Chapter Chapter Two Two Measurements in Chemistry Fundamentals of General, Organic, and Biological Chemistry 5th Edition James E. Mayhugh James E. Mayhugh Oklahoma City University Oklahoma City University 2007 Prentice Hall, Inc. 2007 Prentice Hall, Inc.
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Chapter Two Measurements in Chemistry Fundamentals of General, Organic, and Biological Chemistry 5th Edition James E. Mayhugh Oklahoma City University.
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ChapterChapter Two TwoMeasurements in
Chemistry
Fundamentals of General, Organic, and Biological Chemistry
5th Edition
James E. MayhughJames E. MayhughOklahoma City UniversityOklahoma City University2007 Prentice Hall, Inc.2007 Prentice Hall, Inc.
OutlineOutline► 2.1 Physical Quantities, Metric System► 2.2 Measuring Mass► 2.3 Measuring Length and Volume► 2.4 Measurement and Significant Figures► 2.5 Scientific Notation► 2.6 Rounding Off Numbers► 2.7 Converting a Quantity from One Unit to Another► 2.8 Problem Solving: Estimating Answers► 2.9 Measuring Temperature► 2.10 Energy and Heat► 2.11 Density► 2.12 Specific Gravity
Physical properties such as height, volume, and temperature that can be measured are called physical quantities. Both a number and a unit of defined size is required to describe physical quantity.
Relationships between metric units of length and volume and the length and volume units commonly used in the United States are shown below and on the next slide.
A mA m33 is the volume of a cube 1 m or 10 dm on edge. is the volume of a cube 1 m or 10 dm on edge. Each mEach m33 contains (10 dm) contains (10 dm)3 3 = 1000 dm= 1000 dm33 or liters. Each or liters. Each liter or dmliter or dm33 = (10cm) = (10cm)33 =1000 cm =1000 cm33 or milliliters. Thus, or milliliters. Thus, there are 1000 mL in a liter and 1000 L in a mthere are 1000 mL in a liter and 1000 L in a m33..
► To indicate the precision of a measurement, the value recorded should use all the digits known with certainty, plus one additional estimated digit that usually is considered uncertain by plus or minus 1.
► No further insignificant digits should be recorded.
► The total number of digits used to express such a measurement is called the number of significant figures.
► All but one of the significant figures are known with certainty. The last significant figure is only the best possible estimate.
► When reading a measured value, all nonzero digits should be counted as significant. There is a set of rules for determining if a zero in a measurement is significant or not.
► RULE 1. Zeros in the middle of a number are like any other digit; they are always significant. Thus, 94.072 g has five significant figures.
► RULE 2. Zeros at the beginning of a number are not significant; they act only to locate the decimal point. Thus, 0.0834 cm has three significant figures, and 0.029 07 mL has four.
► RULE 3. Zeros at the end of a number and after the decimal point are significant. It is assumed that these zeros would not be shown unless they were significant. 138.200 m has six significant figures. If the value were known to only four significant figures, we would write 138.2 m.
► RULE 4. Zeros at the end of a number and before an implied decimal point may or may not be significant. We cannot tell whether they are part of the measurement or whether they act only to locate the unwritten but implied decimal point.
Two examples of converting scientific notation back to Two examples of converting scientific notation back to standard notation are shown below. standard notation are shown below.
► The distance from the Earth to the Sun is 150,000,000 km. Written in standard notation this number could have anywhere from 2 to 9 significant figures.
► Scientific notation can indicate how many digits are significant. Writing 150,000,000 as 1.5 x 108 indicates 2 and writing it as 1.500 x 108 indicates 4.
2.7 Problem Solving: Converting a 2.7 Problem Solving: Converting a Quantity from One Unit to AnotherQuantity from One Unit to Another
► Factor-Label Method: A quantity in one unit is converted to an equivalent quantity in a different unit by using a conversion factor that expresses the relationship between units.
(Starting quantity) x (Conversion factor) = Equivalent quantity(Starting quantity) x (Conversion factor) = Equivalent quantity
Writing 1 km = 0.6214 mi as a fraction restates it in the form of a conversion factor. This and all other conversion factors are numerically equal to 1.
The numerator is equal to the denominator. Multiplying by a conversion factor is equivalent to multiplying by 1 and so causes no change in value.
►The directions on the bottle of cough syrup say to The directions on the bottle of cough syrup say to give 4.0 fl oz to the child, but your measuring spoon give 4.0 fl oz to the child, but your measuring spoon is in units of mL. How many mL should you is in units of mL. How many mL should you administer?administer?
Problem 2.15 Problem 2.15 from McMurry:from McMurry:
►One international nautical mile is defined as exactly One international nautical mile is defined as exactly 6076.1155 ft, and a speed of 1 knot is defined as one 6076.1155 ft, and a speed of 1 knot is defined as one nautical mile per hour. What is the speed in m/sec of nautical mile per hour. What is the speed in m/sec of a boat traveling at 14.3 knots?a boat traveling at 14.3 knots?
212oF - 32oF = 180oF covers the same range of temperature as 100oC - 0oC = 100oC covers. Therefore, a Celsius degree is exactly 180/100 = 1.8 times as large as a Fahrenheit degree. The zeros on the two scales are separated by 32oF.
► Converting between Fahrenheit and Celsius scales is similar to converting between different units of length or volume, but is a little more complex. The different size of the degree and the zero offset must both be accounted for.
► ooF = (1.8 x F = (1.8 x ooC) + 32C) + 32► ooC = (C = (ooF – 32)/1.8F – 32)/1.8
ProblemProblem
►A patient has a temperature of 38.8A patient has a temperature of 38.8ooC. What is her C. What is her temperature in temperature in ooF?F?
We know 2 equations:We know 2 equations: ooF = (1.8 x F = (1.8 x ooC) + 32C) + 32 ooC = (C = (ooF – 32)/1.8F – 32)/1.8
► Knowing the mass and specific heat of a substance makes it possible to calculate how much heat must be added or removed to accomplish a given temperature change.
► (Heat Change) = (Mass) x (Specific Heat) x (Temperature Change)
► H in cal; mass in g; C in cal/goC; Temp in oC► Using the symbols for change, H for heat, m
for mass, C for specific heat, and T for temperature, a more compact form is:
H = mCT
ProblemProblem
►What is the specific heat of Aluminum if it takes 161 What is the specific heat of Aluminum if it takes 161 cal to raise the temperature of 75 g of Al by 10.0cal to raise the temperature of 75 g of Al by 10.0ooC?C?
H = mCH = mCTT
solve for C (specific heat, cal/gsolve for C (specific heat, cal/g .o.oC)C)
Density relates the mass of an object to its volume. Density is usually expressed in units of grams per cubic centimeter (g/cm3) for solids, and grams per milliliter (g/mL) for liquids.
Density =Density = Mass (g)Mass (g)
Volume (mL or cmVolume (mL or cm33))
ProblemProblem
►What volume in mL should you measure out if you What volume in mL should you measure out if you need 16 g of ethanol which has a density of 0.79 g/mL? need 16 g of ethanol which has a density of 0.79 g/mL? (You only have a graduated cylinder, no balance.)(You only have a graduated cylinder, no balance.)
Specific gravity (sp gr): density of a substance divided by the density of water at the same temperature. Specific gravity is unitless. The density of water is so close to 1 g/mL that the specific gravity of a substance at normal temperature is numerically equal to the density.
Density of substance (g/ml)Density of substance (g/ml)
Density of water at the same temperature (g/ml)Density of water at the same temperature (g/ml)Specific gravity =Specific gravity =
The specific gravity of a liquid can be measured using an instrument called a hydrometer, which consists of a weighted bulb on the end of a calibrated glass tube. The depth to which the hydrometer sinks when placed in a fluid indicates the fluid’s specific gravity.
► Physical quantities require a number and a unit.► Preferred units are either SI units or metric units.► Mass, the amount of matter an object contains, is
measured in kilograms (kg) or grams (g). ► Length is measured in meters (m). Volume is
measured in cubic meters in the SI system and in liters (L) or milliliters (mL) in the metric system.
► Temperature is measured in Kelvin (K) in the SI system and in degrees Celsius (°C) in the metric system.
► The exactness of a measurement is indicated by using the correct number of significant figures.
► Significant figures in a number are all known with certainty except for the final estimated digit.
► Small and large quantities are usually written in scientific notation as the product of a number between 1 and 10, times a power of 10.
► A measurement in one unit can be converted to another unit by multiplying by a conversion factor that expresses the exact relationship between the units.
► Problems are solved by the factor-label method.► Units can be multiplied and divided like numbers.► Temperature measures how hot or cold an object is.► Specific heat is the amount of heat necessary to
raise the temperature of 1 g of a substance by 1°C. ► Density relates mass to volume in units of g/mL for a
liquid or g/cm3 for a solid.► Specific gravity is density of a substance divided by