Solutions and Titrations

Solutions and Titrations 9-1

Solutions and Titrations

In addition to reading this lab, be sure you have viewed the ChemPages modules on the

following subjects:

Titration (also see all modules in Additional Topics)

Buret

Flask, volumetric (also see the “Self Check Exercises” in Additional Topics)

Introduction

A solution is defined as a homogeneous mixture of two or more components. Any of these components may exist in

any of the three physical states and may be elements or compounds. In view of such a wide range of possibilities the

discussion here will be limited to mixtures of two components in which one component is water. However, most of

the general ideas presented here can be applied to other types of solutions with little, if any, modification.

In the formation of a solution the components become uniformly mixed with one another. Thus it is said that one

substance dissolves in the other. Based on the dissolution (mixing) process the following designations are made.

solvent The substance that causes the dissolution of the other to take place; this substance is usually

present in the larger quantity.

solute The substance that is dissolved by the solvent.

solution The uniform mixture that results on mixing the solvent and the solute. The total mass of the

solution is equal to the sum of component masses present; however, the total volume of the

solution is not necessarily equal to the sum of the component volumes, i.e., masses are additive

but volumes are not.

Another important aspect that arises from the above designations is the way in which the amounts of the components

are designated or how the composition of the solution is specified. Generally, this is accomplished by means of one

of several concentration scales. A concentration is simply a means of expressing an amount of one component in

relation to an amount of the other component or an amount of the total solution. Several scales are available but

molarity is one of the most commonly used.

Molarity (M) = the number of moles of solute per volume of solution in liters,

or

M

moles of solute

liters of solution (1)

Two examples illustrating useful molarity calculations follow:

Example 1:

A 4.101 g sample of CuSO4 (MW=159.60) was weighed out and transferred to a 250.00 mL volumetric flask in which

it was dissolved in water and diluted to volume. What is the molarity of the solution?

44

444 CuSO mole 0.02569

CuSO g 159.61

CuSO mol 1 CuSO g 4.101 = CuSO of moles

solution L 25000.0mL 1000

L 1mL 250.00=solution of L

Substituting in equation (1) gives:

M= 0.02569 mol CuSO4

0.25000 L soln=0.1028 M CuSO4


Example 2:

How many grams of CuSO4 should be weighed out to make 100.00 mL of a 0.500 M CuSO4 solution in a volumetric flask?

Rearranging equation (1) above and substituting, we have

moles of CuSO4 = L of solution × M CuSO4

= 0.10000 L × 0.500 mol CuSO4/L = 0.0500 mol CuSO4

The mass of CuSO4 needed is obtained by converting moles to grams:

44

44 CuSO g 7.98

CuSO mol

CuSO g 159.61CuSO mol 0.0500

Preparing solutions:

When preparing a solution in the laboratory, it is sometimes necessary to know the exact concentration of the solution,

such as 0.2140 M NaCl (four significant figures). For other purposes it may be sufficient to prepare a solution of

approximate concentration only, such as 0.2 M NaCl (one significant figure).

The following discussion and examples deal mainly with making solutions of exact (precisely measured and known)

concentration. The principles outlined here can be carried over to solutions whose concentrations need only be

approximate or to solutions that can only be prepared approximately. The main difference lies in the type of equipment

required.

Note that the markings on beakers and Erlenmeyer flasks are notoriously inaccurate—they are in place to give an

approximate value, but would be unreliable in making standard solutions with more than one significant figure. On

the other hand, pipets and volumetric flasks are calibrated individually and thus the markings are generally quite

accurate. You should make it a habit to write the appropriate number of decimals for volumes associated with pipets

(e.g., 10.00 mL, not 10 mL or 10.0 mL) and volumetric flasks (e.g., 50.00 mL, not 50 mL or 50.0 mL).

Solutions whose exact concentration is specified are principally of two types:

a) those that the exact concentration can be calculated directly from the amounts used to make up the solution by:

1) weighing out exactly some very pure solute or

2) diluting a more concentrated solution whose exact concentration is known.

b) those that can only be prepared to an approximate concentration and need to be standardized, i.e., their exact

concentration must be determined by some additional chemical or physical means after the solution has been

prepared. For example, one of the most common laboratory bases, NaOH, cannot be produced and maintained in a

highly purified form since it readily reacts with the carbon dioxide in air to form sodium hydrogen carbonate. Thus

if you weigh a sample of NaOH in air, it will actually be a mixture of NaOH and NaHCO3.

Hence, a concentration based on a mass of NaOH can only be approximate since the actual amount of the base is

known only approximately. Silver nitrate, on the other hand, can be obtained and maintained in a highly purified form

and a sample of AgNO3 will be essentially 100.0% pure silver nitrate and the concentration can be accurately

calculated on the basis of this mass. Some knowledge of chemical purity is required in the preparation of solutions;

often this can be obtained directly from the reagent bottles which often specify either the general chemical grade of

the reagent or an exact assay of the chemical.

The equipment and procedural considerations that are needed in the preparation of solutions of exact concentrations

are given in the following example. Particular attention should be paid in these examples to the types of equipment

required and how each is used.

In this chemistry lab, you will use carefully calibrated lab equipment (so-called “Class A” glassware). This means that

the precision of the pipets and volumetric flasks are carefully controlled during manufacture. For pipets (1, 5, 10, or

25-mL volumes), assume two places after the decimal place. For volumetric flasks, the tolerance is based on the size.

Volumetric flasks from 1 to 100 mL may be assumed to have two places after their decimal points (thus, a 50-mL

volumetric flask will hold 50.00 mL while a 100-mL volumetric flask will hold 100.00 mL); larger volumetric flasks

(200 mL to 2000 mL will only have one decimal place (thus, a 250-mL volumetric flask is calibrated to hold 250.0

mL and a 500-mL volumetric flask is calibrated to hold 500.0 mL).


Example 3-Weighing out a pure solute:

A 2.000 M solution of copper(II) sulfate is needed for a certain experiment. Reagent grade CuSO4·5H2O is available

along with balances, volumetric flasks, pipets and other glassware.

The total volume of the solution must be decided upon before the amount of the solid solute can be calculated. Since

a 250 mL volumetric flask is available, this can be used. (Other sizes would also be possible.) To obtain 250 mL of a

2.000 M solution the following amount of the solute must be weighed out.

44

4 CuSO mole 5000.0L

CuSO mol 2.000

mL 1000

L 1mL 250.0 = CuSO of moles

*CuSO g 124.8mol

*g 249.68mol 0.5000 = CuSO of grams 44

* 249.68 is used since the CuSO4 that is actually weighed out is the hydrate, CuSO4·5H2O

The next step is to weigh out the solute. Procedurally, the solid should be weighed into a clean dry beaker. Next the

solid should be dissolved in a small amount of water and transferred to the volumetric flask with the aid of a funnel.

This is illustrated below. A wash bottle is used to aid in the transfer and to rinse the beaker completely. The flask is

then swirled to dissolve all the solute before the final dilution to the mark is made.1 After complete mixing by repeated

inversion of the flask, the solution is ready to use.

Example 4- Diluting a more concentrated solution.

One hundred milliliters of a 0.5000 M solution of CuSO4 is needed;

a 2.000 M solution is available. The same type of procedure used

above could be used to prepare this solution but an alternate means

now exists since a 2.000 M solution is available. This solution can

be diluted to give a 0.5000 M solution. The first step is to determine

how much of the more concentrated solution needs to be diluted to

100.00 mL to achieve the desired concentration.

moles solute before dilution = moles solute after dilution

Minitial × Vinitial = Mfinal × Vfinal

2.000 M × Vinitial = 0.5000 M × 100.00 mL

Vinitial = 25.00 mL

Since the 25.00 mL needs to be transferred from the concentrated

container to the 100.00 mL volumetric flask, a pipet is required (in

this case, one that can deliver (TD) 25.00 mL). A volumetric

transfer pipet with a 25 mL capacity would work. Some of the

concentrated solution is placed in a dry beaker and a 25 mL aliquot of this solution is transferred to the 100 mL

volumetric flask. Water is added to the flask with mixing and then enough water is added to fill the flask to the mark.

The 0.5000 M solution has been prepared and is ready to use as soon as the flask has been capped and inverted

repeatedly to insure complete mixing.

Without belaboring all the types of variations that could be applied to these examples, one additional point should be

made. Namely, in the examples given there could be a great variety of ways to achieve the same end, for example,

using different size flasks, pipets, etc. but the method of manipulating the equipment and making the transfers would

be the same to insure a known concentration in the end.

For solutions that cannot be made up exactly from mass or volume data, the preparation of the solution is essentially

the same but less precise equipment can be used, e.g., graduated cylinders or approximate masses. Thus only an

1 This is a really important point—all of the solid must be dissolved before you fill the flask to the final volume.

Failure to do so will result in a miscalibration of the concentration and you will need to remake the solution.

Quantitative transfer of a solid.


approximate concentration will be known. But an important step follows the preparation. This step is referred to as

the "standardization" of the solution. A standard solution is one whose exact concentration is known.

One of the most common means of carrying out the standardization is to titrate the solution just prepared with a

standard solution. This step is illustrated in the following example.

Example 5:

An approximately 0.2 M solution of NaOH is standardized by titrating a 25.00 mL aliquot2 of the solution with a

standard 0.2826 M oxalic acid solution. It required 10.09 mL of the oxalic acid solution to reach the endpoint of the

titration. What is the concentration of NaOH?

To calculate the exact concentration of the NaOH using molar concentrations the equation for the reaction must be

known and the mole-to-mole ratio between the acid and base must be known.

2NaOH + H2C2O4 Na2C2O4 + 2H2O

In using 10.09 mL of 0.2826 M oxalic acid the following number of moles of the acid was used.

moles of acid = 10.09 mL mL 1000

L 1

L 1

mol 0.2826 = 0.002851 moles acid

From the stoichiometry of the reaction, the number of moles of NaOH present is calculated:

NaOH mole 005702.0OCH mol 1

NaOH mol 2OCH moles 0.002851 = NaOH of moles

422422

The concentration of the base is then:

NaOH M 2281.0L 0.02500

NaOH mol 0.005702=MNaOH

Thus the exact concentration of the base was calculated based on its reaction with a standard acid. The base solution

is now considered a standard solution since its concentration is precisely known.

In standardizing solutions by titration, the means of detecting the endpoint3 of the titration, the solutions of known

concentration used, and other considerations will vary from one experiment to another and it generally requires some

understanding of the chemical reaction to determine the optimum conditions for carrying out the reaction. Besides

determining the exact concentration of solutions where an approximate value is known, this process can also be used

to determine concentrations in solutions where the composition is not known.

In the procedure for this experiment you will be preparing solutions in some of the ways described and also using the

process of titration to determine exact concentrations for known and unknown quantities. These procedures should

serve to illustrate many of the salient points of solution preparation and the use of solutions of known concentration.

Procedure In the following procedure keep in mind the following general points relating to types of equipment and their usage:

1. To transfer an aliquot of a solution from one container to another carefully, a pipet is used. If the transfer

need only be approximate, a less precise piece of equipment can be used, e.g. a graduated cylinder.

2. To accurately measure the total volume of a solution as it is being prepared a volumetric flask is used. If

accuracy is not required, a less precise procedure can be used, e.g. adding the solvent with a graduated

cylinder.

3. A buret is usually used in a titration to measure accurately the amount of one reactant required to react

completely with another chemical species. It is typically not used to transfer an aliquot of a solution from

one container to another.

2 An aliquot is a known fraction of a precisely prepared solution of standard or sample. 3 The endpoint in a titration is the point at which you stop adding the known solution because you have reacted all of

the unknown reagent.


Pre-lab Calculations

Before coming to the lab for this experiment calculate the amount of oxalic acid to be weighed out in part A. The

oxalic acid you will be using has the formula H2C2O4·2H2O (see prelab question 2.)

A. Preparation of a standard oxalic acid solution:

A standard oxalic acid solution must first be prepared. A standard solution is one whose exact concentration is known

or can be calculated. To prepare your standard oxalic acid solution, first calculate the exact amount of oxalic acid (a

solid) that is required to give 100.00 mL of a 0.2500 M solution, when dissolved in water (prelab question 2). Next

tare a clean, dry 150 mL beaker. Into the beaker, weigh approximately the mass of oxalic acid you calculated (recorded

to the nearest milligram). Now add 50 to 70 mL of deionized water to the beaker to dissolve the oxalic acid completely.

It may take some time to dissolve, so be patient and stir the mixture with a glass rod. Be sure all oxalic acid is

dissolved before you transfer the solution to the volumetric flask.4 Carefully transfer this solution to the 100.00 mL

volumetric flask. Use about 10 mL of deionized water from your wash bottle to rinse all the solution from the beaker

into the volumetric flask. Now add deionized water to the flask until the water level is about 1 cm below the etched

line on the neck of the flask. Use a plastic dropper to add water until the bottom of the meniscus is exactly level with

the etched line. Use ParafilmTM to seal the flask and invert repeatedly for complete mixing.

B1. Cleaning and filling the buret:

To standardize the unknown sodium hydroxide solution, the first step is to clean and fill your buret. Rinse the buret

several times with deionized water and allow it to drain. A clean buret does not retain drops of water in the graduated

area (if yours does, see the instructor). Now assemble the buret and rinse it three times with ~5 mL of the solution that

will be used to fill the buret (the NaOH solution in this case), delivering the solution directly from the carboy into the

buret (to avoid contamination). Allow the buret to drain well between rinsings. This is routine procedure every time a

buret is prepared for a series of titrations. (Note that multiple small rinsings are more effective than one large rinsing

and are less wasteful of the solution to be standardized.)

When you attach the buret clamp to the ringstand, be sure to use the central screw to secure the buret clamp tightly

(the picture on the left above). Using the approach on the right side of the figure leaves the buret very unstable.

Now fill the buret with the NaOH solution to slightly above the zero mark. Briefly open the stopcock fully to flush air

bubbles out of the tip. Be sure there are no air bubbles left in the tip. The meniscus should fall below the zero mark.

Read the buret to the nearest hundredth of a milliliter (0.01 mL) and record this initial reading on the data sheet.

Remember to read the bottom of the meniscus at eye level for the most accurate estimate.

4 This is a really important point—all of the solid must be dissolved before you fill the flask to the final volume.

Failure to do so will result in a miscalibration of the concentration and you will need to remake the solution.

Correct Incorrect

!


B2. Rinsing the pipet:

Obtain a pipet. Check to see that the pipet drains cleanly by squeezing some water from a deionized (DI) water bottle

into the end that the bulb fits on to. Put about ten milliliters of the liquid that you will be pipetting (the acid solution)

into a small clean dry beaker. Wipe the pipet tip and from the beaker, draw up a few milliliters of solution into the

pipet, roll it around the walls to rinse off the inside; drain the pipet, and repeat with two additional small rinsings.

C. Standardizing a sodium hydroxide solution with oxalic acid:

To standardize a solution means to determine its concentration precisely by titrating it with a solution whose

concentration is already known. In this case the reference solution is the standard oxalic acid solution, which you

made up precisely and whose concentration, therefore, you can calculate to four significant figures.

Pour a small amount of oxalic acid into the beaker, then pipet 10.00 mL of the oxalic acid into a clean 250 mL

Erlenmeyer flask. The Erlenmeyer flask must be clean, but it does not have to be dry. Add 2 drops of phenolphthalein

indicator to the flask with the acid. This indicator is colorless in acid and pink in base. Add deionized water to

bring the volume in the flask up to about 50-60 milliliters. To help you see the faint pink color that will develop, place

a white paper towel under the flask. Hold the flask so that the buret tip is in the neck of the flask and swirl the flask

gently. Use your other hand to control the buret stopcock. Begin the titration by adding NaOH from the buret while

continuing to swirl the flask. At first you may add the NaOH rapidly, but as the pink color begins to persist longer,

decrease the rate of addition until you are adding drop wise. Just before the endpoint, stop the titration and use a

deionized water wash bottle to rinse down the inside walls of the flask. Continue to titrate slowly while swirling. When

one drop changes the color of the solution to pink which persists for 20 seconds or more, the endpoint has been

reached. Record the final buret reading on your data sheet. Refill the buret if less than half full. Rinse your Erlenmeyer

flask very well with DI water, then pipet 10.00 mL of oxalic acid into it and repeat the titration. You should have three

good trials before you leave lab. Calculate the net volume for each trial and show this to your instructor BEFORE

you throw out your oxalic acid solution!

WASTE DISPOSAL Throw all solutions (and rinse all glassware) into the sink using plenty of water.

CAUTION!! Phenolphthalein has been identified as a Particularly Hazardous Substance by

Environmental Health and Safety at USC Columbia. Use gloves when handling these solutions. Make

sure you are wearing your lab coat and goggles. Dispose of solutions containing these in the approved

hazardous waste containers. The specific hazards of this chemical are given below in the Globally

Harmonized System (GHS) where the most hazardous substances are rated with a 1 and less severe

hazards have higher numbers up to 4.

Phenolphthalein

Germ cell mutagenicity Category 2

Carcinogenicity Category 1B

Reproductive toxicity Category 2


Checklist of items to turn in:

Solutions and Titrations Report (page 10 & 11)

Post-lab questions (page 12-13)

Spreadsheet for calculation of NaOH molarity


Solutions and Titration Prelab Questions

Show all calculations.

1. In this lab, you will be titrating oxalic acid (H2C2O4), but the chemical you will measure on the balance is oxalic

acid dihydrate (H2C2O4∙2H2O).

(a) What is the formula mass of oxalic acid (H2C2O4)?

(b) What is the formula mass of oxalic acid dihydrate (H2C2O4∙2H2O)?

(c) Which has more moles of H2C2O4? 1.00 g of H2C2O4 or 1.00 g of H2C2O4∙2H2O? Calculate an answer.

(d) Which formula mass should you use for this lab?

2. What mass of oxalic acid dihydrate (H2C2O4·2H2O) is needed to make 100.00 mL of a 0.2500 M solution? You

will make this solution in part A of this experiment.

3. Why is it impossible to make a standard NaOH solution, as is done with oxalic acid, by weighing out solid NaOH

pellets?

4. What volume of a 3.079 M HCl stock solution must be diluted to prepare 100.00 mL of a 0.3079 M HCl solution?


5. The chemical phenolphthalein is an “indicator” which is added to the solution being titrated to signify when enough

base (NaOH) has been added. What color is phenolphthalein in an acidic solution? What color is phenolphthalein in

a basic solution? How will you know when the “endpoint” of the titration has been reached (that is, how will you

know to stop adding NaOH from the buret)?

6. Balance the following equation, then calculate the molarity of an HCl solution if 25.44 mL were needed to neutralize

15.00 mL of 0.3000 M Ba(OH)2.

HCl + Ba(OH)2 BaCl2 + H2O

7. As shown by the examples on page 1-7 (BLT Lab), choose the standard deviation with the correct number of

significant figures for each average value.

Average = 23 Average = 18.96

(a) Standard Dev. = 1 (a) Standard Dev. = 0.

(b) Standard Dev. = 1.2 (b) Standard Dev. = 0.2

(c) Standard Dev. = 1.24 (c) Standard Dev. = 0.24

(d) Standard Dev. = 1.242 (d) Standard Dev. = 0.236

8. What is the reading on each buret shown below?

1

2

28

29

Initial buret reading: ________ Final buret reading: ________

Net volume: __________


Solutions and Titration Report Name: _____________________________

1 Write the balanced equation for the titration reaction of oxalic acid with sodium hydroxide. (Hint: you may

ignore the dihydrate part of the oxalic acid—it will float away in the aqueous solution anyway and is not part of the

titration reaction.)

2. Show the calculation for the molarity (M) of the standard oxalic acid solution you prepared. Your target

concentration was 0.2500 M. Were you reasonably close? (If not, you probably have a calculation error!)

3. For Trial 1 only, show the calculation for the molarity of NaOH for the titration with oxalic acid:


Note: Before attempting ANY of the calculations below,

answer ALL of the questions on the previous page!

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

A B C D E F G

Name:

Date:

A. Record the data for the preparation of standard oxalic acid solution

in cells E7 and E8. Calculate its molarity in cell E9:

Molar mass of oxalic acid dihydrate (g/mol) 126.0654

Mass of oxalic acid dihydrate (g)

Volume of volumetric flask (mL)

Concentration of oxalic acid (mol/L)

C. Record data for your 3 best titrations to standardize the NaOH

solution in rows 15-17. Read the buret to 2 decimal places so that results

may be calculated to 4 sig figs. Complete the calculations in rows 18-21.

Trial 1 2 3

Volume of oxalic acid pipetted (mL)

Final buret reading (mL)

Initial buret reading (mL)

Net volume of NaOH in titration (mL)

Average volume of NaOH (mL) Std Dev

Molarity of NaOH for each trial (mol/L)

Average molarity of NaOH (mol/L) Std Dev

Be sure to round all values to the correct number of significant figures.


Solutions and Titration Name: ______________________________ Post Lab Questions (Show all work)

1a. Relative standard deviation (RSD) is the standard deviation of a set of numbers divided by the average of that set

of numbers (usually expressed as a percentage.) RSD measures precision.

RSD =Standard Deviation

Average 100

What is your RSD for the NaOH titration volumes calculations in part C? SHOW ALL WORK!!

1b. Is it advantageous to have a large RSD or small RSD? Why?

2. List two sources of potential errors encountered with this experiment. DO NOT say “human error”. What,

specifically, had an error (uncertainty) associated with it? Assume that your calculations were correct, so please ignore

“calculation error” as an answer (if they are in error, go correct them!!). THINK about the uncertainty in your

measurements; where did you make assumptions?

3a. What mass of FeCl3∙6H2O would be needed to make 250.00 mL of 0.150 M FeCl3 solution? Show your work.

3b. Describe the physical process of how you would actually make the 0.150 M FeCl3 solution above. Tell what

glassware you would use; be specific with respect to size, type, etc.


4a. Calculate the volume (in mL) of 0.300 M K3PO4 needed to make 500.00 mL of a 0.00600 M K3PO4 solution.

4b. Describe the physical process of how you would actually make the 0.00600 M K3PO4 solution, assuming you are

starting with a 0.300 M K3PO4 solution (hint: use the answer from the previous question). Tell what glassware you

would use; be specific with respect to size, type, etc.

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Solutions and Titrations