INTRODUCTION

 In this experiment you will gain experience in the use of the volumetric transfer pipet and volumetric flask, the technique of standard dilutions, the use of computerized spreadsheets for analysis of data, and graphical analysis.  The mathematical relationship between the molar concentrations of sodium chloride solutions and their density will be determined.

Volumetric glassware consists of specialized pieces of glassware that are used to measure volumes of liquids very precisely in quantitative laboratory work.  Among these are graduated cylinders, burettes, pipets, and volumetric flasks.  These are carefully manufactured and expensive items and should be treated with great care.  Ordinary beakers and flasks are not used for accurate volume measurements; the markings on these pieces of glassware are generally only accurate to within 5%.

The volumetric flask is calibrated to contain a fixed amount of solution with high accuracy.  The flask is used in two major ways.  In one technique, a solid sample of known mass (the solute) is placed in the flask and dissolved.  The solution is then made up to the mark on the flask by adding solvent, giving a solution of precisely known volume containing a precisely known amount of solute.  If the solute is pure ("primary standard" grade), it is then possible to calculate the molarity of the solution (moles of solute per liter of solution).  Click on the following link to see the NT Curriculum Project materials on volumetric flasks.  The second use of the volumetric flask is to dilute a solution in a precisely known manner.  This technique involves placing an aliquot (sample of precisely known volume) of a solution of known molarity in the flask, then diluting to the mark with solvent.  The new concentration may then be calculated using the volumes of the original aliquot and the new total volume (equation 1).

                              M₁ x V₁  =  M₂ x V₂                                                                             (1)

Note that the product of molarity and volume gives the number of moles of solute.  While the amount of solvent, and thus the total volume, changes, the amount of solute remains constant in a dilution process.  In this experiment a series of solutions is to be prepared by successive dilutions of a stock solution.  The density of each solution is determined by measuring the mass of a known volume of the solution.  The data are analyzed to determine the precise mathematical relationship between density and concentration, i.e., to discover an equation which relates these two quantities.

 A spreadsheet is simply the arrangement of numerical data in columns and rows.  Data tables may be regarded as a form of simple spreadsheet.  Computer spreadsheets such as Lotus 1-2-3, Quattro Pro, and Excel have become widely used in recent years.  One of the chief advantages of such spreadsheets is the ability to enter mathematical formulas once and then to simply copy the formula down an entire column; the computer then carries out the same type of calculation for the whole column, substituting the appropriate values from each row.  This process is far faster and less tedious than manually carrying out the same type of calculation several times, each time entering a new set of numbers.  Further advantages of computer spreadsheets include the ability to easily produce a variety of high-quality graphs from the data contained in the spreadsheet and to carry out various types of numerical and statistical analysis.  The Microsoft Excel program, which is accessible through the Centre College local area network, will be used to treat the data from this experiment.
 

PRE-LAB EXERCISE (do in your notebook before coming to lab)

 1.  Calculate the mass of sodium chloride necessary to prepare 100.0 mL of a 3.000 M solution.  Be careful with significant figures.

 2.  Calculate the volume of 2.000 M sodium chloride solution needed to prepare 250.0 mL of a 0.8000 M solution.

 3.  Calculate the resulting molarity if 50.00 mL of 2.000 M sodium chloride solution is diluted to 250.0 mL.
 

EQUIPMENT:  10-mL and 25-mL volumetric pipets, 100-mL volumetric flask, funnel, Pasteur pipet, 50-mL beaker, three 250-mL Erlenmeyer flasks, wash bottle
 

EXPERIMENTAL

Record the room temperature in your notebook.   Rinse the volumetric flask with deionized water and drain.  If the water does not drain in a smooth, unbroken film, the glass is not clean.  If this is the case, scrub the neck of the flask with warm detergent solution, rinse thoroughly with tap water, and follow with a final rinse of deionized water.

 Weigh out the mass of sodium chloride which you calculated in question 1 above (in a weighing boat).  The mass should be within ±0.3 g of the calculated value and recorded to the full precision of the balance, i.e., to four decimal places.  Carefully transfer the entire sample to the volumetric flask (this is called a quantitative transfer); the wash bottle may be used to assist in this transfer.  Be sure that none of the solid clings to the inside of the neck of the flask.  Fill the flask about two-thirds full with deionized water and mix well to dissolve the solid.  Carefully add water to a point slightly below the index line on the neck of the flask.  Use a Pasteur pipet to carefully bring the water level (bottom of the meniscus) exactly to the mark.  Stopper the flask or cover with Parafilm and shake well to thoroughly mix the contents.  This solution is your original stock solution, which we will call solution number 1.

 Weigh a small clean, dry beaker.  Pipet 10.00 mL of solution number 1 into the beaker and weigh again.  Empty the beaker and repeat the procedure (including the weighing of the "empty" beaker).  Question: Why do you not need to clean and dry the beaker?  From these data you will be able to calculate the density of solution number 1.

 Transfer the remainder of solution number 1 to a clean, dry Erlenmeyer flask.  Question:  Why does this flask need to be clean and dry?  Rinse the volumetric flask thoroughly.  Pipet 50.00 mL of solution number 1 back into the volumetric flask, and use deionized water to make up to the mark as before.  This is solution number 2.  Determine the density of this solution in the same manner as the stock solution.  This procedure is diagrammed in the flow chart below.
 
 

Do two more dilutions in a similar manner, i.e., dilute 50.00 mL of solution number 2 to a total volume of 100.0 mL to make solution 3 and determine the density, then dilute 50.00 mL of solution 3 to a total volume of 100.0 mL to make solution 4 and determine the density.  You should have four sets of density data, for the original stock solution (number 1) and the three dilutions (solutions 2-4).
 

CALCULATIONS

 1. Calculate the molarity of the stock solution.  Use a sufficient number of significant figures for the formula weight of NaCl such that it is consistent with the other data.  The volume of the volumetric flask is good to one decimal place and the volumes of the pipets to two decimal places.

 2. Calculate the molarities of the three diluted solutions 2-4.

 3. Calculate the average mass of a 10.00-mL sample of each of the four solutions.

 4. Set up a spreadsheet in Excel with the following column headings:  Solution no., molarity, average mass (of the 10-mL aliquot), volume (10.00 mL in all cases), and density.  All values should have the appropriate number of significant figures.  There should be four rows of data corresponding to the four solutions.  Use a spreadsheet formula to determine the experimental densities of solutions 1-4. Guidelines to the use of Excel are found here.

 5. Prepare a graph using density as the ordinate (y-value) and molarity as the abscissa (x-value).  Use Excel to print the graph.  Do a linear least squares regression to determine the slope of the graph (remember that it has units) and the y-intercept, plus the uncertainties (standard error) in each.  Also determine the correlation coefficient "R squared".  Plot the data points with markers and the best-fit line defined by the slope and intercept.  The line should pass through the y-intercept.

 Include computer printouts of the spreadsheet, graph, and regression analysis results in your report.  In your discussion of results, you should carefully explain the exact mathematical relationship between density and molarity (give an equation with relevant constants and units).  It is expected that you will include a rigorous error discussion, including sources, effects, and estimated magnitudes of systematic errors, plus discussion of your statistical results (R-squared, slope and intercept with standard errors, and residuals).
 

QUESTIONS (to be included at end of discussion section)

 1. Why is it not necessary that the volumetric flask be dry initially?

 2. If you overshoot the calibration mark on the volumetric flask, what can you do?  What effect would such an error have on the calculated molarity and density?

 3. Although the volumetric flask could be wet before adding samples, the Erlenmeyer flasks had to be dry.  Explain.

 4. Use your results (slope and intercept, not the graph) to calculate the density of a 1.500 M sodium chloride solution.

 5. What is the physical significance of the y-intercept?  Compare your experimental value to the expected value (you will have to look this up for the relevant temperature and reference your source).