5 Steps to a 5: AP Chemistry 2020 - Moore J.T., Langley R.H. 2020
STEP 4 Review the Knowledge You Need to Score High
CHAPTER 19 Experimental Investigations
IN THIS CHAPTER
Summary: The free-response portion of the AP exam will contain a question concerning an experiment, and there may also be a few multiple-choice questions on one or more of these experiments. This chapter reviews the basic experiments that the AP Exam Committee believes to be important. You should look over all of the experiments in this chapter and pay particular attention to any experiments you did not perform. In some cases, you may find, after reading the description, that you did a similar experiment. Not every AP class does every experiment, but any of these experiments may appear on the AP exam.
The free-response questions on recent exams have been concerned with the equipment, measurements, and calculations required. In some cases, sources of error are considered. To answer the question completely, you will need an understanding of the chemical concepts involved.
To discuss an experiment, you must be familiar with the equipment needed. In the keywords section at the beginning of this chapter is a complete list of equipment for the experiments (see also Figure 19.1). Make sure you are familiar with each item. You may know an item by a different name, or you may need to talk to your teacher to get additional information concerning an item.
Figure 19.1 Common laboratory equipment.
In some cases, the exam question will request a list of the equipment needed, while in other cases you will get a list from which to choose the items you need. Certain items appear in many experiments. These include the analytical balance, beakers, support stands, pipets, test tubes, and Erlenmeyer flasks. Burets, graduated cylinders, clamps, desiccators, drying ovens, pH meters, volumetric flasks, and thermometers are also commonly used. If you are not sure what equipment to choose, these serve as good guesses. Most of the remaining equipment appears in three or fewer experiments.
You will need to know the basic measurements required for the experiment. For example, you may need to measure the initial and final temperatures. Do not make the mistake of saying you measure the change in temperature. You calculate the change in temperature from your measured initial and final temperatures. You do not need to give a lot of detail when listing the required measurements, but you need to be very specific in what you measure. Many students have lost exam points for not clearly distinguishing between measured and calculated values.
The basic calculations fall into two categories. Simple calculations, such as the change in temperature or the change in volume, are the easiest to forget. Simple calculations may also include mass-to-mole conversions. The other calculations normally involve entering values into one of the equations given at the beginning of the previous chapters of this book.
Keywords and Equations
Pay particular attention to the specific keywords and equations in the chapters associated with the individual experiments.
A = abc (A = absorbance; a = molar absorbtivity; b = path length; c = concentration)
analytical balance
barometer
beaker(s)
buret
burner
calorimeter
capillary tubes
centrifuge
clamp
crucible and cover
cuvettes
desiccator
drying oven
electrodes
Erlenmeyer flask
evaporating dish
filter crucibles and adapters
filter flasks
forceps
funnel
graduated cylinder
hot plate
ice
ion exchange resin or silica gel
Meker burner
mortar and pestle
pH meter
pipet
power supply (battery)
Pt or Ni test wire
rubber tubing
spectrophotometer
stirrer
stopwatch
support stand
test-tube rack
test tube(s)
thermometer
tongs
triangle crucible support
voltmeter
volumetric flask
wash bottle
watch glass
water bath
wire gauze
Experiment 1: Spectroscopy
Synopsis
Specific experiments that are performed in this investigation are an introduction to the field of spectroscopy. They are designed to demonstrate the relationship between the amount of light absorbed by some solutions and their concentrations. Light of a specific wavelength is passed through both the solvent and a sample. The amount of light transmitted by the solvent is subtracted from the amount of light transmitted by the sample. If you made a number of measurements at different concentrations, you could create a graphical relationship between the amount of light absorbed and the concentration of the solution. By using this relationship, you could determine the concentration of an unknown solution.
Equipment
Spectrophotometer (commonly SPEC 20)
Cuvettes (sample tubes for the spectrophotometer)
Stock solutions (of known concentrations) of the solute (commonly some dye)
Solution of unknown concentration (may be a household substance)
Assorted glassware, including volumetric glassware
Measurements
The student will make several dilutions of the stock solution and will calculate the concentration of each dilution (using M1V1 = M2V2). The transmittance (%T) will be measured for each solution (remembering to subtract the transmittance of the solvent—this may be done by adjusting the spectrophotometer to 100% T and then measuring the transmittance of the solution).
Calculations
To determine the relationship between the concentration of the solution and the transmittance, plot the molarity of the different solutions versus the transmittance (expressed as a decimal). The absorbance (Abs) of the solution (how much light is absorbed) is calculated by the formula Abs = −log (T), where T is the transmittance of the solution (not the percent transmittance). On a SPEC 20 you can read absorbance directly.
Comments
If you are asked for the mass of the solute in the unknown, you first determine its molar concentration using your spectroscopy data. Then, using the molar concentration, the volume of the solution, and the molar mass of the solute, you can calculate the grams of solute present in the sample.
Experiment 2: Spectrophotometry
Synopsis
Specific experiments that are performed in this investigation use the concepts and techniques developed in Experiment 1: Spectroscopy in order to determine the mass percentage of a particular substance in a solid sample. Determination of the amount of copper in a brass sample is a common experiment that is used in this category as well as the amount of iron in a vitamin pill. First, the “best” wavelength to be used is determined. The “best” wavelength is the one that gives the maximum absorbance of the chemical species being determined. Next, solutions of the solute being determined are prepared and their absorbance is measured using a spectrophotometer. A plot of absorbance versus concentration (Beer’s law) is prepared. The solid sample is dissolved and diluted to a certain volume. The absorbance of a portion of this sample is measured and its concentration is determined using the graph. From this information the mass of the substance can be found. Using this mass information and the mass of the sample allows you to calculate the mass percentage of the substance in the sample.
Equipment
Spectrophotometer (commonly SPEC 20)
Cuvettes (sample tubes for the spectrophotometer)
Stock solution (known concentration) of the solute
Sample to be analyzed
Assorted glassware, including volumetric glassware
Measurements
The student will make several dilutions of the stock solution (solution of known concentration of the substance being determined) and will calculate the concentration of each dilution (using M1V1 = M2V2). The absorbance of one of the stock solutions is measured at a number of wavelengths (generally 400—700 nm in 10- to 20-nanometer increments) using a spectrophotometer. The data of absorbance versus wavelength is plotted, and the wavelength that gives the maximum absorbance is chosen to be used for the rest of the experiment. The absorbance of each of the dilutions is measured. A plot of absorbance versus concentration (Beer’s law plot) is prepared either by hand or using a spreadsheet. The solid sample is dissolved (if it is copper, this will require the use of nitric acid) and diluted to a certain volume. The concentration of that solution is determined using the Beer’s law plot. Using the concentration of the solution and the solution’s volume, you can calculate the moles and then grams of the substance. Using the initial mass of the sample, you can finally calculate the mass percentage of the substance in the sample.
Calculations
You can determine the concentrations of the diluted stock solution by using the dilution equation (M1V1 = M2V2). The mass percentage is calculated by:
(grams substance/grams sample) × 100%
Comments
If you are doing a brass analysis for percentage of copper, you will dissolve the brass in concentrated nitric acid. Be extremely careful. The nitric acid is corrosive and the NO gas that is produced is toxic. On the AP exam be sure to stress safety if you are describing this process.
Experiment 3: Gravimetric Analysis
Synopsis
Specific experiments that are performed in this investigation use determination of the mass of a specific substance in a sample by precipitation, drying, and weighing. A common experiment done in this category is determination of the hardness of a water sample. The hardness of a water sample is related to the amounts of calcium, magnesium, and iron ions in solution. These ions may be precipitated as the carbonate salts. For simplicity’s sake, hard- water samples are commonly prepared with only one of these ions, generally calcium. The carbonate salt is precipitated, separated from the solution by suction filtration, and dried in a drying oven. The mass of the dry salt is determined, and the water sample hardness is calculated as mg calcium carbonate per liter of water sample.
Equipment
Various salt solutions of known concentration
Analytical balance
Drying oven
Suction filtration apparatus
Büchner funnel
Filter paper
Aspirator
Ring stands
Assorted glassware, including volumetric glassware
Measurements
The student will make several measurements in gravimetric analysis, especially mass and volume determinations.
Calculations
If a water hardness analysis is being done, the grams of calcium carbonate per milliliter of water sample are initially calculated. This value is then converted to milligrams of calcium carbonate per liter of water sample (hardness) using appropriate conversions.
Comments
All measurements must be done accurately, especially the mass and volume measurements.
Experiment 4: Titration
Synopsis
In the titration procedure, the concentration of an acid is determined by adding small quantities at a time of a base of known concentration until the point at which the moles of base equal the moles of acid present (the equivalence point). It is possible to do a titration by adding small amounts of a solution of a known concentration of acid to determine the concentration of a base solution. Many times this neutralization point cannot be determined unaided, so an indicator or a pH meter is used. The point at which a color change happens with the indicator or an abrupt change in pH occurs with the pH meter is called the endpoint of the titration. Knowing the volume of the unknown acid, the concentration of the base, and the number of milliliters it took to reach the endpoint allows you to calculate the concentration of the unknown acid. The concentration of an unknown base can be determined by titration with an acid of known concentration (Figure 19.2).
Figure 19.2 General acid—base titration setup.
Equipment
Burets
Erlenmeyer flasks
Pipets
Acid-base indicators
pH meter
Base or acid solution of known concentration
Assorted glassware
Measurements
You will be placing a required volume of the unknown acid (or base) solution into the Erlenmeyer flask with a pipet. The buret will be filled with the base (or acid) solution. Be sure to record your initial volume. You will add small amounts of base drop by drop until the indicator changes color. Record the final volume. The final volume reading minus the initial volume reading is the volume of base added.
Calculations
The calculation of the concentration of the base is essentially a stoichiometry reaction. Most of the time you will be able to generalize the process using the equation:
H+ + OH− → H2O
From the molarity of the base and the volume used, you can calculate the moles of base (OH−). Because of the 1:1 stoichiometry that also will be the moles of acid. Dividing that by the liters of acid solution pipetted into the flask gives the acid’s molarity.
Comments
This type of titration can be performed with a pH meter without an indicator. The pH readings will be plotted against the volume. The endpoint is the point of inflection of the curve. A titration, either with an indicator or a pH meter, can be used to determine the acid content of household substances such as fruit juices or sodas.
Experiment 5: Chromatography
Synopsis
Many times the components (solutes) in a solution cannot be separated by simple physical means. This is especially true of polar solutes because of their interactions. One method that is commonly used is chromatography (Figure 19.3). A very small amount of the solution is spotted onto a strip of filter paper or chromatography paper and allowed to dry. The strip is placed vertically into a jar containing a small amount of solvent. As the solvent is drawn up the strip by capillary action, it dissolves the sample. The various solutes have different affinities to the paper and to the solvent and can thus be separated as the solvent moves up the strip. Choice of the solvent is critical and can be related to its polarity; however, the choice sometimes must be done by trial and error.
Figure 19.3 Basic procedure for a paper chromatography experiment.
Equipment
Filter paper or chromatography paper
Chromatography jar
Various solvents
Metric rules
Sample to be analyzed
Assorted glassware
Measurements
The student will make measurements of the distance that each component travels and the distance that the solvent traveled.
Calculations
The calculations involve determining the Rf value for each component. The Rf value is the distance the component travels divided by the distance the solvent traveled. Substances that interact strongly with the paper do not travel very far (low Rf values), while those that interact strongly with the solvent travel much farther (high Rf values).
Comments
Chromatography is a very powerful separation technique.
Experiment 6: Determination of the Type of Bonding in Solid Samples
Synopsis
In this type of experiment, the student is given a set of bottles that contain solids of various types of bonding—ionic, covalent, or metallic. The student uses various physical and chemical tests to determine the bonding type. These tests might include melting point, conductivity, solubility, etc. along with observations of physical properties such as luster and hardness.
Equipment
Assorted solids—ionic, covalent, metals
Assorted solvents—polar and nonpolar
Conductivity tester
pH paper
Thermometer
Assorted glassware
Measurements
A number of measurements and observations may be made:
Luster: Metals tend to have a metallic luster; solid nonmetals often have a dull luster.
Melting point: Ionic solids and metals have high melting points; covalent compounds have lower melting points.
Solubility: Ionic compounds and polar covalent solids are generally soluble in water; metals and nonpolar covalent solids are generally insoluble or very slightly soluble in water.
Conductivity: Aqueous solutions of ionic compounds are conductors; aqueous solutions of most polar covalent compounds are nonconductors.
Calculations
There are generally no calculations associated with this experiment.
Comments
Many other tests could be used: pH of the aqueous solutions, solubility on organic solvents, and so on.
Experiment 7: Stoichiometry
Synopsis
In this experiment, you are asked to verify the results of an experiment by checking both the stoichiometric calculations and the procedure. You will be asked to determine the percent by mass of substances such as sodium bicarbonate in a mixture. You will do this by making use of the unique properties of the components in this mixture.
Equipment
Bunsen burners and strikers
Digital balances
Ring stands and rings
Ceramic triangles
Crucibles and lids
Assorted glassware, including volumetric glassware
Measurements
A weighed sample mixture of sodium bicarbonate and sodium carbonate is heated to constant mass. The sodium bicarbonate decomposes to sodium carbonate, carbon dioxide (gas), and water vapor: 2 NaHCO3(s) → Na2CO3(s) + H2O(g) + CO2(g). The loss of mass is the loss in mass of CO2 + H2O. Examining the equation for the decomposition reaction, you can see that there is a 1:1 ratio of moles of water and carbon dioxide.
Calculations
If you let z = moles CO2 = moles H2O, then the total grams of mass lost can be shown as the sum of the moles of each (which will be the same) times the molar mass of each substance:
Mass lost (grams) = (z × 18.02 g H2O/mole) + (z × 44.01g CO2/mole)
You can then solve for z, the number of moles. As you can see from the balanced equation, the moles of NaHCO3 solid that decomposed is 2z. The mass of NaHCO3 that decomposed will be:
2z × 84.02g NaHCO3/mole
The percent of NaHCO3 in the mixture will be the mass of the sodium bicarbonate divided by the mass of the mixture sample times 100%:
(grams NaHCO3/grams mixture) × 100%
Comments
In order to increase the precision (and hopefully the accuracy) of the determination, several runs should be made and an average taken. This same procedure may be applied to many other reactions and mixtures. These samples could also be analyzed by a titration procedure.
Experiment 8: Redox Titration
Synopsis
In this experiment, the concentration of a substance will be determined by using a redox titration. The titrant will need to be standardized before it can be used in the titration. Commonly, the redox titration involves the titration of hydrogen peroxide (H2O2) with potassium permanganate (KMnO4), with the goal of analyzing the commercial hydrogen peroxide that can be found in a pharmacy. The KMnO4 solution can be standardized against a Fe(NH4)2(SO4)2·6H2O solution. You will prepare a standard (known concentration) solution of the Fe(NH4)2(SO4)2·6H2O, a sulfuric acid solution, and a solution of potassium permanganate. The redox half-reactions involved in the standardization are:
giving an overall redox reaction of:
The half-reactions involved in the titration of the hydrogen peroxide are:
giving the overall redox-reaction:
Equipment
Buret
Ring stand and clamps
Pipets of assorted volumes
Pipet bulbs
Assorted glassware, including volumetric glassware
Measurements
You will be making mass measurements of the Fe(NH4)2(SO4)2·6H2O and the KMnO4 and many volume measurements of the pipets, volumetric flasks, and the buret.
Calculations
For the standardization: from the number of grams of Fe(NH4)2(SO4)2·6H2O used, you can calculate the moles of Fe2+ used. Knowing this, you can determine the moles MnO4− used from the stoichiometry in the overall reaction (1 MnO4− : 5 Fe2+) and then its molarity.
For the peroxide titration: from the buret volume and the molarity of the KMnO4 solution, you can calculate the moles used in the titration, and applying the overall reaction stoichiometry you can get the moles of hydrogen peroxide (5 H2O2 : 2 MnO4−). From the moles, you can get grams and finally mass percent (assuming the mass of the peroxide solution is 1.00 g/mL).
Comments
Be very careful in making your measurements. The same general procedure can be applied to a number of other systems.
Experiment 9: Chemical and Physical Changes
Synopsis
Commonly this experiment involves separating the components of a mixture by using the chemical and physical properties of the mixture components. This is the basis of the analysis of commercially available samples such as over-the-counter acetaminophen- or aspirin-based pain relievers. The binder (many times sucrose), aspirin, and acetaminophen can be separated by the difference in their solubility in water and organic solvents, their acidity, and the difference in the way they react with hydrochloric acid and sodium bicarbonate solutions.
Equipment
Büchner funnels
Vacuum filtration apparatus
Separatory funnel
Hot plate or drying oven
Assorted glassware
Measurements
You will be making mass measurements of the sample, and every time a component is separated as a solid, it is dried and the mass determined.
Calculations
The overall percent recovery for the sample would be the sum of the masses of all the recovered components divided by the initial mass of the sample:
(sum of the grams of all recovered components/grams of sample) × 100%
The percentage of each component can be calculated by dividing the mass of a component by the total mass of all recovered components:
(grams of component/sum of the grams of all recovered components) × 100%
Comments
Be very careful in making your measurements. The same general procedure can be applied to a number of other systems.
Be especially careful when handling the acid solutions and organic solvents. Be sure to vent the separatory funnel before opening it.
Experiment 10: Kinetics
Synopsis
In this experiment, some of the factors involved in the speed of a chemical reaction will be explored. Commonly this experiment focuses on the decomposition of calcium carbonate— limestone, CaCO3(s), and hydrochloric acid, HCl(aq). Pieces of calcium carbonate of different sizes (to test how the speed of reaction varies with surface area) and HCl solutions of different concentrations will be available. The temperature of the reaction mixture can be varied by using an ice bath or heating the mixture. In order to measure the speed of the reaction, the carbon dioxide gas product can be collected in a syringe, or a gas pressure probe can be used to monitor the production of the CO2(g) as a function of time. The mass of sample consumed (or the decrease in the total mass of the reaction flask) versus time can also be used as an indication of the speed of reaction.
Equipment
Balance
Hotplate
Syringes
Stopwatch
Assorted glassware
Magnetic stirrer and stir bar
Gas pressure probe and data collection device
Measurements
Measurements include the initial and final mass of the calcium carbonate sample, the volume of gas evolved, and time measurements.
Calculations
Calculations commonly involve determining the mass of sample consumed (lost) as a function of time. The results of the mass versus time measurements are commonly plotted.
Comments
When plotting the data, the time is commonly the horizontal axis, while the mass lost or mL of gas produced is the vertical axis.
Be especially careful when handling the hydrochloric acid.
Experiment 11: Rate Laws
Synopsis
In this experiment, you will determine the rate law for a specific chemical reaction. Commonly the reaction involved is the reaction of crystal violet (CV) with sodium hydroxide (NaOH). The progress of the reaction is followed with a spectrophotometer or colorimeter. You will initially create a Beer’s law calibration curve by measuring the absorbance of solutions of crystal violet of varying concentrations. Then you will use the same spectrophotometer to follow the change in concentration of crystal violet as it reacts with NaOH as a function of time:
CV+(aq) + OH−(aq) → CVOH(aq)
The rate expression for this reaction would be:
rate = k [CV+]x[OH−]y
If we use a large stoichiometric excess of NaOH, then the rate equation becomes
rate = k* [CV+]x
since there is so much hydroxide ion present that its concentration essentially becomes constant.
Equipment
Spectrophotometer (commonly SPEC 20)
Cuvettes (sample tubes for the spectrophotometer)
Pipettes and bulbs
Assorted glassware, including volumetric glassware
Measurements
You will be making measurements of absorbance and time. Be sure to use a blank containing only water and NaOH but no crystal violet.
Calculations
You will be making different concentrations of the stock crystal violet solution by dilution, so that you will use the dilution equation: M1V1 = M2V2. You will be making three graphs: (1) concentration versus time (straight line indicates zero order with respect to CV [x = 0 in rate expression]); (2) ln(concentration) versus time (straight line indicates first order with respect to CV [x = 1 in rate expression]) and (3) 1/concentration versus time (straight line indicates second order with respect to CV [x = 2 in rate expression]).
Comments
Be especially careful when handling the sodium hydroxide solution.
Experiment 12: Calorimetry
Synopsis
In this experiment, you will be measuring the heat produced during the dissolving of various ionic substances in water with the goal of determining which of the salts is most efficient (with respect to cost) in generating heat. Substances to test might include anhydrous calcium chloride (CaCl2), anhydrous sodium carbonate (Na2CO3), anhydrous ammonium nitrate (NH4NO3), anhydrous sodium acetate (NaC2H3O2), and similar salts. You will calculate the change in enthalpy of dissolution in kJ/mol (ΔHsoln) by using a coffee-cup calorimeter (see Figure 9.1 in Chapter 9, Thermodynamics). You may be using a magnetic stirrer instead of the stirring wire shown in the figure.
Equipment
Thermometers or temperature probes
Polystyrene cups
Magnetic stirrers and stir bars
Assorted glassware
Measurements
You will be making measurements of the initial and final temperatures of the solutions formed by adding a certain mass of solute to a measured amount of water. The ΔT is the final temperature minus the initial temperature. The value of ΔT is a calculated number and not a measured number.
Calculations
You may be given or may have to calculate the calorimeter constant, C, for your calorimeter—the heat absorbed by the calorimeter per degree of temperature change. The energy of solution formation (qrxn) is calculated by multiplying the mass times the specific heat of the solution (given) times the change in temperature (qrxn = mcΔT) and the energy of solution (qsoln) is calculated by: qsoln = −(qrxn + CΔT). The enthalpy of dissolution (ΔHsoln) is calculated by dividing the qsoln (in kJ) by the number of moles of salt used.
Comments
Be especially careful with the ammonium nitrate—it is a strong oxidizer.
Experiment 13: Chemical Equilibrium—Le Châtelier’s Principle
Synopsis
Experiments that fall into this category examine systems that are at equilibrium and what happens when that equilibrium is disturbed. Many times this involves having a small tray of reagents and testing an equilibrium system by mixing selected reagents and making observations. You may change concentrations (adding more reagent) or change the temperature of the solutions. This may involve an acid—base equilibrium or complex ion equilibriums. Reactions will be given, and you should be able to describe the stress that you imposed and how the system reacted to that stress.
Equipment
Test tubes
Stirring rods
Spatula
Assorted glassware
Measurements
This experiment involves no measurements, only estimations of volumes and masses.
Calculations
This experiment involves no calculations.
Comments
Be very careful when working with concentrated ammonia and hydrochloric acid. Always wear goggles, gloves, and an apron, and keep these reagents in the hood.
Experiment 14: Acid—Base Titrations
Synopsis
Experiments that fall into this category are acid—base titrations involving weak acids or weak bases. Many times the course of the titration is followed by a pH meter and the equivalence point is determined graphically. This allows you to determine not only the concentration of the weak acid or base but also its pKa or pKb. Both monoprotic and polyprotic acids may be examined. From an examination of the specific reaction involving a weak acid or base, you should be able to determine whether the solution at the equivalence point will be acidic or basic.
Equipment
Stirring rods
pH meters or pH probes
Buret
Assorted glassware
Measurements
You will be making pH measurements and plotting them against volume of titrant added. In many cases, you will titrate various acids (strong and weak) with a NaOH solution of known concentration. The equivalence point for such a titration is the point at which a dramatic increase in pH occurs; this is called the point of inflection of the curve. The pH at the volume corresponding to half the equivalence point volume is the pKa of the acid. The same is true of bases, except the pH will be decreasing during the titration. A polyprotic acid or base will give you two points of inflection, and two pKs and Ks may be calculated.
Calculations
The Ka of the acid can be calculated by the equation Ka = 10−pKa. If the Kb of a weak base is to be determined, use Kb = 10−pKb.
Comments
Be extremely careful when working with the acids and bases and wear all of your personal protective equipment, especially your goggles. When making dilutions, always add the acid (or base) to water, NOT water to acid.
Experiment 15: Buffer pH
Synopsis
A buffer is a substance that resists a change in pH when an acid or base is added to it. It is normally a mixture of a weak acid and its conjugate base. Experiments in this category involve examining the properties of buffers and household substances that are buffers. This will involve titrating a substance with an acid or base while following the course of the titration with a pH meter, plotting the pH versus mL of titrant added, and determining the equivalence point graphically. At any point before the equivalence point, you have a buffer present. Common household substances may be tested for their buffer ability. The curve of pH versus mL of a substance that has some buffering ability rises sharply initially and then levels off much more than a titration of a substance that is not a buffer. You can use this to determine whether an unknown solution exhibits any buffering capability.
Equipment
pH meter
Burets and clamps
Magnetic stirrer
Assorted glassware
Measurements
You will be making measurements of volume and pH for a wide variety of substances. The point in a titration involving a buffer that corresponds to halfway to the equivalence point is called the point of maximum buffering.
Calculations
The Ka of the acid can be calculated by the equation Ka = 10−pKa. If the Kb of a weak base is to be determined, then use Kb = 10−pKb.
Comments
Be careful in handling the acid and base solutions.
Experiment 16: The Capacity of a Buffer
Synopsis
Experiments in this category are designed to explore the capacity of a buffer, which is the amount of acid or base that can be neutralized by the buffer. You can determine this by using different amounts of the conjugate acid and base components or by changing the concentration of each by the same amount. Normally, the higher the concentration of the conjugate acid and base in the buffer, the more moles of added base or acid can be neutralized and thus the higher the buffer capacity. You will also be asked to create a buffer of a specific pH.
Equipment
Balance
Burets and clamps
Assorted glassware
Measurements
You will be making measurements of volume and pH for a wide variety of substances. You will be making graphs of pH versus mL of titrant added.
Calculations
You can calculate the initial pH of a conjugate acid/base buffer by using the following equations:
[H+] = Ka [weak acid]/[conjugate base]; then pH = −log [H+]
If you want a buffer of a certain pH, then put in the Ka of the weak acid you want to use and the [H+] desired and solve for the ratio of acid to base. If you have a choice of several acid/base systems, then choose the one whose pKa is closest to the desired pH.
Comments
Be extremely careful when working with the acids and bases and wear all of your personal protective equipment, especially your goggles. When making dilutions, always add the acid (or base) to water, NOT water to acid.
Common Mistakes to Avoid
1. You measure initial and final values, but calculate the change.
2. You use an analytical balance to weigh the mass (grams), but not the moles.
Review Questions
Use these questions to review the content of this chapter and practice for the AP Chemistry exam. First are 10 multiple-choice questions similar to what you will encounter in Section I of the AP Chemistry exam. Following those is a long free-response question like the ones in Section II of the exam. To make these questions an even more authentic practice for the actual exam, time yourself following the instructions provided.
Multiple-Choice Questions
Answer the following questions in 15 minutes. You may not use a calculator. You may use the periodic table and the equation sheet at the back of this book.
1. You have an aqueous solution of sugar. The simplest method to separate the sugar from the solution is to:
(A) evaporate the solution to dryness
(B) centrifuge the solution
(C) filter the solution
(D) electrolyze the solution
2. A chemistry student adds 25.0 g of sodium hydroxide, NaOH, to 500.0 g of water. Which of the following procedures should he employ to determine the molarity of the solution?
(A) He should convert the grams of NaOH to moles and measure the volume of the solution.
(B) He should titrate the solution with standard potassium hydroxide solution.
(C) He should determine the freezing point of the solution.
(D) He should determine the vapor pressure of the solution at room temperature.
3. A chemistry student prepares a solution of an unknown solid with a molar mass of 78.3 g/mol. She prepares the solution by dissolving 2.50 g of the unknown substance in 100.0 g of water. Which of the following procedures could she use to determine whether the unknown substance is an electrolyte?
(A) She could measure the specific heat of the solution.
(B) She could measure the volume of the solution.
(C) She could measure the freezing point of the solution.
(D) She could determine the specific heat of the solution.
4. A chemist makes a solution by dissolving 10 g of urea in 100 g of water. What additional information does she need to calculate the molarity of this solution?
(A) She needs the density of the solution and the molar mass of urea.
(B) She needs the density of urea and the molar mass of urea.
(C) She needs the density of water and the density of the solution.
(D) She needs the molar mass of urea and the density of water.
5. A certain reaction follows the rate law Rate = k [Br−] 
[H+]2. What are the units of the rate constant, k?
(A) s−1M−3
(B) M s−1
(C) M3 s
(D) M s
Use the following diagram for questions 6 and 7.
The diagram above represents the idealized titration curve for the reaction of sodium oxalate (Na2C2O4) with a strong acid like hydrochloric acid (HCl). E and F represent the pH at the endpoints. G and H will depend on the composition of the sample with the possibility that one may not be present.
6. A trial run used a sample of pure sodium oxalate. How does the volume of acid necessary to reach G compare to the volume of acid necessary to get from G to H?
(A) The volumes required will be the same.
(B) A larger volume is necessary to reach G.
(C) A larger volume is necessary to get from G to H.
(D) It is impossible to determine.
7. In addition to water, what are the predominant species in solution at E?
(A) Na2C2O4 and HCl
(B) 
(C) 
(D) 
8. A student is attempting to prepare an electrochemical cell, which ideally should produce 1.23 V. Unfortunately, he was unable to make a salt bridge. He reasoned that a copper wire would conduct electricity like a salt bridge, so he used a copper wire in place of the salt bridge. How will the voltage of the cell with the copper wire compare to that of the ideal cell?
(A) The voltage is ideal.
(B) The voltage becomes zero.
(C) The voltage is greater than ideal.
(D) The voltage is less than ideal but greater than zero.
9. A chemist constructs an electrochemical cell with a magnesium anode and a copper cathode. She measures the cell voltage. Next, she replaces the copper electrode with a larger copper electrode. What does she find when she measures the cell voltage of the cell with the larger copper electrode?
(A) There is no change in the voltage.
(B) The voltage becomes zero.
(C) The voltage increases.
(D) The voltage decreases but stays positive.
10. While investigating a radioactive decay process, a chemist constructs a linear graph. What information did she plot?
(A) She plotted the concentration remaining versus time.
(B) She plotted the natural logarithm of the concentration remaining versus time.
(C) She plotted the reciprocal of the concentration remaining versus time.
(D) She plotted the natural logarithm of the concentration remaining versus the inverse of the time.
Answers and Explanations
1. A—Separating materials in solution normally involves a physical change such as removing the solvent through evaporation. B and C will work on a heterogeneous mixture but not a solution (homogeneous mixture). D is a chemical change.
2. A—Molarity is moles per liter. The moles are readily determined from the grams of NaOH. Then, simply measuring the volume (and converting to liters) is all that is needed to determine the molarity. B may seem like a good option because titration is a common method for determining the molarity of a solution; however, one base (KOH) cannot be used to titrate another base (NaOH), as an acid is needed. C could be used to determine the molality of the solution; however, it is easier to determine the molality from the mass of NaOH and the mass of water; to convert to molarity, another measurement would be required. The vapor pressure would help determine the molarity, but it would not be easy to get to the molarity from the vapor pressure.
3. C—If the solute contains an electrolyte, the solution will conduct electricity and the van’t Hoff factor, i, will be greater than 1. The choices do not include any conductivity measurements; therefore, it is necessary to determine the van’t Hoff factor. It is possible to determine the van’t Hoff by measuring the osmotic pressure, the boiling-point elevation, or the freezing-point depression. The freezing-point depression may be found by measuring the freezing point of the solution and comparing the measured freezing-point depression to that expected for a nonelectrolyte.
4. A—To calculate the molarity, the moles of urea and the volume of the solution are necessary. It is possible to calculate the volume of the solution from the density of the solution and the mass of the solution (110 g). The mass of urea and the molar mass of urea give the moles of urea.
5. A—The units on each side must match. The rate has the units of M/s (or M s−1 or mol L−1 s−1). Substituting units for symbols changes the rate law from Rate = k [Br−] 
[H+]2 to M/s = k [M][M] [M 2] or M/s = k[M 4]. From this, k must have the units 1/(s M3) or s−1M −3.
6. A—At G, all the 
has been converted to 
, and the moles of 
will equal the moles of 
originally present. It will require an equal volume of acid to titrate an equal number of moles of 
, as required for the 
.
7. B—The reaction with HCl converts all the 
to 
. The Na+ has not reacted, so it is still present. The Cl− is from the HCl and remains in solution because it has not reacted. The H+ from the acid reacted with the 
to form 
and is no longer present (in a significant amount). Other than water, all species are strong electrolytes and exist as ions in solution.
8. B—A source of cations and anions is necessary for the operation of a cell to keep the charges in each compartment neutral. If there is no salt bridge, there is no ion source and the cell cannot operate (zero voltage).
9. A—The size of the electrode is irrelevant to the cell voltage.
10. B—The radioactive decay process follows first-order kinetics; only B will give a linear graph for a first-order process. A applies to zero-order kinetics. C applies to second-order kinetics. D is not a kinetics graph.
Free-Response Question
You have 15 minutes to answer the following question. You may use a calculator and the tables in the back of the book.
Question
A sample of a solid weak monoprotic acid, HA, is supplied, along with solid sodium hydroxide, NaOH, a phenolphthalein solution, and primary standard potassium hydrogen phthalate (KHP).
(a) Describe how a standardized sodium hydroxide solution may be prepared for the titration.
(b) Sketch a graph of pH versus volume of base added for the titration.
(c) Sketch the titration curve if the unknown acid were really a diprotic acid.
(d) Describe the steps to determine Ka for HA.
(e) What factor determines which indicator should be chosen for this titration?
Answer and Explanation
(a) A sample of sodium hydroxide is weighed and dissolved in deionized water to give a solution of the approximate concentration desired. (Alternatively, a concentrated NaOH solution with unknown concentration could be diluted.) The process is as follows:
1. Weigh samples of dried KHP into flasks and dissolve in deionized water.
2. Add a few drops of the appropriate acid—base indicator (phenolphthalein) to each sample.
3. Rinse a buret with a little of the NaOH solution; then fill the buret with the NaOH solution.
4. Take the initial buret reading.
5. Titrate the NaOH solution into the KHP samples until the first permanent pink color appears.
6. Take the final buret reading.
7. Using the molar mass of KHP, determine the moles of KHP present. This is equal to the moles of NaOH.
8. The difference in the buret readings is the volume of NaOH solution added (convert this to liters).
9. The molarity of the NaOH solution is the moles of NaOH divided by the liters of NaOH solution added.
10. (Repeat the procedure for each sample.)
Give yourself 3 points for this full list, if the items are in order. If three to five items are in the wrong order or missing, you get only 2 points. If five to seven items are in the wrong order or missing, you get only 1 point. You get 0 points for three or fewer items.
(b)
You get 1 point for this graph. You get an additional point for noting that the equivalence point is greater than 7.
(c)
You get 2 points for this graph if you show both steps. You get 1 point for showing only one step.
(d) There are several related ways to do this problem. One method is to split the sample into two portions. Titrate one portion to the equivalence point. Add the titrated sample to the untitrated sample, and add a volume of deionized water equal to the volume of NaOH solution added. The pH of this mixture is equal to the pKa of the acid (this corresponds to a half-titrated sample).
You get 1 point for anything concerning a half-titrated sample and an additional 1 point for pH = pKa.
(e) The pH at the equivalence point must be close to the pKa of the indicator.
You get 1 point for this answer.
Total your points. There are 10 points possible.
Rapid Review
Reviewing the experiments should include looking at the synopsis, apparatus, calculations, and comments, as well as the appropriate concept chapters, if needed.
• Pay particular attention to any experiment you did not perform.
• Be familiar with the equipment used in each experiment.
• Know the basic measurements required in each experiment.
• Know what values are measured and which are calculated.
• Pay attention to significant figures.
• Balances are used to measure the mass of a substance, not the moles.