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**Measurement and Calculation**

Chapter 2 sec 2 and 3 Measurement and Calculation

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Scientific Method Write a brief paragraph describing your concept of the scientific method. Objectives Describe how chemists use the scientific method. Explain the purpose of controlling the conditions of an experiment. Explain the difference between a hypothesis, a theory, and a law.

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**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

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Scientific 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.

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**Scientific Method Steps State/identify a problem (ask a question)**

Form (state) a hypothesis Design and perform an experiment (test the hypothesis) Gather/collect information (research the problem) Draw (a) conclusion(s) (organize your data) Report the results (So others may test your hypothesis for validity)

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continue 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.

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**Scientific 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.

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**Theories and Laws Have Different 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.

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Example 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.

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**2.3 Measurements and Calculations in Chemistry**

Divide a sheet of paper into three columns. In the first column, list measuring devices and instruments. In the second column, list what the devices in the first column measure. Finally, in the last column, list the units in which the devices report their measurements.

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**2.3 Measurements and Calculations in Chemistry**

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**2.3 Accuracy and 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

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**2.3 Accuracy and 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.

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**Accuracy and Precision**

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."

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Example 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.

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**Example of Measurement**

All measurements are assumed to be approximate with the last digit estimated. The length in “cm” here is written as: 1.43 cm 1 2 The last digit “3” is estimated as 0.3 of the interval between 3 and 4.

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**Significant Digits and Numbers**

All non zero numbers are significant Zeros between non zero numbers are significant Leading zeros are never significant Trailing zeros are not significant if no decimal point Trailing zeros are significant if decimal point Rule: cm 2 significant figures cm 5 significant figures cm 4 significant figures 50.0 cm 3 significant figures 50,600 cm 3 significant figures

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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. Example: Least significant factor (45) has only two (2) digits so only two are justified in the answer. The appropriate way to write the answer is: P = 7.0 N/m2

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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: cm cm – 2.89 cm = cm Note 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 way to write the answer is: 15.2 cm

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**Rules for Rounding Numbers**

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

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Examples Rule 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: becomes becomes becomes ,600 95,632 becomes

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Examples Rule 2. If the remainder is greater than 5, increase the final digit by 1. Round the following to 3 significant figures: 2.3452 becomes becomes becomes ,700 23,650.01 becomes

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Rule 3. To prevent rounding bias, if the remainder is exactly 5, then round the last digit to the closest even number. Round the following to 3 significant figures: Examples becomes becomes 96,6500 becomes ,600 becomes

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Sample Problem A A student heats 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.

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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

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**Sample Problem A Solution, continued**

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

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**Practice Quiz Which of the following graph shows endothermic? E N R G**

Y E N R G Y reactant product product reactant Rxn progress Rxn progress

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**Specific 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)

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Calculation How much energy (heat) need substance of mass of m to increase (or decrease) its T? Formula for solving heat (energy)

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