chapter two measurements in chemistry fundamentals of general, organic, and biological chemistry 5th...

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.

Prentice Hall © 2007 Chapter Two 2

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


2.1 Physical Quantities2.1 Physical Quantities

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.


► A number without a unit is meaningless.

► To avoid confusion, scientists have agreed on a standard set of units.

► Scientists use SI or the closely related metric units.


► Scientists work with both very large and very small numbers.

► Prefixes are applied to units to make saying and writing measurements much easier.

► The prefix pico (p) means “a trillionth of.” ► The radius of a lithium atom is 0.000000000152

meter (m). Try to say it.► The radius of a lithium atom is 152 picometers

(pm). Try to say it.


Frequently used prefixes are shown below.Frequently used prefixes are shown below.


2.2 Measuring Mass2.2 Measuring Mass

► Mass is a measure of the amount of matter in an object. Mass does not depend on location.

► Weight is a measure of the gravitational force acting on an object. Weight depends on location.

► A scale responds to weight.► At the same location, two objects with identical

masses have identical weights.► The mass of an object can be determined by

comparing the weight of the object to the weight of a reference standard of known mass.


a) The single-pan balance with sliding counterweights. (b) A modern electronic balance.


Relationships between metric units of mass and the mass units commonly used in the United States are shown below.

ProblemProblem

►Express 3.27 mg in units of grams.Express 3.27 mg in units of grams.

►Express 19.3 kg in units of Express 19.3 kg in units of g.g.



2.3 Measuring Length and Volume2.3 Measuring Length and Volume

► The meter (m) is the standard measure of length or distance in both the SI and the metric system.

► Volume is the amount of space occupied by an object. A volume can be described as a length3.

► The SI unit for volume is the cubic meter (m3).


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..


The metric system is based on factors of 10 and is much easier to use than common U.S. units. Does anyone know how many teaspoons are in a gallon?


2.4 Measurement and Significant 2.4 Measurement and Significant FiguresFigures

► Every experimental measurement has a degree of uncertainty.

► The volume, V, at right is certain in the 10’s place, 10mL<V<20mL

► The 1’s digit is also certain, 17mL<V<18mL

► A best guess is needed for the tenths place.


► 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.


Below are two measurements of the mass of the same object. The same quantity is being described at two different levels of precision or certainty.


► 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.


2.5 Scientific Notation2.5 Scientific Notation

► Scientific notation is a convenient way to write a very small or a very large number.

► Numbers are written as a product of a number between 1 and 10, times the number 10 raised to power.

► 215 is written in scientific notation as:

215 = 2.15 x 100 = 2.15 x (10 x 10) = 2.15 x 102


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.


2.6 Rounding Off Numbers2.6 Rounding Off Numbers

► Often when doing arithmetic on a pocket calculator, the answer is displayed with more significant figures than are really justified.

► How do you decide how many digits to keep?► Simple rules exist to tell you how.


RULE 1. RULE 1. In carrying out a multiplication or division, the answer cannot have more significant figures than either of the original numbers.


►RULE 2. In carrying out an addition or subtraction, the answer cannot have more digits after the decimal point than either of the original numbers.


Rounding► RULE 1. If the first digit you remove is 4 or less,

drop it and all following digits.

2.4271 becomes 2.4 when rounded off to two significant figures.

► RULE 2. If the first digit removed is 5 or greater, round up by adding 1 to the last digit kept.

4.5832 is 4.6 when rounded off to 2 significant figures.

► If a calculation has several steps, it is best to round off at the end.

Problems Problems

►Express 1,066,298 to 5 significant figures using Express 1,066,298 to 5 significant figures using scientific notation.scientific notation.

►Express 2/3 to 4 significant figures.Express 2/3 to 4 significant figures.


ProblemProblem

►Determine the answer to: Determine the answer to:

6.023 x 106.023 x 102323 x 2.32 x 10 x 2.32 x 10-7-7

____________________________________________________________

Calculator gives too many significant figuresCalculator gives too many significant figures

1.397336 x 101.397336 x 1017 17 ?? ?? 1.40 x 101.40 x 101717 (3 sig. figures)(3 sig. figures)



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.


When solving a problem, the idea is to set up an

equation so that all unwanted units cancel, leaving only the desired units. How many km are there in 26.22 mi (a marathon)?

ProblemProblem

►An infant weighs 9.2 lb at birth. How many kg does An infant weighs 9.2 lb at birth. How many kg does the infant weigh?the infant weigh?

1kg = 2.205 lb is the conversion factor1kg = 2.205 lb is the conversion factor


ProblemProblem

►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?

1 L = 0.264 gal1 L = 0.264 gal

1 gal = 4 qt1 gal = 4 qt

1 qt = 32 fl oz 1 qt = 32 fl oz

1L = 1000 mL 1L = 1000 mL


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?

What we know: What we know:

1 knot = 1 naut. mi/hr = 6076.1155 ft/hour1 knot = 1 naut. mi/hr = 6076.1155 ft/hour

1 ft = 0.3048 m1 ft = 0.3048 m

1 hr = 60 min1 hr = 60 min

1 min = 60 sec1 min = 60 sec


Problem Solved !Problem Solved !


naut. mihr

14.3 x1 naut. mi

6.073x103 ftx

1 ft0.3048 m

x1 hr60 min

x 1 min60 sec

units ft/hr m/hr m/min m/sec

= 7.35 m/sec


2.9 Measuring Temperature2.9 Measuring Temperature

► Temperature is commonly reported either in degrees Fahrenheit (oF) or degrees Celsius (oC).

► The SI unit of temperature is the Kelvin (K).► 1 Kelvin, no degree, is the same size as 1 oC.► 0 K is the lowest possible temperature, 0 oC =

273.15 K is the normal freezing point of water. To convert, adjust for the zero offset.

► Temperature in K = Temperature in oC + 273.15► Temperature in oC = Temperature in K - 273.15


Freezing point of H2O Boiling point of H2O

32oF 212oF

0oC 100oC

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.


Fahrenheit, Celsius, and Kelvin temperature scales.


► 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


ProblemProblem


2.10 Energy and Heat2.10 Energy and Heat

► Energy: The capacity to do work or supply heat.► Energy is measured in SI units by the Joule (J); the

calorie is another unit often used to measure energy.► One calorie (cal) is the amount of heat necessary to

raise the temperature of 1 g of water by 1°C.► A kilocalorie (kcal) = 1000 cal. A Calorie, with a

capital C, used by nutritionists, equals 1000 cal.► An important energy conversion factor is:

1 cal = 4.184 J1 cal = 4.184 J


► Not all substances have their temperatures raised to the same extent when equal amounts of heat energy are added.

► One calorie raises the temperature of 1 g of water by 1°C but raises the temperature of 1 g of iron by 10°C.

► The amount of heat needed to raise the temperature of 1 g of a substance by 1°C is called the specific heat of the substance.

► Specific heat is measured in units of cal/gC


► 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)



2.11 2.11 DensityDensity

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.)



►Which is heavier, a ton of feathers or a ton of bricks?

►Which is larger?

►If two objects have the same mass, the one with the higher density will be smaller.


2. 12 Specific Gravity2. 12 Specific Gravity

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.


Chapter SummaryChapter Summary

► 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.


Chapter Summary Cont.Chapter Summary Cont.

► 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.


Chapter Summary Cont.Chapter Summary Cont.

► 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

the density of water at the same temperature.

chapter two measurements in chemistry fundamentals of general, organic, and biological chemistry 5th...

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