Experiment 4 The Relationship of Density and Molarity of an Aqueous Salt Solution Purpose: The purpose of this experiment is to investigate the relationship between the concentration of an aqueous salt solution and its density in order to develop a calibration curve for predicting the value of one entity based on the value of the other. Experience will be gained in preparing dilute solutions from a known stock solution; calculating the concentration of the dilute solutions using the concentration/volume equation; and to use the mass and volume of these solutions to determine the density. Background: A solution in chemical terms is a homogeneous mixture of a solute, or dissolved species, and a solvent, the medium into which the solute has dissolved. Separately, the solute and solvent are distinguishable, but in solution the boundary between solute and solvent can no longer be identified. By convention, the component present in the greatest quantity by mass is the solvent. The solute is present to an extent by mass less than that of the solvent. A solution can be either solid (a metal alloy, such as brass), liquid (sugar or salt), or gaseous (the air we breath) or any combination of these. The most encountered types of solution are solid-in-liquid or liquid-inliquid. Mixtures of this type, of a solute dissolved in a solvent, are frequently encountered in the laboratory environment and it is important to be familiar with the properties of solutions, and the methods used to quantify amounts of solute and solvent present. Solution Concentration Molarity: When preparing solutions for laboratory or other uses, it is important to indicate the relative composition of such solutions in terms of amounts of solute and solvent. The most commonly encountered unit of solution concentration, and used in this experiment, is molarity, which is defined as moles of solute per liter of solution. moles Molarity(M) = = Liter of Solution mol L It is important to contrast molarity with another commonly used measure of concentration that will be utilized in other experiments described in this manual, i.e., molality, which is defined as moles per kilogram of solvent.
moles Molality (m) = = Kilogram of Solvent mol kg The Dilution Equation: In this experiment a stock solution of known concentration will be used to prepare a series of dilute solutions to be used, along with the stock solution and distilled water, in the creation of a calibration curve relating concentration and density. These new solutions are made from taking a known amount in volume of the stock solution (V conc ) of known concentration (C conc ), and adding more solvent (dilution) until a new total volume is achieved (V dil.) The concentration of the new solution (C dil ) is computed from the dilution equation: Thus, (Volume) * (Concentration) = (Volume) * (Concentration) dil dil conc conc or V * C = V * C dil dil conc conc C = dil V conc * C V dil conc Example: Dilution of a Stock Solution Calculate the volume in ml of an aqueous salt solution of concentration 1.75 M required to prepare 1 Liter of aqueous solution of concentration 0.50 M Use the dilution equation, defining the known terms from the information in the problem. C conc = Molarity of stock solution = 1.75 M V conc = Volume of this solution needing to be diluted to a new volume, i.e., the unknown C dil = Molarity of the diluted solution, 0.50 M V dil = Total volume of diluted solution required, 1 Liter (L) V * C = V * C dil dil conc conc V = conc V dil *C C conc dil 1 L * 0.5 mol / L 1000 ml V conc = = 0.286 L * = 286 ml 1.75 mol / L L This answer indicates that if one were to measure 286 ml of a 1.75 M solution, and add water until the total volume was exactly 1.0 L, this solution would have a concentration (a molarity) of 0.50 mol/l.
Density: Physical properties of matters are categorized as either Intensive or Extensive. Properties that depend on the amount of matter present, such as Molarity, a concentration term, weight, volume, etc. are extensive. Properties that do not depend on the amount of matter present, such as color, conductivity, boiling point, and density, are intensive. This means density is not dependent on the amount (mass or volume, for example) of pure matter examined, but only on its identity. For salt water solutions, it is only true that the density of a solution of known molarity can have a precisely defined density. If the molarity is changed, the density necessarily will also change. Density is defined as the mass to volume ratio for a pure substance. For solids and liquids, densities will usually have the units of grams per milliliter, g/ml, or grams per cubic centimeter, g/cm 3. For gaseous substances, density is commonly defined as grams per liter, g/l. Mass Density = d = = grams material (g) 3 Volume volume occupied (ml, cm, L) Densities are temperature dependent, because volume in any phase of matter is itself temperature dependent. Density values are therefore commonly listed in reference tables with the temperature at which the density determination was made. The relationship of solution molarity (concentration in moles per liter) to solution density (ratio of grams per unit volume) is qualitative. As the molarity of a given volume of an aqueous solution increases, say from 0.25 M to 0.50 M, the masses of a constant volume of these two solutions should be different, i.e., different densities. The Experiment: The experimental process will attempt to demonstrate if a linear relationship exists between the concentration of an aqueous Sodium Chloride (NaCl) solution and its density and to create a calibration curve from this relationship as a means of determining the concentration of an unknown solution from its measured density. A stock solution of known concentration (1 st standard solution) will be used to produce three (3) diluted standard solutions of known concentration. Distilled water will be used as the 5 th standard solution. The mass of precise volumes of each of the 5 standard solutions will be determined. The mass and volume will be used to compute the density of each solution. Pre-Lab Report & Notebook: Download from the department data base to your hard drive or flash drive a copy of the lab report template and the data summary tables for the Density experiment: http://chem.gmu.edu/templates Print the data summary tables and use them to record the laboratory results during class. Stock Solution Dilution table
Volume, Mass, Molarity, Density table Unknown Mass Density table Unknown Molarity and Density table Prepare the Pre-lab report according to instructor s instructions Materials & Equipment: Materials Equipment 3 M NaCl ring stand distilled water buret clamp 50 ml buret 10 ml volumetric flask electronic balance calculator Procedure: Determine the mass and density of distilled water 1. Obtain a clean, dry 10 ml volumetric flask with stopper 2. Weigh this empty flask on the balance to the nearest 0.001 g 3. Fill the flask to calibration mark with distilled water 4. Weigh the flask with distilled water 5. Compute the mass of water from the difference of the filled flask and the empty flask 6. Compute the density of water from its mass and volume 7. Record these values as dilution # 5 in the downloaded summary table (see table 4.2 below) Determine the mass and density of the stock solution (3.0 M NaCl) 1. Rinse another 10 volumetric flask with several ml of the 3M NaCl stock solution 2. Fill the flask with stock salt solution up to the calibration mark 3. Dry the flask, if necessary, and weigh the flask and stock solution 4. Compute the mass of stock solution from the difference of the filled flask and the empty flask 5. From the volume and mass of the stock solution, compute the density of stock solution 8. Record the results as dilution #1 in the downloaded summary table (see table 4.2 below)
Prepare solutions for dilutions 2, 3, and 4 Use the Dilution Equation to compute approximate volumes of the concentrated salt solutions needed to prepare 10.00 ml each of the following Molarities: 2 M (moles/liter) (Dilution # 2) 1 M (moles/liter) (Dilution # 3) 0.5 M (moles/liter) (Dilution # 4) V = conc V dil *C C conc dil Note: The actual concentrations of the standard solutions will be based on the measured amount of stock solution used to prepare the solutions. Table 4.1: Approximate volumes of stock solution to be used in preparation of standard solutions Dilution # Molarity Stock Soln (M stock ) Volume Stock Soln (V stock ) Volume Dilute Soln (V dilute ) Molarity Dilute Soln (M dilute ) #1 3.00 M 10.0 ml 10.0 ml 3.00 ml #2 3.00 M ml 10.0 ml 2.00 ml #3 3.00 M ml 10.0 ml 1.50 ml #4 3.00 M ml 10.0 ml 0.50 ml #5 3.00 M 0.00 ml 10.0 ml 0.00 ml Prepare Standard Solutions 1. Setup a buret using a ring stand and buret clamp 2. Rinse buret with a few milliliters of stock 3.0 M NaCl salt solution 3. Fill buret with stock solution 4. Drain sufficient solution through the stopcock to eliminate any air pockets 5. Read the scale at the meniscus, i.e., bottom of liquid curve Note: The liquid level does not have to be at 0.00; any level near top will suffice 6. From the buret deliver into the 10.00 ml volumetric flask designated as dilution #2 a volume of stock salt solution approximately equal to the amount computed to prepare the 2 M standard solution Note: The amount delivered does not have to be the exact amount computed, but the amount delivered from the buret must be determined to the highest precision of the buret, i.e., 0.01 ml 7. Record the beginning and ending liquid levels in the buret in the summary table
8. The volume added is the difference of these readings 9. Add distilled water to the flask until the flask is about ¾ full. Stopper and swirl gently to mix thoroughly 10. Add additional distilled water (drop by drop near the end) until the meniscus is just on the calibration mark 11. Dry the outside of the flask, if necessary, and weigh the filled flask on the balance 12. Determine the mass of the solution in the flask from the mass of the filled flask and the mass of the empty flask 13. From the concentration of the stock solution, the volume of stock solution added, and the volume of the dilute solution (10.0 ml), compute the concentrations for dilutions 3, and 4 14. Record the results for dilution 2, 3, and 41 in the downloaded summary table (see table 4.2 below) Table 4.2: Summary Table for Volume, Mass, Molarity and Density of Sodium Chloride Standard Solutions Dilution #1 (3.00 M NaCl) Dilution #5 (Distilled H 2 O) Volume NaCl stock solution, final ml 0.0 ml Volume NaCl stock solution, initial ml 0.0 ml Volume NaCl stock solution, total ml 0.0 ml Molarity NaCl, diluted solution 3.00 M 0.0 M Mass of volumetric flask + solution g g Mass of volumetric flask g g Mass of solution in flask g g Density of solution in flask g/ml g/ml Dilution #2 Dilution #3 Dilution #4 Volume NaCl stock, final ml ml ml Volume NaCl stock, initial ml ml ml Volume NaCl stock, total ml ml ml Molarity NaCl, diluted M M M Mass of vol flask + solution g g g Mass 10 ml vol flask g g g Mass of soln in vol flask g g g Density of dilute solution g/ml g/ml g/ml
Setup molarity vs density summary table for calibration curve Summarize the applicable molarity and density results from table 4.2 in table 4.3 below. Table 4.3: Molarity vs. Density: Calibration Curve Information Dilution # Molarity Density 1(H 2 O) 0.00 M g/ml 2 M g/ml 3 M g/ml 4 M g/ml 5 (Stock) 3.00 M g/ml Determine the mass of an unknown solution 1. Obtain a sample of sodium chloride solution of unknown concentration from the instructor 2. Note the unknown solution number in the data summary table 3. Rinse a 10 ml volumetric flask with a few ml of the unknown solution. 4. Fill the flask to the calibration mark with the unknown solution 5. Dry the flask and weigh the flask containing the unknown solution 6. Compute the mass of the unknown solution from the masses of the filled and empty flask Compute the density of the unknown solution Compute the density of the unknown solution from the mass and volume (10.00 ml) of the unknown solution. Record the sample unknown results in the summary table 4.4 below. Table 4.4: Mass and Density of Unknown Solution Summary Table Unknown Salt Solution Number Mass of Clean, Dry, 150 ml Beaker, Empty Mass of 150 ml Beaker plus Unknown Salt Solution Mass of Unknown Salt Solution Volume of Unknown Salt Solution Density of Unknown Salt Solution g g g ml ml
Analysis and Conclusions: Data Processing: Use the printed Pre-lab report as a notebook to record the measured volume and mass results. Enter the measured and computed values into the printed results summary table and attach to report. If required by the instructor, transfer the laboratory results to the electronic files and finalize the laboratory report. Spreadsheet Processing: Input Results into Laboratory Database Use one of the laboratory computers and the web-based data entry form shown in Figure 4.5 below to enter the experimental results into the laboratory database. Figure 4.5 Input form for entering Density lab results into laboratory database Part A.
Figure 4.6: Input form for entering Density lab results into Excel database Part B. Mass Data Retrieval: Retrieve the class data for the Density experiment from website http://chem.gmu.edu/results (select Density ) Copy the data presented on the screen and insert into a spreadsheet (Excel, Google, other) and save the spreadsheet on your hard drive or flash drive with an appropriate file name. Your default sheet should be renamed (RawData) and have the following columnar format:
Row Col A B C D E F G H I 1 Chemistry 211 Section 2A1 Density NaCl Solutions 2 Conc_stock Vi_A Vf_A Vi_B Vf_B Vi_C Vf_C m_stock V_stock 3 4 J K L M N O P Q R S m_a V_A m_b V_B m_c V_C m_water V_water m_unkwn V_unkn Column Definitions Sheet #1 (RawData) Lab results entered during lab (all students) Col A Stock Conc (3.00 M) Col B Vol Stock Added (A) Col C Vol of Std Soln A Col D Vol Stock Added (B) Col E Vol of Std Soln B Col F Vol Stock Added (C) Col G Vol of Std Soln C Col H Mass of Stock Soln Col I Vol of Stock Soln Col J Mass of Std Soln A Create Computation Sheet Open a new sheet and rename it DensityResults. Col K Vol of Std Soln A Col L Mass of Std Soln B Col M Vol of Std Soln B Col N Mass of Std Soln C Col O Vol of Std Soln C Col P Mass of Dist H 2 O Col Q Vol of Dist H 2 O Col R Mass of Unknown Col S Vol of Unknown Follow the instructions below to define the columns and setup the appropriate computational algorithms. The final form should look something like the following. Row A B C D E F G Col 1 Chemistry 211 - Section 2A1 Density NaCl Solutions 2 C_DistH 2 O C_Csoln C_Bsoln C_Asoln C_stksoln D_DistH 2 O D_Csoln 3 4
H I J K L M N D_Bsoln D_Asoln D_Stksoln D_Unksoln Slope Intercept C_Unk Column Definitions DensityResults Sheet Algorithms for Density Computations Merge row 1 cells, Cols A-N and enter title info, such as: Chemistry 211 Sec 205 Density of NaCl solutions Rename second row columns (A:O) as follows: Note: C = Concentration; D = Density Ex: C_Bsoln = Concentration of B standard solution Col A C_DistH 2 O Col B C_Csoln Col C C_Bsoln Col D C_Asoln Col E C_Stksoln Col F D_DistH 2 O Col G D_Csoln Col H D_Bsoln Col I D_Asoln Col J D_Stksoln Col K D_Unksoln Col L Slope Col M Intercept Col N C_Unk Enter info and algorithms for Results sheet Enter 0.000 into Cells A3:Bx and 3.000 into cells F3:Fx Compute concentrations of standard solutions C, B, A in columns B, C, D, respectively Student concentrations Enter your algorithm into Cell B3 Enter your algorithm into Cell C3 Enter your algorithm into Cell D3 Copy algorithms for class concentrations to rows B4:Bx; C4:Cx; D4:Dx Select cells B3:Dx For Excel: From Editing box under Home on Menu bar select Fill Down For Google: Press Ctrl D
Compute Densities from mass and volume for all 5 Standard Solutions in columns F:K (Dist Water, Soln C, Soln B, Soln A, Stock, Unk) Enter applicable algorithms into cells F3:K3 Copy density algorithms for class to rows G4 : Lx Select cells F3 : K3 For Excel: From Editing box under Home on Menu bar select Fill Down For Google: press Ctrl D Compute Slope and Intercept Use functions SLOPE & INTERCEPT to compute the slope (Col L) and intercept (Col M) of the calibration plot Enter applicable Slope algorithm into cell L3 Enter applicable Intercept algorithm into Cell M3 Copy Slope and Intercept algorithms for class to rows M3 : Nx Select cells M3 : N3 For Excel: From Editing box under Home on Menu bar select Fill Down For Google: press Ctrl D Create Calibration Curve (Concentration vs. Density just student s data) Transpose Density values from row to columnar format In DensityResults sheet select cells F3:J3 (Density Values) In Clipboard click on Copy Click on an available cell in column A a few rows below the computed data cells Under Paste select Paste Special Click Values Click Transpose Click OK Select cells A3:E3 (Concentration Values) In Clipboard click on Copy Click on the adjacent cell in column C Under Paste select Past Special Click Values Click Transpose Click OK
Insert Scatter Plot / Linear Regression Select the transposed data Click on Insert in menu bar Click on Scatter box Click on Scatter icon Note: The chart is created on the spreadsheet page Enter axis and title information Select (Click) anywhere in the chart Click on Chart Layouts in the Menu Bar Select the first icon in the box, which modifies the chart to accommodate the chart title, the Y-axis title and the X-axis title Right click on each of the title boxes and select edit to enter your titles Add Trend Line (regression curve, equation, coefficient of determination (r 2 )) Click on Chart Tools icon above menu bar Click on Layout Click on Trendline Click on More Trendline Options Click on Linear Regression Click on Display Equation on Chart Click on Display R-squared Value on Chart Select the equation box and move text to upper left corner of chart Determine the mass of an unknown solution Obtain a sample of Sodium Chloride solution of unknown concentration from the Prep room Determine the mass of an empty, clean, dry 10 ml volumetric flask Fill the 10 ml volumetric flask to the mark with the unknown solution Weigh the flask containing the unknown solution Compute the mass of the unknown solution by difference of the filled flask and the empty flask Compute the density of the unknown Compute the density of the unknown solution from the mass and volume (10.00 ml)
Determine the Concentration of the Unknown Locate the unknown density value on the Y-axis of the calibration curve Move horizontally to the calibration curve line Drop down vertically to the X-axis and read the value corresponding to the concentration of the unknown solution. Figure 4.7: Determination of concentration from density using a calibration curve