Chapter 3 Scientific Measurement. 3.1 Using and Expressing Measurements Measurement is a quantity...
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Transcript of Chapter 3 Scientific Measurement. 3.1 Using and Expressing Measurements Measurement is a quantity...
![Page 1: Chapter 3 Scientific Measurement. 3.1 Using and Expressing Measurements Measurement is a quantity that has both a number and a unit. Measurements are.](https://reader035.fdocuments.net/reader035/viewer/2022062421/56649e0f5503460f94afa323/html5/thumbnails/1.jpg)
Chapter 3
Scientific Measurement
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3.1 Using and Expressing Measurements
• Measurement is a quantity that has both a number and a unit.
• Measurements are fundamental to the experimental sciences.
• Scientific notation – a number that is written as the product of two numbers: a coefficient and 10 raised to a power.– Ex. – 602,000,000,000,000,000,000,000 = 6.02 x 1023
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Scientific Notation
In scientific notation, the coefficient is always equal to or greater than one and less than 10.
Ex. – 6.02 x 1023
coefficient, > 1 < 10
In other words, only one digit in front of the decimal.
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Accuracy, Precision, & Error
• Accuracy – a measure of how close a measurement comes to the actual or true value of what is measured.
• Precision – a measure of how close a series of measurements are to one another. – Examine figure 3.2 on page 64 in your text.
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Determining Error
• Accepted value – correct value based on reliable references.
• Experimental value – value measured in the lab.
• Error – difference between the experimental value and the accepted value.– Error = experimental value – accepted value
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Percent Error
• Error can be positive or negative.• The magnitude of error show the amount by which
the experimental value differs from the accepted value.– Thermometer readings
Percent error = the absolute value of the error divided by the accepted value, multiplied by 100.
% error = (error/accepted value) x 100%
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Significant Figures(sig figs)
• Significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.
• The correct number of sig figs must be reported because calculated answers often depend on the number of sig figs in the values used in the calculation.
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Rules for Determining Sig Figs
1. Every nonzero digit in a reported measurement is assumed to be significant.
• 24.7 m, 0.743m,714m = 3 sig figs
2. Zeros appearing between nonzero digits are significant.
• 7003m, 40.79m, 1.503m = 4 sig figs
3. Leftmost zeros appearing in front of nonzero digits are not significant.
• 0.0071m, 0.42m,0.000099m = 2 sig figs
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Rules for determining sig figs, cont.
4. Zeros at the end of a number and to the right of a decimal point are always significant.
• 43.00m, 1.010m, 9.000m = 4 sig figs
5. Zeros at the rightmost end of a measurement that lie to the left of an understood decimal point are not significant if they serve as placeholders to show the magnitude of the number.
• 300m, 7000m, 27,210m = 1,1,&4 sig figs respectively
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Rules for determining sig figs, cont.
6. Two situations in which numbers have an unlimited number of sig figs.
1. If you count 23 items, for example, people in a classroom, then there are exactly 23 people and this value has an unlimited number of sig figs.
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Rules for determining sig figs, cont.
2. Involves exactly defined quantities such as those found w/in a system of measurement.
• Example – 60 min = 1 hr or 100cm = 1m
Each of these numbers has an unlimited number of sig figs.
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Sig Figs in Calculations
A calculated answer cannot be more precise than the least precise measurement from which it was calculated.
Example – an area of carpet measures 7.7m by 5.4m. You get an answer of 41.48m2.
Even though you got an answer with 4 sig figs, the measurements used in the calculation had only two sig figs. So the answer must also be reported to two sig figs.
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Calculating Sig Figs
• Addition & Subtraction– Answer should be rounded to the same number
of decimal places (not digits), as the measurement with the least number of decimal places.
Example – 12.52 meters + 349.0 meters + 8.24 meters = what?
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Calculating Sig Figs
• Multiplication & Division– Answer must be rounded to the same number of
sig figs as the measurement with the least number of sig figs.
– Position of the decimal point has nothing to do with the rounding process when multiplying and dividing measurements. Only in addition & subtraction problem rounding.
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3.2 International System of Units
• The international System of Units (SI) is a revised version of the metric system.
• The five SI base units commonly used by chemists: meter, kilogram, Kelvin, second, and the mole.
• Refer to table 3.1 on page 73.
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Units and Quantities
• Units of length (Table 3.3, p. 74)– Meter and its prefixes
• Units of volume (Table 3.4,p. 75)– Liter and its prefixes– Cubic centimeters
• Units of mass (Table 3.5, p. 76)– Gram and its prefixes, especially kilo- & milli-
• Units of temperature – Kelvin = °C + 273
• Units of energy– Joule
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Temperature
• Kelvin is an absolute scale.
• There are no negative Kelvin temperatures.– It is incorrect to say degrees Kelvin or Kelvin
degrees.
The zero point on the Kelvin scale, 0 K is called absolute zero.
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Energy (Joules)
• The joule (J) and the calorie are common units of energy.
• Energy is the capacity to do work or to produce heat.
• The joule is the SI unit of energy, named after James Prescott Joule, an English physicist.
• One calorie (cal) is the quantity of heat that raises the temperature of 1g of pure water by 1°C.– 1 J = 0.2390 cal & 1 cal = 4.184 J
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3.3 Conversion Factors
Equivalent Measurements– 1 dollar = 4 quarters = 10 dimes = 20 nickels =
100 pennies– 1 meter = 10 decimeters = 100 centimeters =
1000 millimeters
• A conversion factor is a ratio of equivalent measurements.
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Conversion Factors
• When measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the measured quantity remains the same.
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Dimensional Analysis
• Dimensional analysis is a way to analyze and solve problems using units, or dimensions, of the measurements. – Turn to page 82, sample problem 3.5 for an
example.
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Converting Between Units
• Often a measurement needs to be expressed in a unit different from the one given or measured initially.– Turn to page 84 and examine sample problem
3.7.
• Conversion between units often involves more than one conversion factor. – Turn to page 85 and examine sample problem
3.8.
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Converting to Complex Units
• More steps must be employed when given a ratio of two units, such as mpg, miles per gallon, or g/cm3.– Examine sample problem 3.9 on page 86.
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Sec. 3.4 Density
• Density = mass/volume– Mass = density x volume
– Volume = density/mass
Density of solids & liquids measured in g/cm3
Density of gases measured in g/L
Density is an intensive property that depends on the composition of a substance, not on the size of the sample.
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Density & Temperature
Knowns• Mass = 3.1 g• Volume = 0.35 cm3
Unknown• Density = ?g/ cm3
A copper penny has a mass of 3.1 g & a volume of 0.35 cm3. What is the density of copper?
Density of a substance generally decreases as its temperature increases.
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Calculate & Evaluate• Solve for the unknown
– D = m/v = 3.1 g/0.35 cm3 =
8.8571 g/cm3 = 8.9 g/ cm3
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Conclusion of Ch. 3
• Accuracy and Precision– Accuracy involves the measured value against
the correct value.– Precision involves comparing values of
repeated measurements.
• SI units
• Conversion Factors & Dimensional Analysis
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Conclusion of Ch. 3• Significant Figures (Sig Figs)
– Multiplication & Division - answer must be rounded to the same number of sig figs as the measurement with the least number of sig figs
– Addition & Subtraction - answer should be rounded to the same number of decimal places (not digits), as the measurement with the least number of decimal places.
• Density = mass/volume– Mass = density x volume– Volume = density/massDensity is an intensive property that depends only on the composition
of a substance.The density of a substance generally decreases as its temperature
increases.
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Questions?