Experiment 4
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-in-liquid. 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 mol Molarity(M) = =
Liter of Solution 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.
The Relationship of Density
and Molarity of an
moles mol Molality (m) = =
Kilogram of Solvent 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 (Vconc) of known
concentration (Cconc), and adding more solvent (dilution) until a new total volume is achieved
(Vdil.) The concentration of the new solution (Cdil) is computed from the dilution equation:
dil dil conc conc
dil dil conc conc
(Volume) * (Concentration) = (Volume) * (Concentration) or V * C = V * C Thus, conc conc dil dil V * C C = V
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.
Cconc = Molarity of stock solution = 1.75 M
Vconc = Volume of this solution needing to be diluted to a new volume, i.e., the unknown Cdil = Molarity of the diluted solution, 0.50 M
Vdil = Total volume of diluted solution required, 1 Liter (L)
dil dil conc conc
dil dil conc conc conc V * C = V * C V * C V = C 1 L * 0.5 mol / L 1000 ml V = = 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/cm3. For gaseous substances, density is commonly defined as grams per liter, g/L.
3
Mass grams material (g) Density = d = =
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 (1st standard solution) will be used to produce three (3) diluted standard solutions of known concentration. Distilled water will be used as the 5th 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) dil dil conc conc V * C V = C
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 (Mstock) Volume Stock Soln (Vstock) Volume Dilute Soln (Vdilute) Molarity Dilute Soln (Mdilute) #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
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 H2O)
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(H2O) 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 g
Mass of 150 ml Beaker plus Unknown Salt Solution g
Mass of Unknown Salt Solution g
Volume of Unknown Salt Solution ml
Density of Unknown Salt Solution 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 4.6: 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.
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 K – Vol of Std Soln A Col B – Vol Stock Added (A) Col L – Mass of Std Soln B Col C – Vol of Std Soln A Col M – Vol of Std Soln B Col D – Vol Stock Added (B) Col N– Mass of Std Soln C Col E – Vol of Std Soln B Col O – Vol of Std Soln C Col F – Vol Stock Added (C) Col P – Mass of Dist H2O
Col G – Vol of Std Soln C Col Q – Vol of Dist H2O
Col H – Mass of Stock Soln Col R – Mass of Unknown Col I – Vol of Stock Soln Col S – Vol of Unknown Col J – Mass of Std Soln A
Create Computation “Sheet”
Open a new sheet and rename it “DensityResults.”
Follow the instructions below to define the columns and setup the appropriate computational algorithms. The final form should look something like the following.
Row Col
A B C D E F G
1 Chemistry 211 - Section 2A1 Density NaCl Solutions
2 C_DistH2O C_Csoln C_Bsoln C_Asoln C_stksoln D_DistH2O 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_DistH2O Col H – D_Bsoln
Col B – C_Csoln Col I – D_Asoln Col C – C_Bsoln Col J – D_Stksoln Col D – C_Asoln Col K – D_Unksoln Col E – C_Stksoln Col L – Slope Col F – D_DistH2O Col M – Intercept
Col G – D_Csoln 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 (r2))
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
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.
