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# Job's Method of Continuous Variation

By Randy Griffin,2014-06-27 12:01
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Job's Method of Continuous Variation

Job’s Method of Continuous Variation

Purpose

; Determine the stoichiometry of a chemical reaction experimentally

; Determine the chemical formula of a precipitate

; Determine the oxidation state of an ion in solution

Introduction

How can the stoichiometry of a chemical reaction or the formula of a compound be determined experimentally? It can be done using Job’s Method of Continuous Variation, which keeps the total number of moles of reactants constant throughout a series of mixtures and reactants, but varies the mole fraction of each reactant from mixture to mixture. Certain specific measurements are then taken for each of the mixtures. Since the maximum change will occur when the mole fraction of the reactants is closest to the actual stoichiometric mole ratio, both the formula of the product and reactant stoichiometry can be determined using this approach.

Specifically, by measuring the change in temperature, the absorbance, the height and the mass of the precipitate formed for each reaction mixture, and graphing these measurements versus mole fraction, one can determine the mole fraction for each reactant that produces the maximum change.

Keep in mind that the maximum change will occur when each reactant is a limiting reactant. So, the graph of mole fraction versus change will show a region starting when the mole fraction of this reactant is zero and increasing as the mole fraction of this reactant increases until the stoichiometric mole ratio of reactants is reached. In this region, the slope of the change will be positive and the limiting reactant will be the reactant being graphed. When the maximum change is reached, the other reactant becomes the limiting reactant, and the magnitude of the change drops, resulting in a negative slope.

Where the change is biphasic, there will be a region with a positive slope for the mole fraction range in which the reactant graphed is the limiting reactant, and a region with a negative slope for the range in which the reactant graphed is in excess. The point at which these lines intersect is the experimental value for the mole fraction of the reactant that produces maximum change when both reactants are limiting reactants. The ratio of mole fractions of ion in this compound will be used to determine the chemical formula of the product and the stoichiometric ratio. The ratio of these mole fractions is the stoichiometric ratio of the reactants in the chemical reaction. The oxidation number of the reacting ion can then also be determined.

Pre-Lab Questions

Volume of 0.1 M Volume of 0.1 M

Potassium Iodide (mL) Lead Nitrate (mL) Mass of Precipitate Formed (g)

1.0 19.0 0.12

2.0 18.0 0.23

3.0 17.0 0.36

4.0 16.0 0.46

5.0 15.0 0.58

6.0 14.0 0.70

7.0 13.0 0.81

8.0 12.0 0.92

9.0 11.0 1.04

10.0 10.0 1.15

11.0 9.0 1.30

12.0 8.0 1.38

13.0 7.0 1.50

14.0 6.0 1.41

15.0 5.0 1.15

16.0 4.0 0.92

17.0 3.0 0.68

18.0 2.0 0.48

19.0 1.0 0.23

Graph of Mole Fraction vs. Mass of Precipitate

1.60

1.40

1.20

1.00

0.80

0.60Mass Precipitate (g)

0.40

0.20

0.00

0.000.100.200.300.400.500.600.700.800.901.00

Mole Fraction of Iodide Ion

1. a. Why is there no data for the mixture of 20.0 mL of lead nitrate with 0.0 mL of potassium iodide, of for the 20.0 mL of potassium iodide with 0.0 mL of lead nitrate?

b. What would be the mass of the precipitate be if those data points were collected? Please explain briefly.

2. The data in the table has been converted to mole fraction of iodide ion and the mole fraction of iodide ion is plotted versus the mass of precipitate formed. Use the graph to estimate the stoichiometric ratio of lead ion to iodide ion by drawing a best fit line for the data with the positive slope, and a separate best fit line with the negative slope. Drop a perpendicular to the x-axis from the intersection point of these best fit lines to determine the mole fraction of the iodide ion needed to form the maximum mass of precipitate.

a. What is the mole fraction of lead nitrate at the point you created?

b. What is the mole fraction of potassium iodide at this point?

c. Determine the stoichiometric ratios between these ions by taking the ratio of the mole

fractions you determined in questions 2a and 2b. Please show your work.

d. Write the formula of the precipitate.

e. Write the balanced net ionic equation for the reaction that forms this precipitate.

Lab Schedule

Thursday, August 31, 2006

; Single class

addition, at 6:45 7:20 am I will be doing a discussion on this lab.

; Double class

; Prelab discussion

; Start methods 1 and 2 (create the solution for yourselves and Single Class)

Friday, September 01, 2006 (Single and Double)

; Single Class

; Prelab discussion (brief)

; Only do methods 3 and 4 (dry over the weekend)

; Double Class

; Learn how to use the calculator

; Methods 3 and 4 (dry over the weekend)

Tuesday, September 05, 2006

; Single Class

; You will have to come in either lunch time, after or before school sometime this week

to measure height and absorbance from the double class and the rest of you results.

; This should not take more than 20 minutes

; Double Class

; Measure height and absorbance of the solutions and mass of precipitate

Procedures

In the procedural methods that follow, an exothermic reaction between aqueous solutions of sodium hydroxide and a copper ion of unknown oxidation state will be investigated. Since this reaction is a precipitation reaction, you will also measure the height of the precipitate in each test tube after it settles overnight. These experimental data will not only determine the stoichiometry of the reaction, but also be used to determine the formula of the precipitate and the oxidation number of the copper ion:

x+-Cu + x OH ; Cu(OH) (aq)(aq)x(s)

Note: Methods 1 and 2 use identical procedures to make the sample solutions, so the same samples produced during Methods 1 can later be analyzed using Method 2, where the absorbance is at 635 nanometers is measured with a spectrophotometer.

-Test Tube # Volume copper ion (mL) Volume OH (mL)

1 0.00 10.00

2 1.00 9.00

3 2.00 8.00

4 2.50 7.50

5 3.00 7.00

6 3.33 6.67

7 4.00 6.00

8 5.00 5.00

9 6.00 4.00

10 7.00 3.00

11 8.00 2.00

12 9.00 1.00

13 10.00 0.00

Test tube measurements for Methods 1 and 2

Similarly, Methods 3 and 4 are identical procedures to make sample solutions, so the samples whose

temperature change is measured during Method 4 can be used to measure the mass of precipitate

formed in the reaction by filtration in Method 4.

-Volume of copper ion (mL) Volume of OH (mL)

0.00 50.0

5.0 45.0

10.0 40.0 -Volume of copper ion (mL) Volume of OH (mL)

15.0 35.0

20.0 30.0

25.0 25.0

30.0 20.0

35.0 15.0

40.0 10.0

45.0 5.0

50.0 0.00

Measurement ratios for Methods 3 and 4

Method 1: Height of the Precipitate and Qualitative Observations

In this experiment, you will mix known volumes of sodium hydroxide with known volumes of a

copper ion solution, keeping the total volumes of solutions mixed to 10.00 mL. After thoroughly

mixing the reactants and allowing the precipitates to settle overnight, you will take careful

observations of the solid and the solution and measure the height of the precipitate. By graphing the

mole fraction of hydroxide ions versus the height of the precipitate, you will be able to determine the

ratio of mole fractions of the reactants (χand χ). The ratio of these mole fractions (χ/ copper ion OHcopper ion

χ) can be used to determined the stoichiometric ratio of the reactants, and then the formula of the OH

hydroxide product and the oxidation state of the copper ion.

Materials

; Two 50 mL burets

; Standardized 1 M sodium hydroxide solution

; Standardized 1 M copper sulfate solution

; Test tubes and rack

; Stirring rods

; Ruler

Step 1: Label test tubes with the assigned ratios of copper ion to hydroxide you were given. Use a clean and rinsed buret to deliver the volume of copper ion solution to each test tube. Record the exact volume added in your data table.

Repeat the same procedure, this time delivering the appropriate volume of standardize hydroxide solution to the test tube, being careful not to contaminate the buret. Record the exact volume.

Step 2: Stir the mixture carefully with a stirring rod and cover the test tube with parafilm.

Step 3: Let the precipitate settle over the weekend.

Step 4: On Tuesday, remove the test tube from the rack and rest its bottom on the lab bench. Hold the test tube straight upright.

Step 5: Measure the height of the precipitate. Repeat for each sample.

Step 6: Arrange the test tubes side by side in the rack in order of increasing volume of hydroxide added. Placing a sheet of white paper behind your samples, carefully observe both the precipitate and the supernatant that is, the solution on top of the solid. Record your observations.

Calculations

1. Present all your data in tabular form

2. Calculate the mole fraction of both the copper ion and the hydroxide ion in each sample

3. Using your observations, list the test tubes in which the copper ion is the reactant in excess.

4. Using your answers to Calculations 1 3, predict the stoichiometric ratio of the chemical

reaction.

5. Graph the mole fraction of copper ion versus height of the precipitate. Draw a line of best fit

for both the positive and negative slope regions. Drop the perpendicular from the intersection

point to the x-axis to determine the mole fraction of the copper ion that produces maximum

change.

6. Use your answer to Calculation 5 to determine the mole fraction of hydroxide ion at the

intersection point. Use these mole fractions to determine the formula of the ionic compound

that precipitated in the reaction.

7. Determined the stoichiometric ratio of copper ion to hydroxide ion for this reaction.

8. Write a balanced net ionic reaction equation for the precipitation reaction.

Method 2: Absorbance at 635 Nanometers

This method uses the same procedure for Steps 1 3 from Method 1, so the samples sealed in the test

tubes after data collection in Method 1 can be used

Materials

; Precipitated solutions from Method 1 sealed in test tubes

; Spectrophotometer

; Cuvettes

; Transfer pipets

Step 7: Be sure the spectrophotometer is warmed up. Follow my instructions to zero the spectrophotometer at 635 nm.

Step 8: Without disturbing the precipitate, carefully remove sample from the test tube, using a transfer pipet, and place in cuvette. Be sure to fill the cuvette with the appropriate volume of sample.

Step 9: Be sure there is no solid in the sample and remove all air bubbles. Wipe outside of cuvette with damp paper towel to remove any fingerprints or dirt.

Step 10: Place cuvette in spectrophotometer and close the cover. Read absorbance at 635 and record in data table.

Step 11: Repeat for each sample.

Calculations

1. Present all your data in tabular form

2. Calculate the mole fraction of both the copper ion and the hydroxide ion in each sample

3. Graph mole fraction of copper ion versus absorbance

4. Carefully analyze this graph to determine the mole fraction of copper ion when there is a

significant change in the absorbance readings

5. Using your answer Calculation 4, calculate the mole fraction of hydroxide ion at that point, and

then use the ratio of mole fractions of copper ion to hydroxide ion to determine the formula of

the ionic compound that precipitated in the reaction.

6. Determine the stoichiometric ratio of copper ion to hydroxide ion for this reaction.

7. Write a balanced net ionic reaction equation for the precipitation reaction.

Method 3: Temperature Change

Materials

; Two 50.0 mL graduated cylinders

; Two 25.0 mL graduated cylinders

; Standardized 1 M sodium hydroxide solution

; Standardized 1 M of copper sulfate solution

; Polystyrene coffee cup placed in 250 mL beaker

; Thermometer or temperature probe

; Stirring rod

Step 1: Use the appropriate graduate cylinder to measure the volumes of hydroxide ion solution. Record the exact volumes in the data table.

-Volume of copper ion (mL) Volume of OH (mL)

0.00 50.0

5.0 45.0

10.0 40.0

15.0 35.0

20.0 30.0

25.0 25.0

30.0 20.0

35.0 15.0

40.0 10.0

45.0 5.0

50.0 0.00

Step 2: Measure the initial temperature of hydroxide solution. Record the initial temperature in the data table.

Step 3: Rinse the thermometer with distilled water and dry.

Step 4: Use the appropriate graduated cylinder to measure copper ion solution and pour your sample into the coffee cup/beaker apparatus. Record the exact volume added in your data table.

Step 5: Add the thermometer and monitor the solution temperature until unchanged for 1 minute. Record initial temperature in data table.

Step 6: Pour hydroxide solution into the copper ion solution and stir while constantly reading the thermometer. Keep stirring and reading until the maximum temperature is reached. Record the maximum temperature in the data table.

Step 7: Follow my instructions for waste disposal, do not pour down in sink.

Step 8: Rinse coffee cup, thermometer and stirring rod with distilled water and pat to dry.

Step 9: Repeat above steps for the rest of the samples.

Calculations

1. Present all your data in tabular form

2. Calculate the mole fraction of both the copper ion and the hydroxide ion in each sample.

3. Calculate change in temperature (ΔT) for each copper ion sample.

4. Graph mole fraction of copper ion versus ΔT. Draw a line of best fit for both the positive slope

region and the negative slope region. Drop a perpendicular from the intersection point to the x-

axis to determine the mole fraction of the copper ion that produces the maximum change.

5. Use your answer to Calculation 4 to determine the mole fraction of hydroxide ion at the

intersection point. Use the mole fractions to determine the formula of the ionic compound that

precipitated in the reaction.

6. Determine the stoichiometric ratio of copper ion to hydroxide ion for this reaction.

7. Write a balanced net ionic reaction equation for the precipitation reaction.

Method 4: Mass of Precipitate

Materials

; Two 50.0 mL graduated cylinders

; Two 25.0 mL graduated cylinders

; Standardized 1 M sodium hydroxide solution

; Standardized 1 M of copper sulfate solution

; Beakers

; Stirring rod

; Filter paper and funnels

; Ring stands and rings

; Electronic balance (0.00)

Step 1: Use the appropriate graduate cylinder to measure the volumes of hydroxide ion solution. Record the exact volumes in the data table.

-Volume of copper ion (mL) Volume of OH (mL)

0.00 50.0

5.0 45.0

10.0 40.0

15.0 35.0

20.0 30.0

25.0 25.0

30.0 20.0

35.0 15.0

40.0 10.0

45.0 5.0

50.0 0.00

Step 2: Use the appropriate graduated cylinder to measure hydroxide ion solution and record the exact volume in your data table.

Step 3: Pour hydroxide solution into the copper ion solution and stir while constantly reading the thermometer. Stir for about 1 minute to ensure complete mixing and allow the precipitate to form.

Step 4: Repeat steps 1 3 for the other samples

Step 5: Label the filter papers and measure the mass of each. Record each mass in your data table.

Step 6: Set up ring stand, ring and funnel, then place a pre massed filer paper, rinse the beaker with distilled water and pour into filter paper.

Step 7: Repeat above steps for other samples.

Step 8: Remove the filter paper from funnel, place on watch glass and allow to dry.

Step 9: Measure the mass of precipitate and filter paper and record in the data table. Repeat for each sample.

Step 10: Follow my instructions on waste disposal, do not pour filtrate down the sink.

Calculations

; Present all your data in tabular form.

; Calculate the mole fraction of both the copper ion and the hydroxide ion in each sample. ; Calculate the mass of precipitate formed from each copper ion sample

; Graph mole fraction of copper ion versus mass of precipitate. Draw a line of best fit for both

the positive slope region and the negative slope region. Drop a perpendicular line from the

intersection point to the x-axis to determine the mole fraction of the copper ion that produces

the maximum change.

; Use your answer to Calculation 4 to determine the mole fraction of hydroxide ion at the

intersection point. Use the mole fractions to determine the formula of the ionic compound that

precipitated in the reaction.

; Determine the stoichiometric ratio of copper ion to hydroxide ion for this reaction. ; Write a balanced net ionic reaction equation for the precipitation reaction.

Post Lab Questions

1. Can the stoichiometric ratio be determined by the colors of the resulting supernatants? Please

explain.

2. Could the oxidation state of the copper ion be determined by looking at the solution? Please

explain.

3. Would any of these methods work to determine the reaction stoichiometry for a reaction

between the hydroxide ion and the zinc ion? If yes, which methods could you use and why

would they work?

4. Could the graphs use the mole fraction of hydroxide ion instead of mole fraction of copper ion

to determine the reaction stoichiometry? If no, explain why not. If yes, explain how the shapes

of the graphs would change.

5. Could pH work as one of the methods of continuous variation? If pH could work in

determining the stoichiometric ratios, briefly outline a general procedure for its use.

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