Chemistry / Biology. Subject: Senior High. Grade Levels: applications? How do. a specified. dilution? Math Objectives: dilution and.

Transcription

1 NSF Research Experiences for Teachers RET SOLUTION CHEMISTRY: D ILUTIONS AND MOLARITY Subject: Grade Levels: Essential Questions: Chemistry / Biology Senior High What are parallel and series dilutions and what are their applications? How do I calculate and perform a specified dilution? Science Objectives: Students will observe and explain, qualitatively and quantitatively, a dilution and relate it to the molarity of the solution. Math Objectives: Students will plot data on a coordinate graph and develop a mathematical relationship of the quantities from that data. Students will develop a formula relating the initial molarity and volume of a solution to final molarity and volume (M 1 V 1 =M 2 V 2 ). LESSON ACTIVITIES Engage: Explore: Explain: Students will be asked to consider the following situation: Start with 100,000 pennies in a jar. How many pennies is 1/10 th of that amount? How many timess would you have to take 1/10 th of the successive remaining amounts to have 1 penny remaining? What was thee original concentration of pennies in the jar? What is the final concentration of penniess in the jar? In their lab groups students willl be asked to graph the results of the successive trials in the examplee above. What type of curve is produced on standard graph paper? Students will develop and perform a laboratory procedure involving dilution. They will qualitatively comparee the solution produced in their experimental procedure against a standard. Students will develop a usable formula to calculate the amount of solvent and

2 solute to use to arrive at the desired and dilution and solution molarity (M 1 V 1 =M 2 V 2 ). Elaborate: Evaluate: Materials: Students will be asked quantify the different concentration changes in dilutions that utilize dilution factors, such as,.1,.2, and.5. Student results and responses in a lab report will be evaluated. Each Experimental Station: Student Lab Safety Glasses Student Gloves Student Lab Aprons 10 ml graduated cylinder Four 100 ml Erlenmeyer Flasks (or Beakers) 5 or 10 ml pipettes 10 ml 1.0 M NaCl Solution w/ Food Coloring (Stock solution) Labeling Tape Assessment Products: Development of appropriate experimental procedure. Formal lab report. INFORMATION FOR TEACHERS Standards: Chemistry TEKS: (2) Scientific processes. The student uses scientific methods to solve investigative questions. The student is expected to: (A) know the definition of science and understand that it has limitations, as specified in subsection (b)(2) of this section; (B) know that scientific hypotheses are tentative and testable statements that must be capable of being supported or not supported by observational evidence. Hypotheses of durable explanatory power which have been tested over a wide variety of conditions are incorporated into theories; (C) know that scientific theories are based on natural and physical phenomena and are capable of being tested by multiple independent researchers. Unlike hypotheses, scientific theories are well-established and highly-reliable explanations, but may be subject to change as new areas of science and new technologies are developed; (D) distinguish between scientific hypotheses and scientific theories; (E) plan and implement investigative procedures, including asking questions,

3 formulating testable hypotheses, and selecting equipment and technology, including graphing calculators, computers and probes, sufficient scientific glassware such as beakers, Erlenmeyer flasks, pipettes, graduated cylinders, volumetric flasks, safety goggles, and burettes, electronic balances, and an adequate supply of consumable chemicals; (F) collect data and make measurements with accuracy and precision; (G) express and manipulate chemical quantities using scientific conventions and mathematical procedures, including dimensional analysis, scientific notation, and significant figures; (H) organize, analyze, evaluate, make inferences, and predict trends from data; and (I) communicate valid conclusions supported by the data through methods such as lab reports, labeled drawings, graphs, journals, summaries, oral reports, and technology based reports. (10) Science concepts. The student understands and can apply the factors that influence the behavior of solutions. The student is expected to: (A) describe the unique role of water in chemical and biological systems; (B) develop and use general rules regarding solubility through investigations with aqueous solutions; (C) calculate the concentration of solutions in units of molarity; (D) use molarity to calculate the dilutions of solutions Mathematics Grade 11: (M.1) The student uses a variety of strategies and approaches to solve both routine and non-routine problems. The student is expected to: (A) compare and analyze various methods for solving a real-life problem; (B) use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines; and (C) Select a method to solve a problem, defend the method, and justify the reasonableness of the results. (M.2) The student uses graphical and numerical techniques to study patterns and analyze data. The student is expected to: (A) interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, scatter plots, line plots, stem and leaf plots, and box and whisker plots to draw conclusions from the data; (B) analyze numerical data using measures of central tendency, variability, and correlation in order to make inferences; (C) analyze graphs from journals, newspapers, and other sources to determine the validity of stated arguments; and (D) use regression methods available through technology to describe various models for data such as linear, quadratic, exponential, etc., select the most appropriate model, and use the model to interpret information

4 Prior student Learning: Basic chemistry topics up to and including chemical quantities. Algebra II background helpful for regression extension. Possible Prior: Misconceptions Students may consider parallel dilution adequate or optimal for all applications. Students may misinterpret the geometric concentration change that takes place as a result of a serial dilution. Lesson Sequence: This lesson would be introduced as an inquiry lesson to begin discussion of Solution Chemistry. This lesson would be used prior to activities utilizing series dilution in Biology. Background Information: Adaptations for Special Learners: Serial dilution is the standard procedure in the following cases: a) when you need several solutions of the same solute and there is a constant dilution factor b) when the dilution factor is so large that the amount of stock solution needed to make the dilution in one step Manipulatives could be used to illustrate dilution principals. Extensions: Students will be asked to quantify the concentration change in serial dilutions that use different dilution factors. Students will be asked to plot the results of a.1 serial dilution on semi-log graph paper and discuss its significance. Resources: Dilution Tutorial Film Clip: W2m 0&feature=related Serial Dilution Animation: STUDENT HANDOUT Separate Lab /Lesson Handout

5 Solution Chemistry: Dilution and Molarity Inquiry Gregory Adragna Pre Lab Inquiry Answer the following questions individually: Start with 100,000 pennies in a jar. 1) How many pennies is 1/10 th of that amount? 2) How many times would you have to take 1/10 th of the successive remaining amounts to have 1 penny remaining? (Show all calculations) 3) What was the original concentration of pennies in the jar? 4) What is the final concentration of pennies in the jar? In your lab group: 5) Compare and discuss the answers to the above questions. 6) Graph the results. What type of curve is represented? 7) The technique in the penny exercise is similar to a procedure called serial dilution. When do you think that you think that such a procedure may be useful in Chemistry (or Biology)? Why? 8) What is the dilution factor in penny exercise? 9) If each penny = a mole, and the jar = a liter and molarity (M) is defined as moles of solute/ liter of solution, what is the molarity of the last three steps?

6 Dilution Laboratory Introduction Solutions in science are often much more concentrated than are desired or can be managed for a given protocol. So, it is frequently necessary to dilute these solutions to a desired level. This requires a working knowledge of the principles of diluting, dilution factors, molarity, and the calculations involved. Each lab group has been provided with the following equipment and reagents: 10 ml graduated cylinder ml Erlenmeyer Flasks (or Beakers) 5 or 10 ml pipettes 10 ml 1.0 M NaCl Solution w/ Food Coloring (Stock solution) Distilled Water Labeling Tape Design an experiment to produce 10 ml samples of solutions with the following concentrations: a).2 M NaCl b).02 M NaCl c).002 M NaCl d).001 M NaCl Write the procedure in the space provided and check with the instructor before proceeding.

7 Experimental Procedure Compare the color of the.001 M NaCl solution with the standard provided.

8 Analysis 1) Why would it have been difficult to produce the directly.001 solution from the stock solution? 2) Examine the procedure that you used in the dilutions. Compare the molarity and the volume of the solute that you used in each step to attain the desired dilution. Attempt to develop a general formula relating molarity and volume to dilution. (Show all work) Extension Activities 1) Draw Graphic Representations of the following: a) A 4-Step serial dilution with dilution factor of.5. b) A 4-Step serial dilution with a dilution factor of.2. c) A 4-Step serial dilution with a dilution factor of.1. 2) Plot 1c on semi-log graph paper. Discuss the significance. 3) If you performed a dilution with a factor of 1/4 th and then one of 1/6 th on the same solution, what is the total dilution factor of the resultant solution?

9 Teacher Information When you prepare the 1M NaCl stock solution, use an excess of food color to make the color gradient in the dilutions more apparent. Prepare a.001m NaCl solution from the stock solution to use as a standard. Check student dilution calculations before letting lab group begin the experiment. Pre-Lab: Teacher Key 1) 10,000 2) 4 (10,000 to 1) 3) 100,000/jar 4) 1/jar 5) 6) Exponential or Geometric 7) Serial dilution is the standard procedure: a) when you need several solutions of the same solute and there is a constant dilution factor and b) when the dilution factor is so large that the amount of stock solution needed to make the dilution in one step 8).1 9) 100M, 10M, 1M

10 Laboratory: Procedure: Mix each solution well. Dilution 1: 2mL solute, 8mL water Dilution 2: 1mL solute, 9mL water Dilution 3: 1ml solute, 9 ml water Dilution 4: 5mL solute, 5mL water Analysis: 1) It would have been difficult to measure precisely. 2) M 1 V 1 =M 2 V 2 Extension Activities: 1)

11 2) The plot will be linear representing an exponential relationship of the variables.

12 3) 1/24th

13 Molarity Worksheet 1. Sea water contains roughly 28.0 g of NaCl per liter. What is the molarity of sodium chloride in sea water? 2. What is the molarity of g of H 2 SO 4 dissolved in 1.00 L of solution? 3. What is the molarity of 5.30 g of Na 2 CO 3 dissolved in ml solution? 4. What is the molarity of 5.00 g of NaOH in ml of solution? 5. How many moles of Na 2 CO 3 are there in 10.0 L of 2.0 M soluton? 6. How many moles of Na 2 CO 3 are in 10.0 ml of a 2.0 M solution? 7. How many moles of NaCl are contained in ml of a 0.20 M solution? 8. What weight (in grams) of NaCl would be contained in problem 7? 9. What weight (in grams) of H 2 SO 4 would be needed to make ml of 2.00 M solution? 10. What volume (in ml) of 18.0 M H 2 SO 4 is needed to contain 2.45 g H 2 SO 4? 11. What volume (in ml) of 12.0 M HCl is needed to contain 3.00 moles of HCl? 12. How many grams of Ca(OH) 2 are needed to make ml of M solution? 13. What is the molarity of a solution made by dissolving 20.0 g of H 3 PO 4 in 50.0 ml of solution? 14. What weight (in grams) of KCl is there in 2.50 liters of 0.50 M KCl solution? 15. What is the molarity of a solution containing 12.0 g of NaOH in ml of solution? 16. Determine the molarity of these solutions: a) 4.67 moles of Li 2 SO 3 dissolved to make 2.04 liters of solution. b) moles of Al 2 O 3 to make liters of solution. c) grams of Na 2 CO 3 to make liters of solution. d) grams of (NH 4 ) 2 CO 3 to make 250 ml of solution. e) grams of PbCl 2 to form 45.0 ml of solution. 17. Determine the number of moles of solute to prepare these solutions: a) 2.35 liters of a 2.00 M Cu(NO 3 ) 2 solution. b) ml of a molar Pb(NO 3 ) 2 solution. c) 3.00 L of a M MgCO 3 solution. e) 6.20 L of a 3.76-molar Na 2 O solution. 18. Determine the grams of solute to prepare these solutions: a) liters of a M Cu(NO 3 ) 2 solution. b) milliliters of a 5.90-molar Pb(NO 3 ) 2 solution. c) 508 ml of a 2.75-molar NaF solution. d) 6.20 L of a 3.76-molar Na 2 O solution. e) L of a 1.00 M KCl solution. f) 4.35 L of a 3.50 M CaCl 2 solution. 19. Determine the final volume of these solutions: a) 4.67 moles of Li 2 SO 3 dissolved to make a 3.89 M solution. b) moles of Al 2 O 3 to make a M solution. c) grams of Na 2 CO 3 to make a M solution. d) 8.97 grams of (NH 4 ) 2 CO 3 to make a molar solution. e) grams of PbCl 2 to form a 5.0-molar solution.

14 Compound Molar Mass of Moles of Volume of Molarity mass solute solute solution HCl H 2 SO HC 2 H 3 O H 3 PO CaO Mg(OH) ml HBr NaOH KOH Na 2 CrO KMnO Al 2 (SO 4 ) (NH 4 ) 2 SO ml CuNH 4 (NO 3 ) NaHCO K 2 Cr 2 O ml 0.800

15 Dilution Problems Remember that moles = moles, so M 1 V 1 = M 2 V A solution of 1.00 M NaCl is available. How many milliliters of this solution are needed to make a total of ml of M NaCl solution. 2. What volume of M KCl is needed to make ml of M KCl solution? 3. Concentrated H 2 SO 4 is 18.0 M. What volume of 18 M solution is needed to make 2.00 L of 1.00 M H 2 SO 4 solution? 4. Concentrated HCl is 12.0 M. What volume of 12 M solution is needed to make 2.00 L of 1.00 M HCl solution? 5. A solution of 10.0 M NaOH is prepared. From this solution, you need to make ml of M NaOH solution. How many ml will be required? 6. A solution of 6.00 M KOH is prepared. From this solution, you need to make ml of M solution. How many ml will be required? L of M NaNO 3 must be prepared from a solution which 1.50 M in concentration. How many ml of the 1.50 M are required? L of M KNO 3 must be prepared from a solution which 1.50 M in concentration. How many ml of the 1.50 M are required? 9. A M solution is to be diluted to ml with the new concentration to be M. How many ml of the M solution are required? These two are a bit more difficult. Hint - calculate the total moles present and the total volume the moles are dissolved in. 10. Calculate the final concentration if 2.00 L of 3.00 M NaCl and 4.00 L of 1.50 M NaCl are mixed. 11. Calculate the final concentration if 2.00 L of 3.00 M NaCl, 4.00 L of 1.50 M NaCl and 4.00 L of water are mixed. More Solution Problems (included for future reference, not required as HW) 1. Write a balanced equation for the dissolving of potassium chloride (KCl) in water. (KCl ionizes.) 2. When 4.00 grams of potassium chloride dissolve, how many moles of the solid dissolve? 3. How many moles of potassium ions dissolve in question 2? 4. Determine the total number of moles of ions that are formed in question Write a balanced equation for the dissolving of magnesium chloride (MgCl 2 ) in water. (MgCl 2 ionizes.) 6. When grams of magnesium chloride dissolve, how many moles of the solid dissolve? 7. How many moles of chloride ions dissolve in question 6? 8. Determine the total number of moles of ions that are formed in question Write a balanced equation for the dissolving of sugar (C 6 H 12 O 6 ) in water. (Sugar does not ionize.) 10. When grams of sugar dissolve, how many moles of the solid dissolve? 11. How many moles of molecules dissolve in question 10?

16 GRAPH CONSTRUCTION 1. DETERMINE THE RANGE LIMITS OF THE X-AXIS AND THE Y-AXIS Examine the data set and note the minimum and maximum values: X-axis: ordinate (independent or known variable): pre-specified: time, concentration, amount added, etc. Y-axis: abscissa (dependent or unknown variable): resulting measurement: weight, A660, ph, etc (If the zero value of X or Y is important for your graph, it should be included in the limits.) 2. DETERMINE THE LIMITS OF YOUR GRAPH PAPER Count the number of squares available for the X and Y axes, leaving at least 2 squares at the bottom and sides, and 9 squares at the top. 3. ASSIGN VALUES TO AXES WHICH INCLUDE THE RANGE LIMITS Assign values to the coordinates which meet the following requirements: a. They include the limits determined in step 1. b. They make an adequately large graph as large as the available space will accommodate. c. They do not exceed the space available on the page. Determine the value to assign to each square: Divide the range value by the number of squares available along the given axis. Round up so that the first significant figure of the result equals a multiple of ten or decimal fraction of 1, 2, 5 or 10 units per square. 4. CONSTRUCT AXES, MARK WITH REGULAR VALUES Draw lines for the X-axis below and the Y-axis to the left of the selected open area on the graph paper. Label each axis. Mark off the selected regular values with a small line corresponding to units/square selected in step 2: often every 5 or 10 squares. (Do not mark every square.) Label each mark with its corresponding value. Be certain to maintain linearity: all spaces must have equal value. 5. ENTER DATA POINTS For the first point, locate the appropriate value along the X axis and then follow that line up until the appropriate value of Y is reached. Double check that you have not shifted from the desired location, and make a small dot at the point. Draw a small circle around the point, making it easier to see, but preserving the integrity of the point. Repeat until all data have been entered. Use squares to indicate a second data set, triangles the third, etc. 6. CONNECT THE CIRCLES If the function you are graphing is linear, carefully connect the circles by lining a ruler up with the points and drawing a line between them. (Do not violate the interior of the circles so that

17 the value of the point will remain clear.) Alternatively, if the function is non-linear, you may either connect the circles or approximate the curve plots with a "best fit" curve. 7. TITLE THE GRAPH AND AXES Create a title which is meaningful and explicitly reflects the value of the experimental data you have graphed. Place it in CAPITAL LETTERS as the title of the page. Below the title, indicate from where the original data came with a cross reference. Be certain that the axes are correctly and precisely labeled.