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This article incorporates, in modified form, material from Illustrated Guide to Home Chemistry Experiments: All Lab, No Lecture.

 

The process used to determine the concentration of a solution with very high accuracy is called standardizing a solution. To standardize an unknown solution, you react that solution with another solution whose concentration is already known very accurately.

For example, to standardize the hydrochloric acid solution we made up in a preceding lab, we might very carefully measure a known quantity of that solution (called an aliquot) and neutralize that aliquot with a solution of sodium carbonate whose concentration is already known very accurately. Adding a few drops of an indicator, such as phenolphthalein or methyl orange, to the solution provides a visual indication (a color change) when an equivalence point is reached, when just enough of the standard solution has been added to the unknown solution to neutralize it exactly. By determining how much of the sodium carbonate solution is required to neutralize the hydrochloric acid, we can calculate a very accurate value for the concentration of the hydrochloric acid. This procedure is called titration.

Titration uses an apparatus called a burette (or buret), which is a very accurately graduated glass cylinder with a stopcock or pinchcock that allows the solution it contains to be delivered in anything from a rapid stream to drop-by-drop. Because titration is a volumetric procedure, the accuracy of the results depends on the concentration of the reagent used to do the titration. For example, if 5.00 mL of 1.0000 M sodium carbonate is required to neutralize a specific amount of the unknown acid, that same amount of acid would be neutralized by 50.00 mL of 0.10000 M sodium carbonate. If our titration apparatus is accurate to 0.1 mL, using the more dilute sodium carbonate reduces our level of error by a factor of 10, because 0.1 mL of 0.10000 M sodium carbonate contains only one tenth as much sodium carbonate as 0.1 mL of 1.0000 M sodium carbonate. For that reason, the most accurate titrations are those performed with a relatively large amount of a relatively dilute standard solution.

The obvious question is how to obtain an accurate reference solution. For work that requires extreme accuracy, the best answer is often to buy pre-made standard solutions, which are made to extremely high accuracy (and the more accurate, the more expensive). None of the work done in a home lab requires that level of accuracy, so the easiest and least expensive method is to make up your own standard solutions. (In fact, to illustrate the principles of standardization and titration, you don’t even need a truly accurate reference solution; you can simply pretend that a 1 M solution is actually 1.0000 M and proceed on that basis. Your results won’t be accurate, but the principles and calculations are the same.)

When you make up a standard solution, take advantage of the difference between absolute errors and relative errors. For example, if your balance is accurate to 0.01 g, that means any sample you weigh may have an absolute error of as much as 0.01 g. But that absolute error remains the same regardless of the mass of the sample. If you weigh a 1.00 g sample, the absolute error is 1% (0.01g/1.00g·100). If you weigh a 100.00 g sample, the absolute error is 0.01% (0.01g/100.00g·100). Similarly, volumetric errors are absolute regardless of the volume you measure. For example, a 10.00 mL pipette may have an absolute error of 0.05 mL. If you use that pipette to measure 10.00 mL, the relative error is (0.05 mL/10.00 mL·100) or 0.5%. If you measure only 1.00 mL, the relative error is ten times as large, (0.05 mL/1.00 mL·100) or 5.0%.

One way to minimize the scale of errors is to use a relatively large amount of solute to make a starting solution and then use serial dilution to make a dilute standard solution to use as the titrant. Serial dilution simply means repeatedly diluting small aliquots of known volume. For example, we might start with a 1.5 M solution of a chemical. We use a pipette to take a 10.00 mL aliquot of that solution and dilute it to 100.0 mL in a volumetric flask to make a 0.15 M solution. We then take a 10.00 mL aliquot of the 0.15 M solution and dilute it again to 100.0 mL, yielding a 0.015 M solution.

For example, a reference book tells us that the formula weight of anhydrous sodium carbonate is 105.99 g/mol and its solubility at 20 °C is about 200 g/L. A saturated solution of sodium carbonate is therefore about 1.9 M, because (200 g/L)/(105.99 g/mol) = 1.88+ M. In this lab, we’ll make up a 1.5 M solution of sodium carbonate and then use serial dilution to produce a 0.15 M solution to use as our titrant. We’ll titrate our unknown HCl solution once using phenolphthalein as the indicator, and a second time using methyl orange as the indicator. Why two passes with two separate indicators?

As it happens, the neutralization of sodium carbonate by hydrochloric acid is a two-step process. In the first step, one mole of sodium carbonate reacts with one mole of hydrochloric acid to produce one mole of sodium hydrogen carbonate (sodium bicarbonate) and one mole of sodium chloride:

Na2CO3(aq) + HCI(aq) → NaHCO3(aq) + NaCl(aq)

In the second step, a second mole of hydrochloric acid reacts with the sodium hydrogen carbonate formed in the first step:

NaHCO3(aq) + HCI(aq) → NaCl(aq) + CO2(g) + H2O(I)

Each of these reactions has an equivalence point. The first occurs when the first mole of HCl has reacted with the sodium carbonate to form one mole each of sodium bicarbonate and sodium chloride. The pH at the equivalence point of this reaction happens to correspond very closely to the pH range where phenolphthalein changes color, but is well above the pH range of methyl orange. The second equivalence point occurs when the second mole of HCl has reacted with the sodium bicarbonate to form one mole each of sodium chloride, carbon dioxide, and water. The pH at the equivalence point of this reaction happens to correspond very closely to the pH range where methyl orange changes color, but is well below the pH range of phenolphthalein.

figure11.02 Laboratory 11.4: Standardize a Hydrochloric Acid Solution by Titration

Figure 11-2. Methyl orange (left) and phenolphthalein at their equivalence points

Since these reactions occur with exactly a 2:1 proportion of hydrochloric acid, the amount of titrant needed to reach the indicated equivalence point with methyl orange is exactly twice as much as the amount of titrant needed to reach the indicated equivalence point with phenolphthalein. In other words, if you use methyl orange, you miss the first equivalence point completely. If you use phenolphthalein, you are misled into believing that the first equivalence point is the final equivalence point. For this reason, the neutralization of sodium carbonate with hydrochloric acid is often used as a (literal) textbook example of the importance of choosing the proper indicator.

Note that for titrations with multiple equivalence points, it makes a difference which solution is used for the titrant. For example, if we titrate a solution of sodium carbonate by adding hydrochloric acid, we could observe the first (higher pH) equivalence point by using phenolphthalein as an indicator. When sufficient HCl has been added to convert the sodium carbonate to sodium bicarbonate, the phenolphthalein changes from pink to colorless. We could then add some methyl orange indicator to observe the color change from yellow to red at the second (lower pH) equivalence point, when the sodium bicarbonate is converted to sodium chloride. Conversely, if we titrate a solution of hydrochloric acid with sodium carbonate as the titrant, the acid is always in excess until sufficient sodium carbonate has been added to completely neutralize the acid. In this case, we use phenolphthalein as the indicator, because only one equivalence point exists for this reaction, and it is at the higher pH when sodium carbonate is in slight excess.

In this lab, we’ll standardize an approximately 1 M solution of hydrochloric acid by titrating a known volume of the acid with a sodium carbonate solution of known molarity.

Required Equipment and Supplies

  • googles, gloves, and protective clothing
  • balance and weighing papers
  • beaker, 150 mL (2)
  • volumetric flask, 100 mL
  • funnel
  • pipette, 10 mL
  • burette, 50 mL
  • ring stand
  • burette clamp
  • storage bottle, 100 mL (labeled “sodium carbonate, 1.500 M”)
  • hydrochloric acid, 1 M bench solution (~ 10 mL)
  • sodium carbonate, anhydrous (15.90 g)
  • phenolphthalein indicator solution (a few drops)
  • distilled or deionized water

All of the specialty lab equipment and chemicals needed for this and other
lab sessions are available individually from Maker Shed or other laboratory
supplies vendors. Maker Shed also offers customized laboratory kits at special
prices, including the Basic Laboratory Equipment Kit, the Laboratory Hardware Kit, the Volumetric Glassware Kit, the Core Chemicals Kit, and the
Supplemental Chemicals Kit.

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CAUTION

Hydrochloric acid is corrosive. Wear splash goggles, gloves, and protective clothing at all times. (Phenolphthalein, formerly widely used as a laxative, was withdrawn from the market because of concerns about possible links with cancer, but the small amount used in an indicator solution is not ingested and is no cause for concern.)

Substitutions and Modifications

  • You may substitute any suitable containers of similar size for the 150 mL beakers.
  • You may substitute a 100 mL graduated cylinder for the 100 mL volumetric flask and/or a 10 mL graduated cylinder for the 10 mL pipette, with some loss in accuracy.
  • If you do not have a burette, ring stand, and burette clamp, you may substitute a 100 mL graduated cylinder, with some loss in accuracy. To do so, fill the graduated cylinder with titrant and record the starting level. Transfer titrant to the reaction beaker by pouring carefully until the endpoint is near (evidenced by a non-persistent color change in the indicator that disappears when you swirl the beaker). Then use a dropper or beral pipette to transfer titrant dropwise until the end point is reached. Transfer any remaining titrant from the dropper or beral pipette back into the graduated cylinder, record the ending level, and subtract to determine how much titrant was required to reach the endpoint.
  • If you do not have anhydrous sodium carbonate, you may substitute equivalent weights of the monohydrate, heptahydrate, or decahydrate.
  • You may substitute cresol red, thymol blue, or a similar indicator for the phenolphthalein indicator.

Procedure

This laboratory has three parts. In Part I, you’ll make up a stock reference solution of 1.500 M sodium carbonate. In Part II, you’ll use serial dilution to make up a working reference solution of 0.1500 M sodium carbonate solution to use as a titrant. In Part III, you’ll use that tritrant to standardize an approximately 1 M bench solution of hydrochloric acid by titration.

Part I – Make up a stock reference solution of ~1.500 M sodium carbonate

  1. If you have not already done so, put on your splash goggles, gloves, and protective clothing.
  2. Place a weighing paper on the balance and tare the balance to read 0.00 g.
  3. Weigh out about 15.90 g of anhydrous sodium carbonate powder, and record the mass to 0.01 g on Line A of Table 11-4.
  4. Using the funnel, transfer the sodium carbonate to the 100 mL volumetric flask.
  5. Rinse the funnel with a few mL of distilled or deionized water to transfer any sodium carbonate that remains in the funnel into the volumetric flask.
  6. Fill the volumetric flask with distilled or deionized water to a few cm below the reference line.
  7. Stopper the flask and invert it repeatedly until all of the sodium carbonate dissolves.
  8. Finish filling the volumetric flask with water until the bottom of the meniscus is just touching the reference line.
  9. Stopper the flask and invert it several times to mix the solution thoroughly.
  10. Transfer the sodium carbonate solution to the 100 mL storage bottle and cap the bottle.
  11. Use the actual mass of sodium carbonate from step 3 to calculate the actual molarity of the sodium carbonate solution to the appropriate number of significant figures, and record that molarity on Line B of Table 11-4.
  12. Label the bottle with its contents, molarity, and the date.

Part II – Use serial dilution to make up a working reference solution of ~0.1500 M sodium carbonate

  1. If you have not already done so, put on your splash goggles, gloves, and protective clothing.
  2. Rinse the 100 mL volumetric flask, first with tap water and then with distilled or deionized water.
  3. Use the 10 mL pipette to transfer about 10 mL of the ~1.500 M sodium carbonate solution you made up in Part I to the volumetric flask. Record the volume to 0.01 mL on Line C of Table 14-4.
  4. Fill the volumetric flask with water until the bottom of the meniscus just touches the reference line.
  5. Stopper the flask and invert it several times to mix the solution thoroughly.
  6. Use the actual volume of sodium carbonate solution from step 3 to calculate the actual molarity of the working sodium carbonate solution to the appropriate number of significant figures, and record that molarity on Line D of Table 11-4.

Part III – Standardize a bench solution of ~ 1 M hydrochloric acid

  1. If you have not already done so, put on your splash goggles, gloves, and protective clothing.
  2. Use the 10 mL pipette to transfer about 10 mL of the ~1.0 M hydrochloric acid bench solution to a 150 mL beaker. Record the volume to 0.01 mL on Line E of Table 11-4.
  3. Add about 25 mL of water to the beaker and swirl the beaker to mix the solution.
  4. Add a drop or two of phenolphthalein indicator to the beaker and swirl to mix the solution.
  5. Calculate the approximate amount of titrant you expect to need to neutralize the 10 mL of ~1.0 M hydrochloric acid solution, and enter that value on Line F of Table 11.4.
  6. Rinse the burette thoroughly, first with water and then with a few mL of the titrant solution.
  7. Install the burette in the burette clamp and fill it to or above the top (0.00 mL) line with titrant solution.
  8. Run a few mL of titrant through the burette, making sure that no air bubbles remain and that the level of titrant is at or below the top index line at 0.00 mL. (It’s not important that the initial reading be exactly 0.00 mL, but it is important to know the initial reading as closely as possible.) Record the initial reading as accurately as possible on Line G of Table 11-4.
  9. While swirling the beaker, use the burette to dispense into the beaker a few mL less of the titrant than you estimated in step 5 will be required to neutralize the hydrochloric acid.
  10. Begin adding the titrant dropwise but quickly and with continuous swirling. As you approach the equivalence point, you’ll see the solution turn pink where the titrant is being added, but the pink color will disappear with swirling. This indicates that you are rapidly approaching the equivalence point. Using a sheet of white paper or other white background under or behind the beaker makes it easier to detect the first hint of a color change.
  11. Continue adding titrant slowly dropwise, with swirling, until the solution in the beaker shows an overall very slightly pink color that does not disappear when the solution is swirled. A permanent slight pink coloration indicates that you’ve reached the equivalence point. All of the hydrochloric acid is neutralized, and there is a tiny excess of sodium carbonate. A dark pink color (or any color other than pale pink) indicates that the equivalence point has been met and exceeded, which means you need to re-do the titration. If you use a different indicator, such as universal indicator, the indicative color change may be slightly different.
  12. Record the final burette reading on line H of Table 11-4. Subtract line G from line H and record the difference on line I as the volume of titrant required to neutralize the aliquot of hydrochloric acid.
  13. Calculate the number of moles of sodium carbonate contained in the volume of titrant you used, and record that value on line J of Table 11-4.
  14. Calculate the number of moles of hydrochloric acid present in the aliquot (remember that two moles of hydrochloric acid react with one mole of sodium carbonate) and enter that value on line K of Table 11.4.
  15. Calculate the molarity of the HCl bench solution, and enter that value on line L of Table 11.4.

Table 11-4. Standardize a solution by titration – observed and calculated data

Item Data
A. mass of sodium carbonate
___.___g
B. titrant stock solution molarity
___.___mol/L
C. volume of titrant stock solution
___.___mL
D. titrant working solution molarity
___.___mol/L
E. volume of ~1.0 M HCl bench solution
___.___mL
F. Estimated volume of titrant required
___.___mL
G. Initial burette reading
___.___mL
H. Final burette reading
___.___mL
I. Actual volume of titrant used (H – G)
___.___mL
J. Moles of sodium carbonate required
___.___moles
K. Moles of HCl present in aliquot
___.___moles
L. Molarity of HCl bench solution
___.___mol/L

Disposal
Retain the stock sodium carbonate solution and the standardized hydrochloric acid solution for later use. The other solutions can be flushed down the drain with plenty of water.

Optional Activities
If you have time and the required materials, consider performing these optional activities:

  • Repeat the titration once or twice and compare these results with your initial results. If the results are not in close agreement, run additional titrations until you have an accurate value for the molarity of the hydrochloric acid bench solution.
  • Use your standard sodium carbonate solution and your newly standardized hydrochloric acid solution to determine accurate concentrations for various household acids and bases. For example, you might use the sodium carbonate solution (after serial dilution) to titrate aliquots of distilled vinegar (acetic acid) and lemon juice (citric acid), and the standardized HCl solution to titrate aliquots of household ammonia and liquid drain cleaner (sodium hydroxide).

Review Questions

Q1: Best practice when titrating an unknown is to do multiple titrations. Why?

Q2: List at least five possible sources of error in the procedure you followed in this laboratory.

Q3: You are titrating an unknown base solution and have standardized solutions of hydrochloric acid and acetic acid available. Is the acid you choose for the titration likely to affect the accuracy and/or precision of your results? If so, why?

Q4: Other than using an indicator solution, how might you determine the equivalence point(s) for a titration?

4 Responses to Laboratory 11.4: Standardize a Hydrochloric Acid Solution by Titration

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