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Chemistry 311

Lecture Notes

Fall 2009

David E. Henderson

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Chapter 2 & 3

How do we measure things

Chem 311

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RECORDING DATA - USE OFSIGNIFICANT FIGURES

INTEGERS (Things you count) ALWAYS EXACT VALUES eg.you did the

experiment three times. Precision of these numbers is infinite.

REALS (Things you measure) ALWAYS CONTAIN AN UNCERTAINTY.

Assume error is +/- 1 in the last place unless specified. For the number 1.0034 the actual value lies between

1.0033 and 1.0035.

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METHODS FOREXPRESSING

UNCERTAINTY ABSOLUTE UNCERTAINTY.

Buret reading 40.34 +/- .01 ml RELATIVE UNCERTAINTY.

0.01 ml/40.34 ml = .00025 relative .00025 * 100% = .025% rel.unc. .00025 * 1000 ppt= .25 ppt rel.unc. = 0.2 ppt

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8/3/2009 Chem 311 Fall 2009 4

SIGNIFICANT FIGURES

KEEP ONLY THE FIRST UNCERTAINDIGIT IN A RESULT. Assume that data is presented this way

by other responsible scientists.

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SIGNIFICANT FIGURES

ROUND OFF SUPERFLUOUSDIGITS. 5 ROUNDS UP IF ODD DOWN IF EVEN.

Thus the result of rounding the digit 5 is alwaysa number ending in an even digit. eg..435 =>.44 .425=> .42

Round off only once

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SIGNIFICANT FIGURES

ADDING OR SUBTRACTING KEEP ONLY THE NUMBER OF DECIMAL

PLACES IN THE LEAST PRECISERESULT.(Remember these numbers willalways have the same units.)

Note- the number of significant digits in anumber can change dramatically insubtraction.

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8/3/2009 Chem 311 Fall 2009 7

SIGNIFICANT FIGURES

MULTIPLYING OR DIVIDING Rule of Thumb Keep the same

number of significant digits in the resultas in the value with the lowest numberof sig. Figs.

This often doesnt work out 101/99 = 1.02

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SIGNIFICANT FIGURES

COMMON ERROR 0.7834 gm KHP =0.0034 moles KHP

This error appears in far too many labnotebooks.The student has taken anumber with a relative uncertainty of1/7800 and reduced it to a number withan apparent uncertainty of 1/34.

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Common error

1.234*(40.35-40.31)=0.04936 How many significant figures should we

have? 1.234*0.04= 0.04936 0.05

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SIGNIFICANT FIGURES

DURING CALCULATIONS ONE ADDITIONAL INSIGNIFICANT DIGITSHOULD BE CARRIED ININTERMEDIATE RESULTS.

EXCEPTION.The calculation of sumsand sums of squares requires you tokeep all digits

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LOGS

log consists of two parts, characteristic

eg.pH=1.03 characteristic = 1 mantissa = .03 The characteristic is a power of ten and is an

integer (counting decimal pl aces) .

mantissa. Measured value - real The significant figures which denote the

uncertainty of the value are those in themantissa.

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LOGS - General rule Number of Sig. Figs is number of digits to

right of decimal A two digit mantissa corresponds to a relative

error of approximately 2%,

A three digit mantissa to 2 ppt, etc. EXAMPLE

pH 1.03 [H +]=9.3x10 -2 pH 13.03 [H +] = 9.3x10 -14

1.02 < pH < 1.04 13.02 < pH < 13.04 9.1x10 -2 < [H +] < 9.5x10 -2 9.1x10 -14 < [H +]