Chapter 2Chapter 2sec 2 and 3sec 2 and 3

Measurement and Calculation

• Write a brief paragraph describing your concept of the scientific method.

• Objectives1. Describe how chemists use the scientific method.

2. Explain the purpose of controlling the conditions of an experiment.

3. Explain the difference between a hypothesis, a theory, and a law.

Scientific Scientific MethodMethod

The scientific method is a series of steps followed to solve problems, including •collecting data •formulating a hypothesis •testing the hypothesis•stating conclusions

A scientist chooses which set of steps to use depending on the nature of the investigation.•Figure 8 from book

Scientific MethodScientific Method• Scientists often find that their results

do not turn out as expected. Such cases are not failures.

• Rather, scientists analyze these results and continue with the scientific method.

• Unexpected results often give scientists as much information as expected results do.

Scientific MethodScientific MethodSteps1.State/identify a problem (ask a question)2.Form (state) a hypothesis3.Design and perform an experiment (test the hypothesis)4.Gather/collect information (research the problem)5.Draw (a) conclusion(s) (organize your data)6.Report the results (So others may test your hypothesis for validity)

continuecontinue• A hypothesis is a reasonable and testable

explanation for observations.Variables -A factor that could affect the results of an

experiment • Independent (MV) - The variable you investigate

to determine its effect. This is the thing you change.

• Dependent (RV) - The variable you measure to see if the Manipulated Variable has any effect. This is the thing that changes in response to what you changed.

• Controlled (CV) - Variables in the experiment that do not change. They are kept the same in every part of the experiment.

Scientific ExplanationsScientific Explanations• What is your own opinion what a law and a

theory is? Think and write.• Share your opinion with your group.• Each group share their opinion in class.

Data from Experiments Can Lead to a Theory• In science, a theory is a well-tested explanation

of observations.• Theories are explanations, not facts, so they

can be disproved but can never be completely proven.

Theories and Laws Have Theories and Laws Have

Different PurposesDifferent Purposes• Some facts in science always hold true.

These facts are called laws.• A law is a statement or mathematical

expression that reliably describes a behavior of the natural world.

Difference• While a theory is an attempt to explain the

cause of certain events in the natural world, a scientific law describes the events.

ExampleExample• the law of conservation of mass states that

the products of a chemical reaction have the same mass as the reactants have.

• This law does not explain why matter in chemical reactions behaves this way; the law simply describes this behavior.

• Keep in mind that a hypothesis predicts an event, a theory explains it, and a law describes it.

2.3 Measurements and 2.3 Measurements and Calculations in ChemistryCalculations in Chemistry• Divide a sheet of paper into three columns.Divide a sheet of paper into three columns.• In the first column, list measuring devices and In the first column, list measuring devices and

instruments.instruments.

• In the second column, list what the devices in the In the second column, list what the devices in the first column measure.first column measure.

• Finally, in the last column, list the units in which Finally, in the last column, list the units in which the devices report their measurements.the devices report their measurements.

2.3 Measurements 2.3 Measurements and Calculations in and Calculations in

ChemistryChemistry

2.3 Accuracy and 2.3 Accuracy and Precision: Precision:

• Definitions: In outline and book page 55• Dart board example in book.

• How would you Explain this to a 5th grader?

• Know the difference between the two. • Compare accuracy of the same measurement

devices

2.3 Accuracy and 2.3 Accuracy and Precision: Precision:

Objectives•Distinguish between accuracy and precision in measurements.

•Determine the number of significant figures in a measurement, and apply rules for significant figures in calculations.

•Calculate changes in energy using the equation for specific heat, and round the results to the correct number of significant figures.

Accuracy and Accuracy and PrecisionPrecision

• The dictionary definitions of these two words do not clearly make the distinction as it is used in the science of measurement.

• Accurate means "capable of providing a correct reading or measurement."

• Precise means "exact, performance, or repeatable, reliable, getting the same measurement each time."

ExampleExample

To reduce the impact of error, scientists repeat their measurements and calculations many times.

If their results are not consistent, they will try to identify and eliminate the source of error.

Example of Example of MeasurementMeasurement

All measurements are assumed to be All measurements are assumed to be approximate with the last digit approximate with the last digit

estimated.estimated.

0 1 2

The length in The length in ““cmcm” here is ” here is written as:written as:

1.43 cm1.43 cm

The last digit “The last digit “33” is estimated as ” is estimated as 0.3 of the interval between 3 and 0.3 of the interval between 3 and

4.4.

Significant Digits and NumbersSignificant Digits and Numbers1.1. All non zero numbers are significantAll non zero numbers are significant

2.2. Zeros between non zero numbers are significantZeros between non zero numbers are significant

3.3. Leading zeros are never significantLeading zeros are never significant

4.4. Trailing zeros are not significant if no decimal pointTrailing zeros are not significant if no decimal point

5.5. Trailing zeros are significant if decimal point Trailing zeros are significant if decimal point

4.0500 cm 5 significant figures0.1061 cm 4 significant figures50.0 cm 3 significant figures50,600 cm 3 significant figures

Rule:Rule:

Rule 1. When approximate numbers are multiplied or divided, the number of significant digits in the final answer is the same as the number of significant digits in the least accurate of the factors.

Rule 1. When approximate numbers are multiplied or divided, the number of significant digits in the final answer is the same as the number of significant digits in the least accurate of the factors.

245 N 6.97015 N/m

(3.22 m)(2.005 m)P ExamplExampl

e:e:

Least significant factor (45) has only two (2) digits so only two are justified in the answer.The appropriate The appropriate way to write the way to write the answer is:answer is:

P = 7.0 N/m2P = 7.0 N/m2

Rule 2. When approximate numbers are added or subtracted, the number of significant digits should equal the smallest number of decimal places of any term in the sum or difference.

Rule 2. When approximate numbers are added or subtracted, the number of significant digits should equal the smallest number of decimal places of any term in the sum or difference.Ex: Ex: 9.65 cm + 8.4 cm – 2.89 cm = 9.65 cm + 8.4 cm – 2.89 cm = 15.16 cm15.16 cmNote that the least precise measure is 8.4 cm. Thus, answer must be to nearest tenth of cm even though it requires 3 significant digits.The appropriate The appropriate way to write the way to write the answer is:answer is:

15.2 cm15.2 cm

Rules for Rounding Rules for Rounding NumbersNumbers

Rule 2. If the remainder is greater than 5, increase the final digit by 1.

Rule 3. To prevent rounding bias, if the remainder is exactly 5, then round the last digit to the closest even number.

ExamplesExamplesRule 1. If the remainder beyond the last digit to be reported is less than 5, drop the last digit.

Round the following to 3 significant figures:

4.994994.99499

0.09400.09403395,63295,632

0.02030.020322

becomes becomes 4.994.99

becomes becomes 0.09400.0940

becomes becomes 95,60095,600

becomes becomes 0.02030.0203

ExamplesExamples

2.34522.3452

0.08750.08757723,650.023,650.0114.995024.99502

becomes becomes 2.352.35

becomes becomes 0.08760.0876

becomes becomes 23,70023,700

becomes becomes 5.005.00

ExamplesExamples

3.77503.7750000.024450.024450096,65096,650005.09505.095000

becomes becomes 3.783.78

becomes becomes 0.02440.0244becomes becomes 96,60096,600

becomes becomes 5.105.10

Sample Problem A

A student heats 23.62 g of a solid and observes that its temperature increases from 21.6°C to 36.79°C. Calculate the temperature increase per gram of solid.

Sample Problem A Solution

Calculate the increase in temperature by

subtracting the initial temperature (21.6°C)

from the final temperature (36.79°C).

temperature increase = final temperature −

initial temperature

36.79°C − 21.6°C = 15.19°C = 15.2°C

Sample Problem A Solution, Sample Problem A Solution,

continuedcontinuedCalculate the temperature increase per gram of solid by dividing the temperature increase by the mass of the solid (23.62 g).

Practice QuizPractice Quiz• Which of the following graph shows endothermic?

reactant

product

E

N

E

R

G

Y

Rxn progress

reactant

product

Rxn progress

ENERGY

Specific Heat CapacitySpecific Heat Capacity• Official definition: The amount of energy

required to heat one gram of a substance by one degree Celsius (or Kelvin)

• Symbol: c

How well things heat up and cool off.Conductors: Heat up and cool easily/quickly (Low

SHC)Insulators: Heat more slowly, cool slowly. (High

SHC)

CalculationCalculation• How much energy (heat) need substance

of mass of m to increase (or decrease) its T?

• Formula for solving heat (energy)

if TTT

TmcQ