Chemistry - Measurement

8/13/2019 Chemistry - Measurement

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CHY 102

Introduction to ChemistryLecture 1: Measurement

Systme Internationale UnitsDimensional Analysis

Uncertainty in Measurements


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Irrational System of Units Inch: 1/4, 1/8, 1/16 , etc; Milesium = 1/1000 in. Foot: 12 inches; 3 ft = 1 yard Stat. Mile: 5280 feet; naut. mile = 1.151 stat.

miles

Pound (avoirdupois): 16 adp. oz., 256 drams,7000 grains

Pound (troy): 12 troy oz., 5760 grains

Acre: 43,560 ft2 (66 ft x 660 ft)

Ton: short ton 2000 lbs.; long ton 2200 lbs. Pint: Brit. pint 20 Brit. fl. oz; Amer. 16 U.S. fl. oz.

Horsepower: 550 ft-lb/s


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Metric System and SI

The metric system was invented by scientistswho wanted a rational system of units for use inscientific measurements.

Originally based on measurements of the earthand the properties of gases and liquid water.

Systme International (SI, aka mks): a

consistent set of metric units for which baseunits include the metre, kg and second.

(In the cgs system--also metric, used in Britain--units are derived from cm, gram, and second.)


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The Metre: SI Unit of Length

The metre was originally (late1700s) based onmeasurements of the earth:

1 metre = 1 ten -millionth ofthe distance along the primemeridian from the north pole to

the equator.

(New definition: the distance light travelsin a vacuum in 3.335 640 95 ns.)


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Volume and Mass The SI unit of volume is

the cubic metre (m 3). It is not a convenient

measure of milk from the

grocers. The litre (L) is a derived

volume unit, equivalent toa cube that is 0.1m x 0.1mx 0.1m = 10 -3 m 3.

{It is not SI.}

0.1 m

0 . 1

m1.00 L

The kilogram (kg) was originally defined asthe mass of 1 L of pure water at 4 C.


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The Kelvin Temperature Scale

Based on measurements of gas volumes withtemperature at constant pressure.

Isobars all intersected

the temperature axisat -273 C (absolute zero).

10

20

30

40

50

60

70

V o l u m e

( L )

1.00 bar

2.00 bar

4.00 bar

K and C scales are

identical except fora 273.15 offset.

T = t(K/ C) + 273.15K


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Examples Derived SI Units

Volume: cu. metre (m3

) = 103

L Force: newton (N) = 1 kg m s -2 Pressure: pascal (Pa) = 1 N m -2

Energy: joule (J) = 1 N m Power: watt (W) = 1 J s -1 Frequency: hertz (Hz) = 1 s -1

Electrical charge: coulomb (C) = 1 A s Electrical potential: volt(V) = 1 J C -1


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Derived SI Unitse.g. What is the SI unit of momentum?

We know that r = mv.v = speed = change in distance per unit time

Base unit of distance is m, time is s ; SIunit of v = m s -1

m = mass; base unit is kg

Hence, the SI unit of momentum is kg m s -1

Show that a kg m s -1 is the same as a N s


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Derived SI Units

What is the SI unit of density?

Density = (mass)/(volume)SI unit of mass is kgSI unit of volume is m 3

SI unit of density is kg/m 3

Show that kgm -3 is numerically equivalent

to gL-1

, mgcm-3

, or mgmL-1


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Why Is This Important?


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Solving Problems with SI Units

(0) Read the question carefully.(1) Decide on an approach (choose equation).(2) Convert all given quantities to SI units.

(3) Substitute all converted values WITHUNITS into equation. Make sure thatdimensional analysis gives reasonable final

units.(4) Enter numbers into calculator and crunch.(5) Convert answer to units required by

question (if necessary).


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Example

What is the pressure in bar of 1.30 mol ofideal gas at 25 C in a 1.62 L vessel?

(1) Decide on approach: Ideal gas law

PV = nRT

R = gas constant = 8.31441 J K -1mol -1 (SI)


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(2) Convert Units to SIn = 1.30 mol (already SI)T = t(K/ C) + 273.15 K

= 298.15 KV = (1.62 L)x(10 -3 m3/L) = 1.62 x 10 -3 m3

(3) Enter Values WITH UNITSP = nRT/V

= (1.30 mol)(8.31441 J K -1mol -1) (298.15 K)(1.62x10 -3 m3)

= 1.99 x10 6 J m -3 = 1.99 x 10 6 N m m -3 = 1.99 x10 6 N m -2 = 1.99 x 10 6 Pa


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The answer should be in Pa because Pa is theSI unit of pressure, and we used SI units

throughout calculation.

Carrying the units through is a good check ofthe method.

(4) Convert to desired units (bar)

1 bar = 105

PaP = (1.99 x 10 6 Pa)x(1 bar)/(10 5 Pa)

= 19.9 bar (Final answer)


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Dimensional Analysis The conversion of units in steps 2, 3, and 4 is

referred to as dimensional analysis. I recommend two levels of dimensional

analysis:

Conversion of quantities given to SI unitsBEFORE beginning the calculation

Dimen. analysis during calculation as a check

The two levels builds redundancy into yourcalculation. This will help you to avoid sillyerrors.

Remember: the tests in this course aremultiple choice-- accuracy counts !


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ExampleThe work of expansion , w, when a gas expandsby an amount, V, against a constant externalpressure, P ext , is

w = - P ext Vwhere negative values indicate work done on the

surroundings.

gas

Pext

piston

cylinderWhat is the work ofexpansion (in joules)

when a volume of gasincreases from 2.00 Lto 5.00 L under aconstant pressure of3.55 atm?

releaseconstraint

w


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How NOT to Proceed:

= - (3.55)(5.00 - 2.00)= - 10.65

No units for given quantities or for answer

No consideration of significant figures No thought about dimensional analysis at all

INCORRECT!

w = - P ext V= - P ext(V f - V i)


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The Right WayConvert units to SIP ext = (3.55 atm) (101 325 Pa/atm) = 3.597 x 10 5 Pa

V = V f - V i = 5.00 L - 2.00 L = 3.00 L= (3.00 L)x(1 m 3/1000 L) = 3.00 x 10 -3 m 3

Substitute values WITH UNITSw = - P ext V = -(3.597 x 10 5 Pa)(3.00 x 10 -3 m 3)

= - 1.08 x 10 3 Pam 3 = - 1.08 x 10 3 Nm -2 m 3 = - 1.08 x 10 3 Nm = - 1.08 x 10 3 J


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Conversion factors are equivalentto multiplying by 1

e.g. Convert 8.00 inch-lbs into Nm:

lbin00.8

in1

cm54.2

cm100

m1

lb1

N44822.4

= 0.904 Nm

Notes:(1) Converting units does not change the quantity, only its

appearance.(2) The precision in the 1 st and 2 nd conversion factors is infinite.(3) The precision in the answer is 3 figures because of 8.00.


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Precision and Accuracy

Precision: is a measure of reproducibilityof a measurement.

Accuracy: is a measure of the deviationfrom the true value of a measurement.

A measurement can be precise withoutbeing accurate, but not the other wayaround.


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Example: measurement of a 5.000ppm solution of Zn by 3 methodsMethod 1:

4.9904.9914.996

5.0085.0085.0055.008

Mean: 4.99795% CI: 0.005

(Good accuracy

and precision.)

Method 2:5.5045.4955.494

5.4985.5085.4945.507

Mean: 5.50195% CI: 0.004

(Poor accuracy,

good precision.)

Method 3:4.7904.2715.0754.8835.5744.8015.945

Mean: 4.88495% CI: 0.557

(Poor accuracy and

precision.)


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Exact Numbers

NOT ALL NUMBERS USED INCALCULATIONS ARE MEASUREMENTS

Counting numbers e.g. If you have 2 shoes, the 2 has no error

Defined scalar quantities The value of a dime is exactly 10 cents

Defined conversion factors There are exactly 2.54 cm per inch There are exactly 101 325 Pa per atm


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Rules for Significant Figures(1) All non-zero digits in a value are significant.(2) Zeros between 2 sig. figs are significant.(3) Zeros at the end of a value after the decimal

place are significant; e.g. 0. 200 has 3 sig.

figs.(4) Leading zeros are not significant; e.g.0.00 200 has 3 significant figures.

(5) Zeros at the end of a value with no decimal

place are ambiguous. Best to write thesenumbers in scientific notation; e.g. 13,7 00 has either 3, 4, or 5 sig. figs, but 1.370 x 10 4 has 4 sig. figs.


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Examples

1.010 x 10 3 m2 Value Significant Figures

4: rules 2 & 3

1 010 m 2 3, maybe 4: rules 2 and 5

1 010.0 m 2 5: rules 2 & 3

1.000 x 10 3 m2 4: rule 3

103 m2 0: exponents are not significant

0.0001 m 2 1: rule 4


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Sig. Figs and Calculations

Multiplication and Division: The result is reported with the same number of

significant digits as appear in the measurementwith the fewest significant digits.

e.g. (0.234 m)x(10.01 m) = 2.3423 m 2 = 2.34 m 2

Addition and Subtraction: The result is reported with the precision of the

least precise measurement. e.g. 10.01 m + 0.234 m = 10.244 m = 10.24 m


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Examples

1. V = (1.15 m)(6.01 m)(22.0 m) + (32.0 m3)= 152.053 m 3 + 32.0 m 3

= (a) 184 m 3 (b) 184.1 m 3 (c) 1.8 x 10 2 m3?

ANS: (a) 184 m3

Three significant figures: 1 st term = 152 m 3.Significant figures follow rules of order of

operations.


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2. (1.339 m)x(6.80 m)x(0.016 m) + 38 L= 0.145 683 2 m 3 + (38 L)x(10 -3 m3/L)= 0.145 683 2 m 3 + 0.038 m 3 = (a) 0.1837 m 3

(b) 0.184 m 3 (c) 0.18 m 3?

ANS: (c) 0.18 m3Two sig. figs because 0.016 m has two figures.

Terms are additive only if they have the same units.

Examples


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Rules for Rounding Off

ONLY ROUND OFF AT THE END OF ACALCULATION

If the numeral to the right of the lastsignificant figure is < 5, then rounding isnot required; the value is simply truncated: e.g. 6.02249 N = 6.022 N

If the numeral to the right of the last sig.fig. is 5, then round up: e.g. 6.02157 N = 6.022 N


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Summary

Review 1.1-1.8 Metric System and SI

base units and derived units

prefixes dimensional analysis

Precision and Accuracy

rules for significant figures rules for sig. figs in calculations rounding off

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