Quantitative Chemical Analysis Seventh Edition Quantitative Chemical Analysis Seventh Edition Chapter 3 Experimental Error Copyright © 2007 by W. H. Freeman.

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Presentation transcript:

Quantitative Chemical Analysis Seventh Edition Quantitative Chemical Analysis Seventh Edition Chapter 3 Experimental Error Copyright © 2007 by W. H. Freeman and Company Daniel C. Harris

a cubic decimeter of water at its point of maximum density, °C, has a mass that is parts per million less than the kilogram.parts per million Cleaning the prototypes removes between 5 and 60 µg of contamination short-term instability of about 30 µg over a period of about a month in its after-cleaned mass

Random error Systematic error

In experimental data, the first uncertain figure is the last significant figure

significant figure: The number of significant digits in a quantity is the minimum number of digits needed to express the quantity in scientific notation..

Adding and subtracting with sig figs: Keep least sig figs beyond the decimal point

Adding and subtracting with sig figs: Keep least sig figs beyond the decimal point WATCH OUT: SAME POWERS OF 10!

Multiplying and dividing with sig figs: Keep least sig figs.

logarithms with sig figs: sig figs. in mantissa = sig figs in number

logarithms with sig figs: sig figs. in mantissa = sig figs in number log(3.39 x 10 2 ) = log(3.39) + log (10 2 ) = = log(3.39 x ) = log(3.39) + log (10 -5 ) = – 5 =

NB 1 sig fig!

Propagation of Uncertainty from Random Error

This is like adding systematic errors

Propagation of Uncertainty from Random Error

The real rule: The first uncertain figure is the last significant figure. TIP: In our calculations, we retain extra insignificant digits and round off only at the end.

For systematic uncertainty, we add the uncertainties of each term in a sum or difference.

Vernier scale