Exam 1 Lecture 3

Question 1

the method of least squares

Answer 1

used to draw the “best” straight line through experimental data points that contain some scatter
- some points will lie above and some below the line (equation y=mx+b can be used to quantify the unknown from its signal)
- for most chemical analyses, the response obtained by the given lab procedure must be compared to known quantities (called standards); in this way the response from an unknown quantity can be interpreted

Question 2

method of least squares steps

Answer 2

• prepare a calibration curve from known standards
• work in a region where the calibration curve is linear (usually)

Question 3

method of least squares assumptions

Answer 3

• uncertainty in y values is much greater than uncertainty in x values
• uncertainties of all y values are similar

Question 4

method of least squares equation

Answer 4

di^2= (yi-mxi-b)^2

Question 5

method of least squares overview

Answer 5

• deviations from the line (yi-y) are squared and summed
• why squared? direction doesn’t matter, and large deviations are weighted more heavily
• the sum is minimized by changing the slope and y-intercept of the fitted line
• i.e. we solve for the best m and b that give the minimal sum of squared differences

Question 6

calibration curves

Answer 6

shows the response of an analytical method to known quantities of analyte

• standard solutions: contain known concentrations of analyte
• blank solutions: contain all reagents and solvents used in the analysis but contain no deliberately added analyte

Question 7

steps to constructing calibration curves

Answer 7

1. prepare standards in the relevant range
2. subtract blank measurements (corrected response)
3. graph corrected response vs. [analyte] (get m and b with least squares analysis!)
4. unknown analysis; run sample, substract blank (get y), solve for x using y=mx+b

Question 8

linear range (calibration curve)

Answer 8

concentration range over which calibration curve is linear

Question 9

dynamic range (calibration curve)

Answer 9

concentration range over which there is measurable response

Question 10

detection limit (lower limit of detection)

Answer 10

smallest quantity of analyte that is significantly different from the blank

Question 11

quantitation limit (lower limit of quantitation)

Answer 11

smallest quantity of analyte that can be measured with reasonable accuracy

Question 12

what is the minimum detectable signal, y of dl, defined as?

Answer 12

signal detection limit: y of dl = y of blank + 3s
(where s is the standard deviation associated with the sample measurements)

Question 13

limit of detection

Answer 13

the corrected signal, ysample-yblank, is proportional to the sample concentration:

calibration line: ysample-yblank = m * sample concentration (where ysample is the signal ovserved for the sample and m is the slope of the linear calibration curve)
- the minimum detectable concentration is obtained by substituting y of dl for y sample to get the detection limit
- detection limit: minimum detectable concentration = 3s/m

Question 14

reporting limit

Answer 14

the concentration below which regulations say an analyte is “not detected”

• it does not mean that analyte is not observed, it means the analyte is below the prescribed level
• the reporting limit is set at least 5 to 10 times higher than the detection limit

Question 15

Matrix effect (Calibration challenges)

Answer 15

change in analytical sensitivity caused by something in the sample other than analyte