimal point are significant. 4. Trailing zeros that fall before a decimal point are significant. 5. Leading zeros (zeros to the left of the first nonzero number)

are NOT significant. They only serve to locate the decimal point.

6. Trailing zeros at the end of a number, but before an implied decimal point, are ambiguous and should be avoided.

Zeros & Determining the Number of Significant Figures

0.0035

1.080

2371

2.97×105

1 dozen = 12

100.00

100,000

How many significant figures are in each number?

two significant figures

four significant figures

four significant figures

three significant figures

unlimited significant figures

five significant figures

ambiguous

Significant Figures in CalculationsAddition and Subtraction Rule:

In addition or subtraction calculations, the result carries the same number of decimal places as

the quantity carrying the fewest decimal places.

Significant Figures in CalculationsAddition and Subtraction Rule:

We round the intermediate answer (in blue) to two decimal places because the quantity with

the fewest decimal places (5.74) has two decimal places.

Significant Figures in CalculationsAddition and Subtraction Rule:

We round the intermediate answer (in blue) to one decimal place because the quantity with the

fewest decimal places (4.8) has one decimal place.

Try These…

• What is the result of the following problem expressed with the correct number of significant figures? 20.15 – 10.569 =

Significant Figures in Calculations

Multiplication and Division Rule:

The result of multiplication or division carries the same number of significant

figures as the factor with the fewest significant figures.

Significant Figures in Calculations

Multiplication and Division Rule:

The intermediate result (in blue) is rounded to two significant figures to reflect the least

precisely known factor (0.10), which has two significant figures.

Significant Figures in CalculationsMultiplication and Division Rule:

The intermediate result (in blue) is rounded to three significant figures to reflect the least

precisely known factor (6.10), which has three significant figures.

Try These….

• What is the result of the following problem expressed in scientific notation with the correct number of significant figures?

(6.05 × 106) ÷ (4.020 × 10–9) =

Significant Figures in CalculationsRules for Rounding:

• When numbers are used in a calculation, the result is rounded to reflect the significant figures of the data.

• For calculations involving multiple steps, round only the final answer— do not round off between steps. This prevents small rounding errors from affecting the final answer.

Significant Figures in CalculationsRules for Rounding:

• Use only the last (or leftmost) digit being dropped to decide in which direction to round—ignore all digits to the right of it.

• Round down if the last digit dropped is 4 or less; round up if the last digit dropped is 5 or more.

Calculations Involving Both Multiplication/Division and Addition/Subtraction

In calculations involving both multiplication/division and addition/subtraction, do the steps in parentheses first; determine the correct number of significant figures in the intermediate answer without rounding;

then do the remaining steps.

Calculations Involving Both Multiplication/Division and Addition/Subtraction

In the calculation 3.489 × (5.67 – 2.3);

do the step in parentheses first. 5.67 – 2.3 = 3.37Use the subtraction rule to determine that the intermediate answer has only one significant decimal place.To avoid small errors, it is best not to round at this point; instead, underline the least significant figure as a reminder.

3.489 × 3.37 = 11.758 = 12

Use the multiplication rule to determine that the intermediate answer (11.758) rounds to two significant figures (12) because it is limited by the two significant figures in 3.37.

Calculations Involving Both Multiplication/Division and Addition/Subtraction

• What is the result of the following problem expressed in scientific notation with the correct number of significant figures?(6.051 × 106) ÷ (4.020 × 10–9) × (9.89 + 1.832) =

The Basic Units of Measurement

The unit system for science measurements, based on the metric system, is called the International System of units (Système International d’unités) or SI units.

Basic Units of Measurement

• The standard of length The definition of a meter, established by international agreement in 1983, is the distance that light travels in vacuum in 1/299,792,458 s. (The speed of light is 299,792,458 m/s.)

Basic Units of Measurement

• The standard of mass The kilogram is defined as the mass of a block of metal kept at the International Bureau of Weights and Measures at Sèvres, France. A duplicate is kept at the National Institute of Standards and Technology near Washington, D.C.

Basic Units of Measurement

• The standard of time The second is defined, using an atomic clock, as the duration of 9,192,631,770 periods of the radiation emitted from a certain transition in a cesium-133 atom.

Basic Units of Measurement

• The kilogram is a measure of mass, which is different from weight.

• The mass of an object is a measure of the quantity of matter within it.

• The weight of an object is a measure of the gravitational pull on that matter.

• Consequently, weight depends on gravity while mass does not.

Prefix Multipliers

Converting Between Units

• Units are multiplied, divided, and canceled like any other algebraic quantities.

• Using units as a guide to solving problems is called dimensional analysis.

Always write every number with its associated unit.

Always include units in your calculations, dividing them and multiplying them as if they were algebraic quantities.

Do not let units appear or disappear in calculations. Units must flow logically from beginning to end.

Converting Between Units using Dimensional Analysis

• In solving problems, always check if the final units are correct, and consider whether or not the magnitude of the answer makes sense.

• Conversion factors can be inverted because they are equal to 1 and the inverse of 1 is 1.

QuickTime™ and a decompressor

are needed to see this picture.

We can diagram conversions using a solution map.

• The solution map for converting from inches to centimeters is:

• The solution map for converting from centimeters to inches is:

Dimensional Analysis:

General Problem-Solving Strategy

• Identify the starting point (the given information).• Identify the end point (what you must find).• Devise a way to get from the starting point to the end point

using what is given as well as what you already know or can look up.

• You can use a solution map to diagram the steps required to get from the starting point to the end point.

• In graphic form, we can represent this progression asGiven Solution Map Find

Dimensional Analysis:

General Problem-Solving Strategy• Sort. Begin by sorting the information in the problem. • Strategize. Create a solution map—the series of steps that

will get you from the given information to the information you are trying to find.

• Solve. Carry out mathematical operations (paying attention to the rules for significant figures in calculations) and cancel units as needed.

• Check.

Dimensional Analysis:

Solving-Multistep Unit Conversion Problems

• Each step in the solution map should have a conversion factor with the units of the previous step in the denominator and the units of the following step in the numerator.

Dimensional Analysis:

Conversions with several units:

Format is called “Fishbone”, “railroad tracks”…..

When it comes time to do the math, the first number can be overlooked perhaps because it is visually different and not in line with other values.

An error of omission is less likely using the following non-fraction format:

Suppose you wanted to convert the mass of a 250 mg aspirin tablet to its equivalent in grams. Start with what you know and let the conversion factor units decide how to set up the problem. If a unit to be converted is in the numerator, that unit must be in the denominator of the conversion factor to cancel.

Now lets convert 250 mg to kg…

After cancelling, the only unit remaining is the one you want in the answer.

Metric Conversions

• problem: 4.4 km = ? cm solution: 4.4 km x 1000 m x 1 cm = 4.4 x 105 cm

1 km 0.01 m solution using scientific notation: 4.4 km x 1 x 103 m x 1 cm = 4.4 x 105 cm

1 km 1 x 10-2 m

Derived Units

• A derived unit is formed from other units. • Many units of volume, a measure of space, are

derived units. • Any unit of length, when cubed (raised to the third

power), becomes a unit of volume. • Cubic meters (m3), cubic centimeters (cm3), and cubic

millimeters (mm3) are all units of volume. • 1 cm3 is equal to 1 mL

Units Raised to a Power

Convert 1.2 cm3 to m3…

When converting quantities with units raised to a power, the conversion factor must also be raised to that power.

Dimensional Analysis:

Density

• Why do some people pay more than $3000 for a bicycle made of titanium?

• For a given volume of metal, titanium has less mass than steel.

• We describe this property by saying that titanium (4.50 g/cm3) is less dense than iron (7.86 g/cm3).

Calculating Density

• We calculate the density of a substance by dividing the mass of a given amount of the substance by its volume.

• For example, a sample of liquid has a volume of 22.5 mL and a mass of 27.2 g.

• To find its density, we use the equation d = m/V.

A Solution Map Involving the Equation for Density

• In a problem involving an equation, the solution map shows how the equation takes you from the given quantities to the find quantity.

Density as a Conversion Factor

• Density: • The density of a substance is its mass divided by its volume,

d = m/V , and is usually reported in units of grams per cubic centimeter or grams per milliliter.

• Density is a fundamental property of all substances and generally differs from one substance to another.

• For a liquid substance with a density of 1.32 g/cm3, what volume should be measured to deliver a mass of 68.4 g?

Density as a Conversion FactorSolution Map

Solution:

Measure 51.8 mL to obtain 68.4 g of the liquid.

Density as a Conversion Factor

• This table provides a list of the densities of some common substances.

• Density is a physical property of material.

Dimensional Analysis Problems… • Use conversion factors from the SI system to do the following conversions:

a. 2.4 meters to centimeters b. 65.5 centigrams to milligrams c. 5 liters to cubic decimeters d. The density of a substance is 2.7 g/cm3. What is the density of the substance in kilograms per liter?

• A car is traveling 65 miles per hour. How many feet does the car travel in one second?

• The density of water is one gram per cubic centimeter. What is the density of water in pounds per liter?

• How many basketballs can be carried by 8 buses? 1 bus = 12 cars 3 cars = 1 truck 1000 basketballs = 1 truck

Direct Proportion• Two quantities are directly

proportional to each other if dividing one by the other gives a constant value.

y kx• Read as “y is proportional

to x.”• Graph is a straight line.

Inverse Proportion• Two quantities are

inversely proportional to each other if their product is constant.

y 1/x• Read as “y is proportional

to 1 divided by x.” • Graph is a hyperbola.