Measurements in Chemistry

Measurements in Chemistry
Fundamentals of General, Organic & Biological Chemistry Chapter Two Measurements in Chemistry

Stating a Measurement In every measurement, a number is followed by a unit. Observe the following examples of measurements: number + unit m L lb hr

The Metric System (SI) The metric system is
A decimal system based on 10. Used in most of the world. Used by scientists and in hospitals.

Units in the Metric System
In the metric and SI systems, a basic unit identifies each type of measurement:

Length Measurement In the metric system, length is measured in meters using a meter stick. The metric unit for length is the meter (m).

Volume Measurement Volume is the space occupied by a substance.
The metric unit of volume is the liter (L). The liter is slightly bigger than a quart. A graduated cylinder is used to measure the volume of a liquid.

Mass Measurement The mass of an object is the quantity of material it contains. A balance is used to measure mass. The metric unit for mass is the gram (g).

Learning Check In each of the following, indicate whether the unit describes 1) length 2) mass or 3) volume. ____ A. A bag of tomatoes is 4.6 kg. ____ B. A person is 2.0 m tall. ____ C. A medication contains 0.50 g Aspirin. ____ D. A bottle contains 1.5 L of water.

Solution In each of the following, indicate whether the unit describes 1) length 2) mass or 3) volume. 2 mass A. A bag of tomatoes is 4.6 kg. 1 length B. A person is 2.0 m tall. 2 mass C. A medication contains 0.50 g Aspirin. 3 volume D. A bottle contains 1.5 L of water.

Learning Check Identify the measurement that has a metric unit.
A. John’s height is 1) 1.5 yards 2) 6 feet 3) 2 meters B. The volume of saline in the IV container is 1) 1 liter 2) 1 quart 3) 2 pints C. The mass of a lemon is 1) 12 ounces 2) 145 grams 3) 0.6 pounds

Solution A. John’s height is 3) 2 meters
B. The volume of saline in the IV container is 1) 1 liter C. The mass of a lemon is 2) 145 grams

Scientific Notation A number in scientific notation contains a coefficient and a power of 10. coefficient power of ten coefficient power of ten x x 10-4 Place the decimal point after the first digit. Indicate the spaces moved as a power of ten. = x = x 10-3 4 spaces left spaces right

Learning Check Select the correct scientific notation for each.
1) 8 x 106 2) 8 x ) 0.8 x 10-5 B 1) 7.2 x 104 2) 72 x 103 3) 7.2 x 10-4

Solution Select the correct scientific notation for each. A. 0.000 008
2) 8 x 10-6 B 1) 7.2 x 104

Learning Check Write each as a standard number. A. 2.0 x 10-2
1) ) ) 0.020 B x 105 1) ) )

Solution Write each as a standard number. A. 2.0 x 10-2 3) 0.020
B x 105 1)

Measured Numbers You use a measuring tool to determine a quantity such as your height or the mass of an object. The numbers you obtain are called measured numbers.

Reading a Meter Stick . l l l l l cm To measure the length of the blue line, we read the markings on the meter stick. The first digit plus the second digit 2.7 Estimating the third digit between 2.7–2.8 gives a final length reported as 2.75 cm or cm

Accuracy – how close a measurement is to the true value
Precision – how close a set of measurements are to each other accurate & precise precise but not accurate not accurate & not precise Chapter 01 Slide 19

Mass of a Tennis Ball good accuracy good precision
The assumption is that the analytical balance is properly calibrated. The data only varies in the fourth decimal place.

Mass of a Tennis Ball good accuracy poor precision
The data varies in the first decimal place. While the accuracy is reasonable compared to the analytical balance, the precision is not.

Mass of a Tennis Ball poor accuracy poor precision
The bathroom scale is not something one would want to use for scientific measurements! It is possible to have good precision and poor accuracy. An instrument calibrated improperly, for example.

Known + Estimated Digits
In the length measurement of 2.76 cm, the digits 2 and 7 are certain (known). the third digit 5(or 6) is estimated (uncertain). all three digits (2.76) are significant including the estimated digit.

Learning Check . l8. . . . l . . . . l9. . . . l . . . . l10. . cm
What is the length of the red line? 1) cm 2) cm 3) cm

Solution . l l l l l cm The length of the red line could be reported as 2) cm or 3) cm The estimated digit may be slightly different. Both readings are acceptable.

Zero as a Measured Number
. l l l l l5. . cm The first and second digits are 4.5. In this example, the line ends on a mark. Then the estimated digit for the hundredths place is 0. We would report this measurement as 4.50 cm.

Exact Numbers An exact number is obtained when you count objects or use a defined relationship. Counting objects 2 soccer balls 4 pizzas Defined relationships 1 foot = 12 inches 1 meter = 100 cm An exact number is not obtained with a measuring tool.

Learning Check A. Exact numbers are obtained by
1. using a measuring tool 2. counting 3. definition B. Measured numbers are obtained by

Solution 2. counting 3. definition B. Measured numbers are obtained by
A. Exact numbers are obtained by 2. counting 3. definition B. Measured numbers are obtained by 1. using a measuring tool

Learning Check Classify each of the following as an exact (1) or a
measured (2) number. A.__Gold melts at 1064°C. B.__1 yard = 3 feet C.__The diameter of a red blood cell is 6 x 10-4 cm. D.__There are 6 hats on the shelf. E.__A can of soda contains 355 mL of soda.

Solution Classify each of the following as an exact (1) or a
measured(2) number. A A measuring tool is required. B This is a defined relationship. C A measuring tool is used to determine length. D The number of hats is obtained by counting. E The volume of soda is measured.

2.4 Measurement and Significant Figures
Every experimental measurement, no matter how precise, has a degree of uncertainty to it because there is a limit to the number of digits that can be determined.

Accuracy, Precision, and Significant Figures
Chapter 01: Matter and Measurement Accuracy, Precision, and Significant Figures 1 2 4 3 cm 1.7 cm < length < 1.8 cm length = 1.74 cm Chapter 01

25.00 m has four significant figures 2, 5, 0, and 0.
Rules for determining significant figures 1. Zeroes in the middle of a number are significant g has four significant figures, 6, 9, 0, and 8. 2. Zeroes at the beginning of a number are not significant g has two significant figure, 8 and 9. 3. Zeroes at the end of a number and after the decimal points are significant g has three significant figures 2, 5, and 0. 25.00 m has four significant figures 2, 5, 0, and 0.

4. Zeroes at the end of a number and before an implied decimal points may or may not be significant kg may have two, three, or four significant figures. Zeroes here may be part of the measurements or for simply to locate the unwritten decimal point.

Which of the following measurements has three significant figures?

Which of the following numbers contains four significant figures?
230,110 23,011.0

2.6 Rounding off Numbers Often calculator produces large number as a result of a calculation although the number of significant figures is good only to a fewer number than the calculator has produced – in this case the large number may be rounded off to a smaller number keeping only significant figures.

Rules for Rounding off Numbers:
Rule 1 (For multiplication and divisions): The answer can’t have more significant figures than either of the original numbers.

Rule 2 (For addition and subtraction): The answer should have minimum decimal places.

How many significant figures should be shown for the calculation?
1 2 3 4 5

How many significant figures are there in the following number: 1
How many significant figures are there in the following number: X 109? 4 3 2 1 Cannot deduce from given information.

Correct Answer: 4 3 2 1 Cannot deduce from given information. 1.200  109 Zeros that fall both at the end of a number and after the decimal point are always significant.

How many significant figures are there in the following summation:
2 3 4 5 6 6.220 1.0 + 125

Correct Answer: 2 3 4 5 6 6.220 1.0 + 125 In addition and subtraction the result can have no more decimal places than the measurement with the fewest number of decimal places.

How many significant figures are there in the result of the following multiplication:
(2.54)  (6.2)  (12.000) 2 3 4 5

Correct Answer: (2.54)  (6.2)  (12.000) = 188.976 = 190 2 3 4 5
In multiplication and division the result must be reported with the same number of significant figures as the measurement with the fewest significant figures.

2.7 Problem Solving: Converting a Quantity from One Unit to Another
Factor-Label-Method (Unit Conversion Factor): 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.

When solving a problem, set up an equation so that all unwanted units cancel, leaving only the desired unit. For example, we want to find out how many kilometers are there in mile distance. We will get the correct answer if we multiply mi by the conversion factor km/mi.

Problem Setup In working a problem, start with the initial unit.
Write a unit plan that converts the initial unit to the final unit. Unit Unit 2 Select conversion factors that cancel the initial unit and give the final unit. Initial x Conversion = Final unit factor unit Unit x Unit 2 = Unit 2 Unit 1

Setting up a Problem How many minutes are 2.5 hours? Solution:
Initial unit = 2.5 hr Final unit = ? min Unit Plan = hr min Setup problem to cancel hours (hr). Inital Conversion Final unit factor unit 2.5 hr x 60 min = min (2 SF) 1 hr

Learning Check A rattlesnake is 2.44 m long. How long is the snake in cm? 1) cm 2) 244 cm 3) 24.4 cm

Solution A rattlesnake is 2.44 m long. How long is the snake in centimeters? 2) 244 cm 2.44 m x cm = 244 cm 1 m

Using Two or More Factors
Often, two or more conversion factors are required to obtain the unit of the answer. Unit 1 Unit 2 Unit 3 Additional conversion factors are placed in the setup to cancel the preceding unit Initial unit x factor 1 x factor 2 = Final unit Unit x Unit 2 x Unit = Unit 3 Unit Unit 2

Example: Problem Solving
How many minutes are in 1.4 days? Initial unit: 1.4 days Unit plan: days hr min Set up problem: 1.4 days x 24 hr x 60 min = 2.0 x 103 min 1 day hr 2 SF Exact Exact = 2 SF

Check the Unit Cancellation
Be sure to check your unit cancellation in the setup. What is wrong with the following setup? 1.4 day x day x hr hr min Units = day2/min is Not the final unit needed Units don’t cancel properly. The units in the conversion factors must cancel to give the correct unit for the answer.

Learning Check An adult human has 4650 mL of blood.
How many gallons of blood is that? Unit plan: mL qt gallon Equalities: 1 quart = 946 mL 1 gallon = 4 quarts

Solution Unit plan: mL qt gallon Setup:
4650 mL x qt x gal = gal 946 mL qt 3 SF exact exact 3 SF

Typical Steps in Problem Solving
Identify the initial and final units. Write out a unit plan. Select appropriate conversion factors. Convert the initial unit to the final unit. Cancel the units and check the final unit. Do the math on a calculator. Give an answer using significant figures.

Learning Check If a ski pole is 3.0 feet in length, how long is the ski pole in mm?

Solution 3.0 ft x 12 in x 2.54 cm x 10 mm = 1 ft 1 in. 1 cm
Check factor setup: Units cancel properly Check final unit: mm Calculator answer: mm Final answer: 910 mm (2 SF rounded)

Learning Check If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7500 feet?

Solution 7500 ft x 12 in. x 2.54 cm x 1 m 1 ft 1 in. 100 cm
x 1 min = 35 min 65 m final answer (2 SF)

Clinical Factors Conversion factors are also possible when working with medications. A drug dosage such as 20 mg Prednisone per tablet can be written as 20 mg Prednisone and tablet 1 tablet mg Prednisone

Learning Check The dosage ordered is 400 mg of Erythromycin four times a day (q.i.d)*. If the oral suspension contains 200 mg Erythromycin/5 mL, how many mL will be given each time? 1) 5 mL 2) 10 mL 3) 40 mL *:Latin quater in die

Solution The dosage ordered is 400 mg of Erythromycin four times a day (q.i.d). If the oral suspension contains 200 mg Erythromycin/5 mL, how many mL will be given each time? 2) 10 mL 400 mg x mL = 10 mL 200 mg

Temperature Scales Temperature is measured using the Fahrenheit, Celsius, and Kelvin temperature scales. The reference points are the boiling and freezing points of water.

Learning Check A. What is the temperature of freezing water?
1) 0°F ) 0°C ) 0 K B. What is the temperature of boiling water? 1) 100°F ) 32°F ) 373 K C. How many Celsius units are between the boiling and freezing points of water? 1) ) ) 273

Solution A. What is the temperature of freezing water? 2) 0°C
B. What is the temperature of boiling water? 3) 373 K C. How many Celsius units are between the boiling and freezing points of water? 1) 100

Fahrenheit Formula On the Fahrenheit scale, there are are 180°F between the freezing and boiling points and on the Celsius scale, there are 100 °C °F = 9°F = °F °C 5°C °C In the formula for Fahrenheit, the value of 32 adjusts the zero point of water from 0°C to 32°F. °F = 9/5 T°C or °F = T°C

Celsius Formula The equation for Fahrenheit is rearranged to calculate T°C. °F = T°C Subtract 32 from both sides and divide by 1.8. °F – = 1.8T°C ( +32 – 32) °F – = 1.8 T°C °F – = T°C 1.8

Solving A Temperature Problem
A person with hypothermia has a body temperature of 34.8°C. What is that temperature in °F? °F = 1.8 (34.8°C) exact tenth's exact = = 94.6°F tenth’s

Learning Check The normal temperature of a chickadee is 105.8°F. What is that temperature in °C? 1) °C 2) °C 3) °C

Solution 3) 41.0 °C °C = (°F – 32) 1.8 = (105.8 – 32) = 73.8°F
= (105.8 – 32) = 73.8°F 1.8° = °C

Learning Check A pepperoni pizza is baked at 455°F. What temperature is needed on the Celsius scale? 1) 437 °C 2) 235°C 3) 221°C

Solution A pepperoni pizza is baked at 455°F. What temperature is needed on the Celsius scale? 2) 235°C (455 – 32) = 235°C

Learning Check On a cold winter day, the temperature is –15°C.
What is that temperature in °F? 1) 19°F 2) 59°F 3) 5°F

Solution 3) 5°F °F = 1.8(–15°C) + 32 = – 27 + 32 = 5°F
= – = 5°F Note: Be sure to use the change sign key on your calculator to enter the minus – sign x 15 +/ – = –27

2.10 Energy and Heat Energy: Capacity to do work or supply energy.
Classification of Energy: 1. Potential Energy: stored energy. Example: a coiled spring have potential energy waiting to be released. 2. Kinetic Energy: energy of motion. Example, when the spring uncoil potential energy is converted to the kinetic energy.

Learning Check Identify the energy as 1) potential or 2) kinetic
A. Roller blading. B. A peanut butter and jelly sandwich. C. Mowing the lawn. D. Gasoline in the gas tank.

Solution Identify the energy as 1) potential or 2) kinetic
A. Roller blading. (2 kinetic) B. A peanut butter and jelly sandwich. (1 potential) C. Mowing the lawn. (2 kinetic) D. Gasoline in the gas tank. (1 potential)

Forms of Energy Energy has many forms: Mechanical Electrical
Thermal (heat) Chemical Solar (light) Nuclear

Heat Heat energy flows from a warmer object to a colder object.
The colder object gains energy when it is heated. During heat flow, the loss of heat by a warmer object is equal to the heat gained by the colder object.

Some Equalities for Heat
Heat is measured in calories or joules. 1 kilocalorie (kcal) = 1000 calories (cal) 1 calorie = Joules (J) 1 kJ = 1000 J

Specific Heat Specific heat is the amount of heat (calories or Joules) that raises the temperature of 1 g of a substance by 1°C.

Learning Check A. A substance with a large specific heat
1) heats up quickly 2) heats up slowly B. When ocean water cools, the surrounding air 1) cools ) warms 3) stays the same C. Sand in the desert is hot in the day and cool at night. Sand must have a 1) high specific heat ) low specific heat

Solution A. A substance with a large specific heat 2) heats up slowly
B. When ocean water cools, the surrounding air 2) warms C. Sand in the desert is hot in the day and cool at night. Sand must have a 2) low specific heat

Learning Check When 200 g of water are heated, the water temperature rises from 10°C to 18°C. If 400 g of water at 10°C are heated with the same amount of heat, the final temperature would be 1) 10 °C 2) 14°C 3) 18°C 400 g 200 g

Solution When 200 g of water are heated, the water temperature rises from 10°C to 18°C. If 400 g of water at 10°C are heated with the same amount of heat, the final temperature would be 2) 14°C 400 g 200 g

Calculation with Specific Heat
To calculate the amount of heat lost or gained by a substance, we need the Specific Heat of substance, T, and the mass of the substance. Heat = g x T x cal (or J) = cal ( or J) g °C

Sample Calculation for Heat
A hot-water bottle contains 750 g of water at 65°C. If the water cools to body temperature (37°C), how many calories of heat could be transferred to sore muscles? The temperature change is 65°C - 37°C = 28°C. heat (cal) = g x T x Sp. Ht. (H2O) 750 g x 28°C x cal g°C = cal

Learning Check How many kcal are needed to raise the temperature of 120 g of water from 15.0°C to 75.0°C? 1) 1.8 kcal 2) 7.2 kcal 3) 9.0 kcal

Learning Check How many kcal are needed to raise the temperature of 120 g of water from 15.0°C to 75.0°C? 2) 7.2 kcal

In chemical reactions, the potential energy is often converted into heat. Reaction products have less potential energy than the reactants – the products are more stable than the reactants. Stable products have very little potential energy remaining as a result have very little tendency to undergo further reaction. SI unit of energy is Joules (J) and the metric unit of energy is calorie (cal).

2.11 Density Density relates the mass of an object with its volume. Density is usually expressed in units as - Gram per cubic centimeter (g/cm3) for solids, and Gram per milliliter (g/mL) for liquids. Mass (g) Density = Volume (mL or cm3)

Learning Check Osmium is a very dense metal. What is its density in g/cm3 if g of the metal occupies a volume of 2.22 cm3? 1) g/cm3 2) g/cm3 3) g/cm3

Solution Place the mass of the osmium metal in the numerator of the density setup and its volume in the denominator. D = mass = g volume cm3 calculator = g/cm3 final answer = g/cm3

Density Using Volume Displacement
The volume of zinc is calculated from the displaced volume mL mL = 9.5 mL = 9.5 cm3 Density zinc = mass = g = 7.2 g/cm volume cm3

Learning Check What is the density (g/cm3) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? 1) 0.2 g/ cm3 2) 6 g/cm ) 252 g/cm3 25 mL mL object

Solution 2) 6 g/cm3 Calculate the volume difference.
33 mL – 25 mL = mL Convert the volume in mL to cm3. 8 mL x 1 cm3 = cm3 1 mL Set up the density calculation Density = mass = 48 g = 6 g = 6 g/cm3 volume cm cm3

Sink or Float Ice floats in water because the density of ice is less than the density of water. Aluminum sinks because it has a density greater than the density of water.

Learning Check Which diagram correctly represents the liquid layers in the cylinder? Karo (K) syrup (1.4 g/mL), vegetable (V) oil (0.91 g/mL,) water (W) (1.0 g/mL) W K V V W K V W K

Solution 1) vegetable oil 0.91 g/mL water 1.0 g/mL Karo syrup 1.4 g/mL

Density as a Conversion Factor
Density represents an equality for a substance. The mass in grams is for 1 mL. For a substance with a density of 3.8 g/mL, the equality is: 3.8 g = 1 mL For this equality, we can write two conversion factors. Conversion 3.8 g and mL factors 1 mL g

Learning Check The density of octane, a component of gasoline, is g/mL. What is the mass, in kg, of 875 mL of octane? 1) kg 2) 614 kg 3) kg

Solution 1) 0.614 kg Unit plan: mL  g  kg
Equalities: density 1 mL = g and kg = 1000 g Setup: 875 mL x g x 1 kg = kg 1 mL g density metric factor factor

Learning Check If blood has a density of 1.05 g/mL, how many liters of blood are donated if 575 g of blood are given? 1) L 2) L 3) L

Solution 1) 0.548 L Unit Plan: g mL L 575 g x 1 mL x 1 L = 0.548 L
density metric factor factor

Density Using Volume Displacement
The volume of zinc is calculated from the displaced volume mL mL = 9.5 mL = 9.5 cm3 Density zinc = mass = g = 7.2 g/cm volume cm3

Learning Check A group of students collected 125 empty aluminum cans to take to the recycling center. If 21 cans make 1.0 pound of aluminum, how many liters of aluminum (D=2.70 g/cm3) are obtained from the cans? 1) 1.0 L 2) 2.0 L 3) 4.0 L

Solution 1) 1.0 L 125 cans x 1.0 lb x 454 g x 1 cm3
21 cans lb g x 1 mL x L = L 1 cm mL

Learning Check You have 3 metal samples. Which one will displace the greatest volume of water? 25 g of aluminum 2.70 g/mL 45 g of gold 19.3 g/mL 75 g of lead 11.3 g/mL

Solution 25 g of aluminum 2.70 g/mL 1) Calculate the volume for each metal and select the metal that has the greatest volume. 1) 25 g x 1 mL = mL aluminum g 2) 45 g x 1 mL = mL gold g 3) 75 g x 1 mL = mL lead g

2. 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. At normal temperature, the density of water is close to 1 g/mL. Thus, specific gravity of a substance at normal temperature is equal to the density. Density of substance (g/ml) Specific gravity = Density of water at the same temperature (g/ml)

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, as shown in the following Fig The depth to which the hydrometer sinks when placed in a fluid indicates the fluid’s specific gravity.

Learning Check Corn oil has a density of 0.92 g/mL. What is the specific gravity of corn oil? 1) ) 0.92 g 3) 1.1

Solution Corn oil has a density of 0.92 g/mL. What is the specific gravity of corn oil? 1) 0.92 specific gravity = 0.92 g/mL = 1.00 g/mL

Learning Check A bone sample has a mass of 52 g. If bone has a specific gravity of 1.8, what is the volume in milliliters of the bone sample? 1) 1.8 mL 2) 29 mL 3) 94 mL

Solution 2) 29 mL Convert the specific gravity to its density
using the density of water 1.8 x g/mL = g/mL Use the density factor to cancel the initial unit. Volume = 52 g x 1 mL = mL 1.8 g

Chapter Summary Physical quantity, a measurable properties, is described by both a number and a unit. Mass, an amount of matter an object contains, is measured in kilograms (kg) or grams (g). Volume is measured in cubic meters (m3) or in liter (L) or milliliters (mL). Temperature is measured in Kelvin (K) in SI system and in degrees Celsius (oC) in the metric system.

Chapter Summary Contd. Measurement of small or large numbers are usually written in scientific notation, a product of a number between 1 and 10 and a power of 10. A measurement in one unit can be converted to another unit by multiplying by a conversion factor. Energy: the capacity to supply heat or to do work. Potential energy – stored energy. kinetic energy – energy of moving particles.

Chapter Summary Contd. Heat: kinetic energy of moving particles in a chemical reaction. Temperature: is a measure of how hot or cold an object is. Specific heat: amount of heat necessary to raise the temperature of 1 g of the substance by 1oC. Density: grams per milliliters for a liquid or gram per cubic centimeter for a solid. Specific gravity: density of a liquid divided by the density of water.

End of Chapter 2

Measurements in Chemistry

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