 the minimum number of digits needed to write a given value in scientific notation without any loss of accuracy 

 estimate all readings to the nearest tenth of the distance between scale divisions 

significant figures in arithmetic 
 in a series of calculations, carry the extra digits through to the final result then round. 

significant figures in rounding 
 if the digit is to be removed and is less than 5, the preceding digit stays the same if greater than 5, the preceding digit increases by 1 if equal to 5, preceding digit remains the same or increases by 1, whichever gives an even digit 

significant figures and addition and subtraction 
 round according to the number with the most uncertainty, that is, the answer is limited by the least certain number 

significant figures and multiplication and division 
 the answer is limited to the number of digits contained in the number with the fewest significant figures 

significant figures and logarithms and antilogarithms 
 the number of digits in the mantissa of (log x) is the number of significant figures in x. 

 the part of a logarithm to the left of the decimal point 

 the part of a logarithm to the right of the decimal point 

significant figures in graphs 
 depends on the purpose of the graph. if to display qualitative behavior of data, then sig figs are irrelevant. if to display precise values, then several sig figs 

systematic error determinate error 
 occurs in the same direction each time (high or low), often resulting from poor technique 

how to detect systematic error 
 analyze samples of known composition, ‘blank’ samples containing none of the sought analyte; use different analytical methods to measure same quantity; Round Robin experiment 

 assign different people/labs to analyze identical samples 

random error indeterminate error 
 measurement has an equal probability of being high or low; obeys laws of statistics 

 agreement of a particular value with the “true” value. 

 degree of agreement among several elements of the same quantity 

 expression of the margin of uncertainty associated with a measurement 

 compares the size of the absolute uncertainty with the size of its associated measurement 

percent relative uncertainty 
 100 * relative uncertainty 

propagation of uncertainty from random error addition and subtraction 
 if A=B+C+D Ua=(Ub^2+Uc^2+Ud^2)^1/2 abs uncertainty used 

propagation of uncertainty from random error multiplication and division 
 A=B*/C*/D %RUa=[(%RUb)^2+(%RUc)^2+(%RUd)^2]^1/2 percent relative uncertainty used 

propagation of uncertainty mixed operations 
 same manner as the calculations are performed 

real rule of significant figures 
 THe first uncertain figure is the last significant figure 

propagation of uncertainty exponents 
 
propagation of uncertainty logarithms 
 
propagation of uncertainty natural log 
 
propagation of uncertainty power of 10 
 
propagation of uncertainty base e 
 
uncertainty in molecular masses 
 Use rule for addition and subtraction, then multiply by n moles per identical atom 

 Theoretical bellshaped distribution of measurements when all error is random. The center of the curve is the mean, and the width is characterized by the standard deviation. 

 
 measure of how closely the data are clustered to the mean. [image]


 the number of independent measurements 

 standard deviation squared 

relative standard deviation 
 
significant figures in mean and standard deviation 
 where uncertainty begins according to std. dev., that’s where significant figures are. 

formula for Gaussian curve 
 
 
 
 statistical tool used to express confidence intervals and to compare results from different experiments. 

 used to compare one set of data with another to decide whether or not they are “the same” 

 the two sets of data are the same 

 the two sets of data are different 

when to use Student’s t test 
 comparing a measured result with a known value, replicate measurements, individual differences 

t calc equation known value 
 
t calc equation replicate measurements if std. devs. equal 
 
s pooled replicate measurements 
 
t calc equation replicate measurements if std. devs. inequal 
 
 compares standard deviations 

 
 determines whether one measurement can be thrown away — whether it is an outlier or not 

 
 Dropped sample? Pretty obvious Be hesitant if not certain Grubbs test is not very reliable 

 a graph showing the value of some property versus concentration of analyte. When the same property of an unknown is measured, its concentration can be determined from the graph. [image]


 process of fitting a mathematical function to a set of measured points by minimizing the sum of the squares of the distances from the points to the curve. 

 a solution whose composition is known by virtue of the way it was made from a reagent of known purity or by virtue of its reaction with a known quantity of standard reagent 

 a solution that does not contain analyte; used to correct for interferences 

 the analyte concentration range over which response is proportional to concentration 

 the analyte concentration range over which there is a measurable response to analyte. 

 Quantitative indications that indicate whether data requirements have been met. Also refers to the broader process that includes quality control, quality assessment, and documentation of procedures and results designed to ensure adequate data quality. 

 states the purpose for which results will be used 

 describes how good analytical results need to be and what precautions are required in an analytical method. 

 a conclusion that the concentration of analyte exceeds a certain limit when, in fact, the concentration is below the limit 

 a conclusion that the concentration of analyte is below a certain limit when, in fact, the concentration is above the liimit. 

 being able to distinguish analyte from other species in the the sample 

 the capability of responding reliably and measurably to changes in analyte concentration. Slope of the calibration curve 

 a sample containing all components except analyte and is taken through all steps of the analytical process. Response is subtracted from sample’s response. 

 a solution prepared from all of the reagents, but no analyte; for measuring response of analytical method to impurities in reagents and other effects caused by anything but the analyte 

 a blank sample exposed to the environment at the sample collection site and transported in the same manner as other samples between the lab and the field. 

 everything in the sample other than analyte Also, the virtual reality which the machines have set us in while they harvest our bodies for energy. Ignore that it would be incredibly inefficient. 

 addition of a known compound (with known concentration) to an unknown 

 
 the analysis of a solution formulated by the analyst to contain a known concentration of analyte Ensures that procedures and instruments are functioning correctly. 

 inserted in a series of measurements to see if a procedures gives correct results when the analyst does not know the right answer 

standard operating procedures 
 a written procedure that must be rigorously follow to ensure the quality of a chemical analysis 

 a visual representation of a confidence interval for a Gaussian distribution 

 the process of collecting data to show that analytical procedures operating within specified limits and verifying that final results meet use objectives 

 the process of proving that an analytical process is acceptable for its intended purpose 

 the ability of an analytical method to distinguish the analyte from everything else that might be in the sample 

 measures how well a calibration curve follows a straight line 

square of the correlation coefficient 
 measure of goodness of fit of data points to a straight line. Closer to 1 = better 

how to demonstrate accuracy 
 Analyze a standard reference material compare results of different methods spike a blank sample with analyte standard additions 

reproducibility of results 
 precision (alternate definition) 

 concentration interval over which linearity, accuracy, and precision are all acceptable 

 the smallest quantity of analyte that is “significantly different” from the blank. * * 

procedure for detection limit determination 
 
 
 the concentration below which regulatory rules say that a given analyte is reported as “not detected” 

 the ability of an analytical method to be unaffected by small, deliberate changes in operating parameters 

 known quantities of analyte are added to the unknown and the responses are recorded. This keeps any matrix effect constant. 

 a change in the analytical signal caused by anything in the sample other than the analyte 

standard addition equations 
 
standard addition with constant total volume 
 
standard addition with varying total volume 
 
 a known amount of a compound, different from analyte, that is added to the unknown. Signal from the analyte is compared with signal from the internal standard to find out how much analyte is present. 

 