Preliminary Lab Exercise Part 1 Calibration of Eppendorf Pipette

Transcription

1 Preliminary Lab Exercise Part 1 Calibration of Eppendorf Pipette Pipettes allow transfer of accurately known volume of solution from one container to another. Volumetric or transfer pipettes deliver a single fixed volume of liquid. Measuring pipettes are calibrated in convenient units and permit delivery of variable volumes of liquid up to a maximum capacity. Digital pipettes deliver adjustable microliter volumes of liquid. In recent years digital pipettes have become the most widely used mode of accurate liquid transfer. There are several manufacturers of digital pipettes. In this laboratory you will be using Eppendorf digital pipettes. Digital pipettes operate on the principle that a known and adjustable volume of air is displaced from a disposable tip by depressing a button on the top of the pipette to a first stop. Digital pipettes are easy to use and deliver consistently reproducible, and when calibrated, highly accurate volumes of solution. Due to the mechanical nature of these pipettes, the accuracy may change over time due to the mechanical component wear or to misuse by the operator. In order to have confidence in the accuracy of the volume delivered, digital pipettes should be calibrated on regular basis. In this lab you will learn correct procedures for operating and calibrating of Eppendorf pipettes. Operation of Eppendorf Pipettes Volume setting: The volume is adjusted continuously by turning the setting ring. The digits of the volume display should be read from top to bottom. Pipette tips: Pipette becomes a functional unit only when a suitable tip is attached. The color of the control button of the pipette matches the color of the tip or the tip rack. Filling (Aspirating): 1. Securely attach appropriate pipette tip. 2. Press control button down to first stop (measuring stroke). 3. Hold pipette vertically and immerse tip approximately 3 mm into the liquid. 4. Let control button glide back slowly, wait 3-5 sec. for the liquid to enter the tip. Be careful to not let the tip come out of the liquid during this step, or liquid can enter the air displacement cylinder which can cause permanent damage to the pipette. 5. Slide the tip out of the liquid along the inside of the vessel. Wipe off any droplets with lint-free tissue. Ensure that no liquid is aspirated out of the tip.

2 Note: if the tip is removed from the liquid too quickly, coaxial forces may push liquid out of the tip. This may result in the pipetted volume being too low. Warning!! Never lay the pipette down with liquid in the tip as liquid can flow into the pipette Emptying (Dispensing): 1. Hold the tip at an angle against the inside of the vessel. 2. Press control button slowly down to the first stop (measuring stroke) and wait until no more liquid is emptied. 3. Press button down to second stop (blow-out) to empty tip completely. 4. Hold down control button. Slide tip out along the inside of the vessel. 5. Let control button glide back. 6. If you have completed all dispensing of the liquid eject the tip by pressing the lateral tip ejector button. Calibration 1. Firmly attach an appropriately sized pipette tip onto the pipette. 2. Adjust to the desired pipette volume. Calibration should be carried out at three volumes: nominal, 50% and the smallest volume. For example, for 1000 µl pipette, calibration should be done at 1000, 500 and 100 µl (see Table 1 below for the calibration volumes for each pipette). 3. Place a receiving vessel onto the pan of the Analytical Balance. Close any open doors and Zero the balance. (Wait until balance stabilizes) 4. Aspirate and dispense three volumes of distilled water into a waste beaker. 5. Open the top sliding door on the analytical balance. Aspirate the volume of distilled water into the pipette. Carefully insert the pipette from the top of the balance and dispense the test volume slowly and uniformly up to the first stop and wait for 1-3 sec. 6. Press the control button to the second stop and dispense any liquid remaining in the tip. 7. Hold down the tip and gently touch it against the weighing vessel. 8. Remove the pipette from the balance and close the sliding glass door. Record the weight after the display has come to a standstill. 9. Perform 10 measurements at each assigned volume. Calculate the inaccuracy and the imprecision. (See equations below.)

3 10. Enter the calculated values on the sheet provided. Compare your values to those provided by the manufacturer. See Table 1. Note: In order to achieve good accuracy and precision for volumes less than or equal to 10 µl, a new tip should be used each time (do not pre-rinse) and the sample should be dispensed into a weighing vessel that already contains a volume of the liquid (i.e. 1.0 ml). Table 1. Technical data for Eppendorf Series 2100 Pipette Model Color of Increment Volume Systematic Error Random Error Button µl µl ( Inaccuracy) (Imprecision; CV) µl light gray ± 2.5% 1.8% 5 ± 1.5% 0.8% 10 ± 1.0% 0.4% µl yellow ± 3.0% 1.0% 50 ± 1.0% 0.3% 100 ± 0.8% 0.2% µl blue ± 3.0% 0.6% 500 ± 1.0% 0.2% 1000 ± 0.6% 0.2% 500-5,000 µl violet ± 2.4% 0.60% 2500 ± 1.2% 0.25% 5000 ± 0.6% 0.15% Liquid: bidistilled water, degassed Room temperature: o C Number of determinations: 10 Table 2. Factor Z (µl/mg) as a function of temperature and air pressure: Temperature o C Pressure (mbar)960 Pressure (mbar) 1013 Z Z For an assigned pipette enter your experimental data and complete the following questions on the tear out sheet provided. Show all sample calculation on the back of the sheet. 1. Convert to actual volume (V I ) dispensed by multiplying each weighing by a correction factor Z (µl/mg). See Table 2 above.

4 (V i ) (µl) = M (mg) Z (µl/mg) 2. Calculate the mean actual volume delivered (V ): (V )(µl) = ( V ) i n where n = number of measurements 3. Calculate the standard deviation (s) for the actual volume delivered: (s) = 1 n n ( x 1 i= 1 i 4. Calculate % Inaccuracy (d): (d ) = x) 2 x x x nominal nominal Calculate the Coefficient of variation or Imprecision (CV): (CV) (%) = V s Calculate the difference between maximum and minimum value or Range (R): R(µL) = V maximum - V minimum 7. Compare your results to manufacturer s specifications in Table Discuss sources of error in the calibration procedure.

5 Micro-pipette Assigned ul Name: Volume measured µl Measured Mass Volume Delivered ( x i - x ) 2 mg µl Random Error Systematic Error 10. Imprecision % Innaccuracy Range Mean Volume SD CV (100%) d R Report: Volume measured µl Measured Mass Volume Delivered ( x i - x ) 2 mg µl Random Error Systematic Error 10. Imprecision % Innaccuracy Range Mean Volume SD CV (100%) d R Report: Volume measured µl Measured Mass Volume Delivered ( x i - x ) 2 mg µl Random Error Systematic Error 10. Imprecision % Innaccuracy Range Mean Volume SD CV (100%) d R Report:

6 Preliminary Lab Exercise -Part 2 Basic Instructions on use of Excel for Mathematical Calculations, Statistical Analysis, Generation of Regression Data and Graphing Spreadsheet applications are an extremely useful tool for carrying out a variety of computational tasks in analytical chemistry. There are a variety of spreadsheet programs available, such as Microsoft Excel, Quattro Pro, Lotus etc. You will only be introduced to the basics of Excel in this course; however, you may use any available spreadsheet. The following steps are a general outline and not intended to be a complete step by step procedure. Your own personal experience and understanding of spreadsheets may be of assistance, and if you have none this should provide you with a relatively simple introduction. Your Analytical text also has a quite useful section on the use of Excel. Excel can be used to analyze experimental data by performing a regression analysis (linear) to obtain the slope, intercept, and the equation of the line. It can also generate a graphical representation of the experimental data with a line of best fit, and the above parameters can be displayed on the graph. Further uses of Excel are to create a calibration curve; to compute mean; standard deviation (SD); pooled standard deviation (PSD); relative standard deviation (RSD); and coefficient of variation (CV). Calibration Curve for Two Dimensional Data: The Least-Squares Method Calibration Curves are used in many analytical methods. For example, a measured quantity y (dependent variable) is plotted as a function of the known concentration x (independent variable) for a series of standards. By plotting the measured value (y) for an unknown sample, its concentration can be extrapolated based on the corresponding value of x. In this exercise you will construct a calibration curve for determination of caffeine in an unknown caffeine sample. The ordinate (the dependant variable) equals the area under the chromatographic peak for a series of caffeine standards, and abscissa (the independent variable) equals the concentration of the caffeine standards in mg/l. It is often easy to identify that a linear relationship exists between a dependent variable y and an independent variable x, which is represented by equation (1): Y = mx + b (1) Where m is the slope and b is the y-intercept (where x = 0) Due to the indeterminate errors introduced during the analytical process, not all data points will lie exactly on the straight line. The analyst must therefore draw a line of best fit through the points. The most widely used and least biased approach is the statistical method of regression analysis, which also allows determination of uncertainties associated with the results. For a twodimensional data set, a simple regression method of least squares is used.

7 Use of Excel functions to calculate slope, intercept, and equation of the line or to determine the concentration of an unknown from a calibration plot For calibration calculations data is normally entered into two separate columns. The top of one column should be labeled for the x values (this is a usually the independent variable such as time, speed or standard concentration). The second column is then labeled for the y values (this is normally the dependent variable, or what you measure, i.e. response from the measurement such as Absorbance, peak area, current etc.). Each value entered has its own cell address based on the spreadsheet array e.g. C5, C6, C7 etc indicating column C row 5, then 6, then 7 etc Cell addresses are used in equations, or functions where they represent the specific values in the cell. For example if you want to add the values of three cells in cells A3 to A5, you could type in cell A6 =A3+A4+A5 or you could insert the function =Sum(A3:A5) Note: Cell addresses can be inserted into functions using mouse clicks for individual cells, or by selecting a range of cells i.e. highlighting cells A3 to A5 while the curser is in the brackets of the =Sum( ) function. For calibration data where we have x values in one column, and y values in another, we can readily determine the values for the slope and y-intercept for a line of best fit using functions that are built into Excel. Once we have established these values, the linear equation can then be arranged to solve for sample values by entering the dependant or measured y values into the expression and solving for x. The program function LINEST allows for the calculation of the slope (m) of the line for the data entered. The format of this function is as follows: =LINEST(cell range for y, cell range for x) The program will return the slope of the line in the cell where you entered this information. Use the program function INTERCEPT to obtain the intercept of the line for the data entered. Follow the format: =Intercept (cell range for y, cell range for x) The program will return the intercept of the line in the cell where you entered this information. Note for advanced users: The Linest function can provide a matrix of values that includes the slope, intercept, the standard deviations associated with each, and the correlation coefficient for the line of best fit. For further information consult the least squares section of your textbook. In order to determine sample x values the regression equation must be rearranged to x = (yb)/m. For example you should have a cell that contains information resembling: =(A10-F8)/G8 where A10 is the y data measurement for the unknown, F8 is the cell containing the intercept value and G8 is the cell containing the slope value. The formula will return the x value, which is the concentration of the unknown.

8 A graphical display can be made for your data by highlighting the cells that contain the calibration values for x and y, and then selecting the chart function from the toolbar, or from the Insert Menu, and selecting the X-Y Scatter chart type. On the chart you can add the line of best fit (a.k.a. the trend line), and the corresponding equation can be displayed. In the exercise that follows you will be using the above functions and features of Excel. Exercise #1a: Performing a Regression Analysis and Determining the Concentration of an Unknown Sample Launch the Excel application and set up a spreadsheet as shown below. The standard concentration values (x) are in cells A2 to A5, with corresponding Peak Areas (y) in Cells B2 to B5. 1) Use both methods to calculate the slope and intercept: Method 1 - calculate the slope (m) and the intercept (b) for the above data as follows: click on cell C2 and in the formula bar type =LINEST(B2:B5,A2:A5); click on cell D2 and in the formula bar type =INTERCEPT (B2:B5, A2:A5); the calculated values will be the slope and the intercept. Method 2 - click on cell C3, then select Insert Function from the menu (or select f(x) from the tool bar if it is visible). Select Statistical as function category, then LINEST as a function name. Next, you will be asked to enter cell ranges for y and x. You can type in the values i.e. B2:B5 for the y-values, or you can use the mouse and select the cell range on the spreadsheet. On the bottom of the box you will find a function definition which can be helpful for some functions. Click o.k. when finished. The value for the slope will appear in C3. It should be the same as in C2. Follow a

9 similar procedure for the intercept in cell D3 (note that other functions can also be done using both methods). 2) Cells B8 to B10 contain the data collected for three replicate samples. In order to determine the concentrations in mg/l for these samples the rearranged linear equation x =(y-b)/m must be entered into the corresponding cells in the A column. Click on cell A8 and in the formula bar type = (B8-D$2)/C$2 which is equal to rearranged formula. (Note: The $ in front of the number indicates a constant, in this case the slope and intercept are constants.) Click on A8 then pull down to highlight cells A9 and A10, select Edit Fill down from the menu (or Ctrl+D for Windows based systems). This will enter formulas and calculate concentrations for the two remaining samples. Note that in the formula for A9 the value for y is automatically adjusted for the corresponding cell address B9, but the cell addresses for the slope and intercept stay the same, as they were defined as constants. Alternate way, highlight cell A8, select Edit Copy, or in the tool bar click on Copy (two page icon). highlight the remaining cells A9 and A10 and select Edit Paste or click on Paste in the tool bar (Clipboard icon). 3) Calculate the Mean sample concentration; In cell A12 enter the column label Mean then click on cell A13 and in formula bar enter = SUM(A8:A10)/3, or type =AVERAGE(A8:A10), or select Insert Formula and Select AVERAGE from the list, then insert the cell range. 4) Calculate the Standard Deviation (SD or s); click on cell B12 and enter the Label STDEV, click on cell B13 and in the formula bar enter =STDEV(A8:A10), or use the insert function method. This will calculate the standard deviation for the three sample concentration. Next, ensure that you report correct number of significant figures for Cells A13 and B13, using one or two significant figures for the SD. (The Mean should not have more significant figures then is indicated by standard deviation. For example if the mean value reads and the SD is 0.246, then the result should be reported as ± 0.25 or 25.7 ± 0.2. If your result indicates that the number of decimal places needs to be adjusted then select Format Cells Number and select the appropriate number of decimal places for the cell, or click on the tool bar icons that show a small arrow beside decimal zeroes to increase or decrease the number of decimal places displayed.

10 *NOTE: When reporting your experimental results you must always report the correct number of significant figures in your mean, SD and 95% CI. Marks will be deducted if incorrect significant figures are reported. 5) Calculate coefficient of variation (CV) for the results. CV = x s x 100% Exercise 1b: Using the Charting Features of Excel to Generate a Calibration Curve and to Perform a Regression Analysis An alternate way of analyzing experimental data is to create a chart (graph) for the data and to perform an automatic linear regression on the graph. In this part of the exercise you will be plotting two sets of data on the same graph, and then you will use the built in functions to add the lines of best fit, the equations for the line, and the correlation coefficients, R 2 (this indicates how well the data fits the line with values that range from 0 to 1, when R 2 equals exactly 1 it indicates a perfect fit. In most cases the value will be less than 1). The displayed equations will then be used to calculate values for unknown samples in a spreadsheet. Data Set 1 Standard Concentration (mg/l) Peak Areas (au) Sample A Data Set 2 Standard Concentration (µg/l) Peak Areas (au) Sample B ) In your file from exercise 1A (called a workbook) select Insert Worksheet from the menu.

11 Enter the data for the two sets above in a neat and organized manner. You might have noticed that the concentration values are not the same for the two data sets. For Data Set 2 add an additional column labeled Concentration (mg/l), and convert the concentration values to mg/l using a mathematical function ( i.e. if you want a value in cell C15 to be ten times greater than in cell B15 then you can enter =B15*10 into cell C15, for subsequent operations that are the same in the column below the cell, i.e. C16 etc, use the Edit Fill Down menu). 2) Highlight the x,y data for Data Set 1, then select Insert Chart, or click on the chart icon from the toolbar. Select XY Scatter with a sub-type without lines, then click on next. 3) To add a second data set to the chart select the series tab at the top of the window, and then select Add. Series 2 should then be displayed below Series 1 (For Mac Users: To add a second data set Select Chart Source Data then select Add under the series box). Set the curser into the x values mailbox, and then select the concentration values from the worksheet (in mg/l) by selecting the cells. Set the curser into the y values mailbox (delete any text already there), and then repeat as per the x values. You can also add names to the series which will be displayed in the legend should you decide to add one.you should now see the two data sets on the chart. Click on Next 4) Add an appropriate title, and axis labels, and click Next. For Mac users titles and axis labels are added using chart tools and selecting the layout tab. 5) Select New Sheet for the chart location and select Finish. For Mac users select Chart Move Chart New Sheet from the menu. 6) Create a line of best fit by selecting Chart Add Trendline from the menu. For Mac users, you might have to select the series by clicking on a data point before going to the Chart menu. Select the desired series and Linear for the type of fit, then select the options tab and select the Display Equation on Chart and Display R 2 on Chart buttons. Then click OK. Repeat for the remaining series. 7) Use the slope and intercept values displayed on the chart to calculate the concentrations for the unknown samples on the worksheet, then calculate the Mean and Standard Deviation for the two samples with the correct significant figures.

12 Report: When you have completed this exercise print out the entire workbook and hand it into the appropriate report box labeled with your demonstrator s name.