Lecture 3&4

Md. Faysal Ahamed KhanLecture 3

Welcome to the class of Chemistry ICourse No. CHEM 211

Credit hours 3

Scientific Measurements and Units

All measurements contain two essential pieces of information:a number (the quantitative piece)a unit (the qualitative piece)

A measurement is useless without its units

The number 60 is somewhat meaningless without units. Consider this for one’s wages:

$ per week$ per hour

Measurement

All measurements have three parts:All measurements have three parts:

1.1. A valueA value

26.97626.97622 gg2. Units2. Units

3.3. An UncertaintyAn Uncertainty

Examples:Examples: 33.2 mL33.2 mL 72.36 mm72.36 mm426 kg426 kg 31 people31 people

Systems of Units - Standards of Measurement

Imperial systemEnglish unitsimperial unitsU. S. Customary Units

Metric system

SI system

Foot-pound-second systems

Metre and gram

Metre –kilogram-second system

The metric system is a decimalized system of measurement based on the metre and the gram.

Both the Imperial units and US customary units derive from earlier English units. Imperial units were mostly used in the British Commonwealth and the former British Empire. US customary units are still the main system of measurement in the United States

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Units of Measurement – SI UnitsUnits of Measurement – SI Units

m/ssecondsmeters

time of unitsdistance of units

velocity of Units

• There are two types of units:– fundamental (or base) units;– derived units.

• There are 7 base units in the SI system.

• Derived units are obtained from the 7 base SI units.

• Example:

Units of Measurement – SI UnitsUnits of Measurement – SI Units

Common SI Prefixes

A Problem-Solving Method

Chemistry problems usually require calculations, and yield quantitative (numerical) answers

For example,1 inch = 2.54 cm

The unit-conversion method is useful for solving most chemistry problems – the focus here is on “unit equivalents”

Dimensional Analysis – Factor Label Method

• In dimensional analysis always ask three questions:

• What data are we given?

• What quantity do we need?

• What conversion factors are available to take us from what we are given to what we need?

Other Equivalents and Conversion Factors

A conversion factor is the fractional expression of the equivalents

1 2.54

2.54 1

inch cmor

cm inch

Dimensional AnalysisDimensional Analysis

Example: we want to convert the distance 8 in. to feet.

(12in = 1 ft)

ftin

ftin 67.0

12

18

ProblemConvert the quantity from 2.3 x 10-8 cm to nanometers (nm)

First we will need to determine the conversion factors

Centimeter (cm) Meter (m)

Meter (m) Nanometer (nm)

Or

1 cm = 0.01 m

1 x 10-9 m = 1 nm

Dimensional AnalysisDimensional Analysis

Problem

Convert the quantity from 2.3 x 10-8 cm to nanometers (nm)

1 cm = 0.01 m

1 x 10-9 m = 1 nm

Now, we need to setup the equation where the cm cancels and nm is left.

Now, fill-in the value that corresponds with the unit and solve the equation.

m

nm

cm

mcm8103.2

nmm

nm

cm

mcm 23.0

101

1

1

01.0103.2

98

Problem

Convert the quantity from 31,820 mi2 to square meters (m2)


Mile (mi) kilometer (km)

kilometer (km) meter (m)

Problem



Mile (mi) kilometer (km), kilometer (km) meter (km)

Or

1 mile = 1.6093km, 1000m = 1 km

Notice, that the units do not cancel, each conversion factor must be “squared”.

km

m

mi

kmmi 2820,31

22

2820,31km

m

mi

kmmi

Problem


2102

26

2

22 102407.8

1

101

1

5898.2820,31 m

km

m

mi

kmmi

ProblemConvert the quantity from 14 m/s to miles per hour (mi/hr).

Determine the conversion factors

Meter (m) Kilometer (km) Kilometer(km) Mile(mi)

Seconds (s) Minutes (min) Minutes(min) Hours (hr)

Or

1 mile = 1.6093 km 1000m = 1 km

60 sec = 1 min 60 min = 1 hr

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ProblemConvert the quantity from 14 m/s to miles per hour (mi/hr).

1 mile = 1.6093 km 1000m = 1 km

60 sec = 1 min 60 min = 1 hr

hrmi

sm

/31

hr1

min60

min1

s60

km6093.1

mi1

m1000

km1/14

Dimensional Analysis

How many mL are in 3.0 ftHow many mL are in 3.0 ft33??

1 ft = 12 in1 ft = 12 in 1 in = 2.54 cm1 in = 2.54 cm 1 cm1 cm33 = 1 mL = 1 mL

(3.0 ft3)(12 in)(12 in)(12 in)(2.54 cm)(2.54 cm)(2.54 cm)(1 mL) (1 ft) (1 ft) (1 ft) (1 in) (1 in) (1 in) (1 cm3)

= 8.5 x 10= 8.5 x 1044 mL

How many ns are in 23.8 s?How many ns are in 23.8 s?

(23.8 s)(109 ns) (1 s)

= 23.8 x 10= 23.8 x 109 9 ns = 2.38 x 10ns = 2.38 x 1010 10 nsns

Mass and WeightMass and Weight

Mass: Mass: the measure of the quantity or amount of the measure of the quantity or amount of matter in an object. The mass of an object does notmatter in an object. The mass of an object does notchange as Its position changes.change as Its position changes.

Weight: Weight: A measure of the gravitational A measure of the gravitational attractionattraction of ofthe earth for an object. The weight of an objectthe earth for an object. The weight of an objectchanges with its distance from the center of the earth.changes with its distance from the center of the earth.

Sample Calculations Involving MassesSample Calculations Involving Masses

How many mg are in 2.56 kg?How many mg are in 2.56 kg?

(2.56 kg)(10(2.56 kg)(1033 g)(10 g)(1066mg)mg) (1 kg) ( 1 g)(1 kg) ( 1 g) = 2.56 x 10= 2.56 x 1099 mg mg

• The units for volume are given by (units of length)3. i.e., SI unit for volume is 1 m3.

• A more common volume unit is the liter (L) 1 L = 1 dm3 = 1000 cm3 = 1000 mL.

• We usually use 1 mL = 1 cm3.

Volume

Sample Calculations Involving VolumesSample Calculations Involving Volumes

How many mL are in 3.456 L?How many mL are in 3.456 L?

(3.456 L)((3.456 L)(1000 mL1000 mL)) LL

= = 3456 mL3456 mL

How many ML are in 23.7 cmHow many ML are in 23.7 cm33??

(23.7 cm(23.7 cm33)()( 1 mL 1 mL )()( 1 L_ _ 1 L_ _)()(101066 ML) ML) (1 cm(1 cm33)(1000 mL)( 1L ))(1000 mL)( 1L )

= = 2.37 x 10 2.37 x 10 44 ML ML= = 23 700 ML23 700 ML

Density

Density - Density - The mass of a unit volume of a material.The mass of a unit volume of a material.

density = mass/volumedensity = mass/volume

What is the density of a cubic block of wood that is What is the density of a cubic block of wood that is 2.4 cm on each side and has a mass of 9.57 g? 2.4 cm on each side and has a mass of 9.57 g?

volume = [2.4 cm x 2.4 cm x 2.4 cm]volume = [2.4 cm x 2.4 cm x 2.4 cm]

density = (9.57 g)/(13.density = (9.57 g)/(13.88 cmcm33))

= 0.69 g/cm= 0.69 g/cm33 = 0.69 g/mL= 0.69 g/mL

Note that 1 cmNote that 1 cm33 = 1 mL = 1 mL

23

Temperature

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Temperature

Kelvin ScaleUsed in science.Same temperature increment as Celsius scale.Lowest temperature possible (absolute zero) is zero Kelvin. Absolute zero: 0 K = -273.15oC.

Celsius ScaleAlso used in science.Water freezes at 0oC and boils at 100oC.To convert: K = oC + 273.15.

Fahrenheit ScaleNot generally used in science.Water freezes at 32oF and boils at 212oF.

Converting between Celsius and Fahrenheit

32-F95

C 32C59

F

Sample Calculations Involving Temperatures

Convert 73.6Convert 73.6ooF to Celsius and Kelvin temperatures.F to Celsius and Kelvin temperatures.

ooC = (5/9)(73.6C = (5/9)(73.6ooF - 32) = (5/9)(41.6)F - 32) = (5/9)(41.6)

ooC = (5/9)(C = (5/9)(ooF - 32)F - 32) K = K = ooC + 273.15C + 273.15

= = 23.123.1ooCC

K = 23.1K = 23.1ooC + 273.15 = C + 273.15 = 296.3 K296.3 K

MemorizeMemorize

• All scientific measures are subject to error.

• These errors are reflected in the number of figures reported for the measurement.

• These errors are also reflected in the observation that two successive measures of the same quantity are different.

Uncertainty in MeasurementUncertainty in Measurement

Precision and Accuracy in Measurements

• Precision refers to how closely individual scientific measurements agree with one another.

• Accuracy refers to the closeness of the average of a set of scientific measurements to the “correct” or “most probable” value.

• Measurements that are close to the “correct” value are accurate.

• Measurements which are close to each other are precise.

• Measurements can be

– accurate and precise

– precise but inaccurate

– neither accurate nor precise


Precision and Accuracy

Precision and Accuracy



• The number of digits reported in a measurement reflect the accuracy of the measurement and the precision of the measuring device.

• All the figures known with certainty plus one extra figure are called significant figures.

• The more significant digits obtained, the better the precision of a measurement

• The concept of significant figures applies only to measurements

• In any calculation, the results are reported to the fewest significant figures (for multiplication and division) or fewest decimal places (addition and subtraction).

Significant Figures

• Non-zero numbers are always significant.

• Zeros between two other significant digits ARE significante.g., 10023

• A zero preceding a decimal point is not significant e.g., 0.10023

• Zeros between the decimal point and the first nonzero digit are not significant

e.g., 0.0010023

Rules for Zeros in Significant Figures


• Zeros at the end of a number are significant if they are to the right of the decimal point

e.g., 0.1002300 1023.00

•Zeros to the right of all nonzero digits in an integer (for example 500) are uncertain. If they indicate only the magnitude of measurement, they are not significant. However, if they also show something about the precision of the measurement, they are significant.

– Example – so for the number 10,300 has 3 significant figures and the rests are uncertain


• If the leftmost digit to be dropped is less than 5, the preceding number is left unchanged.“Round down.”

Example: 7.5543 cm = 7.55 cm

-7.5543 cm = -7.55 cm

• If the leftmost digit to be dropped is 5 or greater, the preceding number is increased by 1. “Round up.”

Example: 7.5561 cm = 7.56 cm

-7.5561 cm = -7.56 cm

Rounding rules


Multiplication / DivisionMultiplication / Division The result must have the same number of The result must have the same number of

significant figures as the least accurately significant figures as the least accurately determined datadetermined data

Example: Example:

12.512 (5 sig. fig.) x 5.1 (2 sig. fig.)12.512 (5 sig. fig.) x 5.1 (2 sig. fig.)

12.512 x 5.1 = 64 12.512 x 5.1 = 64

Answer has only 2 significant figuresAnswer has only 2 significant figures

Q1: 7.07 g/2.02 cmQ1: 7.07 g/2.02 cm33 = 3.50 g/ cm = 3.50 g/ cm33

Q2: 8.2 cm x 4.001 cm = 32.8082 cmQ2: 8.2 cm x 4.001 cm = 32.8082 cm2 2 = 33 cm= 33 cm22

Significant Figures


Addition and Subtraction: the reported results should have the same number of decimal places as the number with the fewest decimal places

NOTE - Be cautious of round-off errors in multi-step problems. Wait until calculating the final answer before rounding.


Example:Example:15.152 (5 sig. fig., 3 digits to the right),15.152 (5 sig. fig., 3 digits to the right),1.76 (3 sig. fig., 2 digits to the right),1.76 (3 sig. fig., 2 digits to the right),7.1 (2 sig. fig., 1 digit to the right).7.1 (2 sig. fig., 1 digit to the right).

15.152 + 1.76 + 7.1 = 24.015.152 + 1.76 + 7.1 = 24.0

24.0 (3 sig. fig., but only 1 digit to the right of 24.0 (3 sig. fig., but only 1 digit to the right of the decimal point)the decimal point)

Significant Figures


Technology

Lecture 3&4