Conductivity and Solution Stoichiometry

Abstract: The conductivity of a base solution will be measured as an acid is added. Changes in conductivity will be related to the chemical species present and processes occurring in solution, and a conductimetric determination of the equivalence point will be developed for the titration of barium hydroxide with sulfuric acid. This method will be used to determine the acid neutralizing power of Milk of Magnesia, or for the titration of sodium hydroxide with sulfuric acid.

Introduction

Reactions in Solution

The nature of the solute (dissolved substance) in an aqueous solution has been the focus of chemists' research throughout the recent history of chemistry. Conductance measurements have been used to reveal the nature of solutions because conductivity is high when concentrations of ions are high. Conductance measurements reveal, for example, that when sulfuric acid is dissolved in water it does not exist as "H₂SO₄". Rather, it must form ions by acting as a proton (H⁺) donor, while H₂O is the proton acceptor:

(1) H₂SO₄ + H₂O ® H₃O⁺ + HSO₄^‑

(2) HSO₄^‑ + H₂O ® H₃O⁺ + SO₄^2‑

overall:

(3) H₂SO₄ + 2 H₂O ® 2 H₃O⁺ + SO₄^2‑

The conductance of an H₂SO₄ solution is high, while that of pure water is low, but not zero, indicating that reactions like

(4) H₂O + H₂O ® H₃O⁺ + OH^‑

do not proceed to a great extent.

When most ionic compounds dissolve in water they dissociate to form ions:

(5) NaOH Na⁺ (aq) + OH^‑ (aq)

(6) Ba(OH)₂ Ba²⁺ (aq) + 2 OH^‑ (aq)

(7) Na₂SO₄ 2 Na⁺ (aq) + SO₄^2‑ (aq)

Milk of Magnesia is magnesium hydroxide, which is only slightly soluble. The ions exist “in equilibrium” with the solid:

(8) Mg(OH)₂ Mg²⁺ (aq) + 2 OH^‑ (aq)

Here the "(aq)" subscript indicates a dissolved, or "aquated" species. Solutions of all these salts will conduct electricity well because of the mobile ions present. Most ions conduct about equally well, but the hydrogen ion in solution (H⁺ or H₃O⁺) conducts about four times as well as most other ions in aqueous solutions. Insoluble salts, of course, remain in the solid (s) crystalline, undissociated state; Barium sulfate, for example, is insoluble and remains as BaSO₄ (s) when added to water, and thus cannot affect the concentration of the water. Magnesium hydroxide is only slightly soluble, so even though the ions conduct well, their concentration is low and there is little conductance in a solution above solid Mg(OH)₂.

Stoichiometry

If aqueous H₂SO₄ is added to a solution of Ba(OH)₂, the "descriptive" equation for the reaction is

(9) Ba(OH)₂ + H₂SO₄ ® 2 H₂O + BaSO₄ (s)

But since aqueous Ba(OH)₂ and H₂SO₄ exist as shown in eq. (3) and (4) above, a better way to write eq. (9) might be:

(10) Ba²⁺ + 2 OH^‑ + 2 H₃O⁺ + SO₄^2‑ ® BaSO₄ (s) + 4 H₂O

We would predict that as a solution of sulfuric acid is added to a solution of barium hydroxide, that the conductivity would steadily decrease until all the OH^‑ ions were converted to H₂O and all the Ba²⁺ ions were converted to insoluble BaSO₄. After that, the conductivity would increase as excess H₂SO₄ is added, as shown by the solid line in the figure:

This behavior demonstrates that for a given amount of barium hydroxide, only a specific amount of sulfuric acid can react. Any more will remain as unreacted ("excess"). The excess, unreacted sulfuric acid is responsible for the increasing conductivity. The point in the addition (or titration) of sulfuric acid where exactly the right amount of H₂SO₄ has been added to react with the barium hydroxide present is called the "equivalence point". This reaction will give minimum conductance at the equivalence point. The crosses in the figure indicate what real data might look like.

Seldom does the titration curve appear as perfect as the line shown in the figure above. Real data points might follow a curve like the one indicated by the "x's" in the graph. The points near the equivalence point are frequently inaccurate, or possibly missing. Still, the data points far from the equivalence point frequently lie on a straight line, and these points can be extrapolated by drawing lines through them. The lines then cross at the equivalence point, as shown in the figure. You can print the titration curve that you plot, and with a pencil and ruler, determine the equivalence point graphically. It is also possible to use the linear regression feature of Lotus to get the best extrapolation lines, but this procedure is optional.

Stoichiometry of the Barium Hydroxide Reaction with Sulfuric Acid

In 0.050 g of Ba(OH)₂·8H₂O, which has a molar mass M = 315.5 g/mol, the amount in moles of Ba(OH)₂ is:

n(mol) = m(g) / M(g/mol) = 0.050 g / 315.5 g/mol = 1.6 x 10^‑4 mol;

An equal amount (in mol) of sulfuric acid must be added to reach the equivalence point.

The concentration in Molar units is defined by

n(mol) = C (M) x V (L) ; since 1 Molar (M) = 1 mol/L

OR

n(mmol) = C (M) x V (mL) ; since 1 Molar (M) = 1 mmol/mL

If the sulfuric acid solution is 0.010 M, the requisite volume will be

V(mL) = n (mol) / C(M) = (1.59 x 10^‑4 mol) / (.010 mol/L) = .0159 L or 15.9 mL.

Thus we would expect the conductivity of a barium hydroxide solution to steadily decrease as 0.01 M sulfuric acid is added until a minimum value is reached at the equivalence point, 15.9 mL; then the conductance will increase because there is no more of the "limiting reagent", barium hydroxide, to destroy the ions from H₂SO₄.

Stoichiometry of the Magnesium Hydroxide Reaction with Sulfuric Acid

If aqueous H₂SO₄ is added to a suspension of Mg(OH)₂, the "descriptive" equation for the reaction is

(11) Mg(OH)₂ (s) + H₂SO₄ (aq) ® 2 H₂O + MgSO₄ (s)

Since magnesium sulfate is soluble, the ionic equation for the reaction of Milk of Magnesia with sulfuric acid is:

(12) Mg(OH)₂ (s) + 2 H₃O⁺ (aq) + SO₄^2‑ (aq) ® 2 H₂O + Mg²⁺ + SO₄^2- (s)

Notice that SO₄^2‑ (aq) appears on both sides unchanged, so it undergoes no reaction and is called a spectator ion. It is cancelled to give the net ionic equation:

(13) Mg(OH)₂ (s) + 2 H₃O⁺ (aq) ® 2 H₂O + Mg²⁺

Initially, H₃O⁺ (and a little OH^- that isn’t significant compared to Mg(OH)₂) is destroyed while Mg²⁺ is formed, so conductivity should be steady or slightly rising. After the equivalence point, ionized sulfuric acid is added and conductivity should rise more rapidly.

Stoichiometry of the Sodium Hydroxide Reaction with Sulfuric Acid

Similarly, if sodium hydroxide solution is added to sulfuric acid solution, the reaction is:

(14) 2 NaOH + H₂SO₄ ® 2 H₂O + Na₂SO₄

In this case, 15.9 mL of 0.010 M sulfuric acid, which contains 1.59 x 10^‑4 mol of acid, will require twice that amount, or 3.18 x 10^‑4 mol (or .32 mmol) of NaOH. If 0.01 M NaOH solution were used, 31.8 mL would be necessary.

Note that equations (3), (5) and (7) indicate that the species exist as ions, and equation (14) can be rewritten as follows:

(15) 2 Na⁺ + 2 OH^‑ + 2 H₃O⁺ + SO₄^2‑ ® 2 H₂O + 2 Na⁺ + SO₄^2‑ + 2 H₂O

Since some ions have undergone no chemical reaction (form no new bonds, and exist unchanged during the reaction), the net ionic equation can be written by canceling these spectator ions:

(16) 2 OH^‑ + 2 H₃O⁺ ® 2 H₂O + 2 H₂O

The conductivity of a solution of sulfuric acid does not change as dramatically as you might expect as sodium hydroxide is added. Unlike the case of barium hydroxide and sulfuric acid where no conducting ions survive, in this case the sulfate ions and sodium ions remain in solution to conduct, as shown by equation (11). As sodium hydroxide solution is added to sulfuric acid, the conductivity decreases slightly as the highly conducting protons are replaced by less conducting sodium ions, and then increases past the equivalence point as excess NaOH is added.

Note: For precise work, it is important to take into consideration the decrease in conductance which results from the dilution of ions as titrant is added (as well as the decrease which occurs as a result of precipitation or destruction ions). Because small volumes of titrant are added to large volumes of solution in this experiment, the volume correction is fairly small and will be ignored.

Conductance Measurements

Conductance measurements are usually by applying alternating current (AC, 60 to 1000 Hz) at about 1 volt to the cell, and measuring the resistance (in Ohms, W) of the cell dipped in a solution. The conductance has units of reciprocal ohms, flippantly named “mhos” originally, but now called “siemens” and abbreviated S.

L(mhos) = 1 / R(W)

The voltage is kept low during conductance measurements because oxidation and reduction at the electrodes is undesirable, and AC is used to minimize net migration of ions and the accumulation of any charged species near the electrodes. The computer measures the resistance by measuring the current (in amperes, A) when a known potential (E) of 0.7 volts (V) is applied to the conductivity cell, and calculating resistance by Ohm’s law: E(V) = I(A) R(W). Rather than applying AC, the computer applies a short pulse of voltage to the cell only during the measurement. If measurements are made in rapid succession, cations (+ ions) do accumulate near the cathode (negative electrode), and “polarization” leads to reduced values of conductivity.

Conductivity Cell

The conductivity cell is just a pair of graphite conductors coated with epoxy insulator except for exposed tips of fixed surface area and fixed distance apart (5 mm x 15 cm graphite rods are used here) which is immersed in the solution to be measured.

The conductance is reported approximately in micromhos (the SI unit is the microsiemen or mS, which is equivalent to a m mho) by LIMSport, calculated as the reciprocal of the resistance in megohms (MW):

L(mS) = 1/R(MW)

Conductivity measurements are initiated by clicking on the conductance button:

Prelaboratory Assignment

Use the LIMSport template CONDUCT.

Procedural:

1. What might happen if the water used to dissolve the barium hydroxide were impure?

2. Assess the safety of this experiment, noting that it deals with sulfuric acid and barium hydroxide.

3. Why is universal indicator added? How will the color correspond to various points in the titration curve?

4. Is it necessary to measure the volume of water that the barium hydroxide is dissolved in for

the titration precisely? Why?

5. From reading about the conductivity cell, do you think it matters how deep it is dipped in the solution?

6. Give several steps to be followed in filling a burette with 0.01 M sulfuric acid.

7. How much titrant should be added before each conductivity measurement in the titration? How do you know how long to wait before measuring conductance?

Theoretical:

8. Write the descriptive and net ionic equations for the reaction of sulfuric acid with solutions of (a) KOH and (b) AgNO₃. AgNO₃ is soluble but Ag₂SO₄ isn't. KOH is soluble and acts like NaOH.

9. How many mL of 0.001 M H₂SO₄ will be required to react with 0.0375 g. of Ba(OH)₂·8H₂O?

10. Try to sketch a conductivity vs. volume added plot for the sodium hydroxide/sulfuric acid reaction. Indicate how it would be different from the plot given for sulfuric acid/barium hydroxide. Remember that hydroxide ion concentration decreases before the equivalence point, and that hydrogen ion increases after it, but that hydrogen ion conducts better because of its higher conductivity per mole.

11. How many mL of 0.01 M H₂SO₄ will be required to react stoichiometrically with 200 mL of 0.001 M NaOH?

12. What species exist in solution when the conductivity is sloping upward in the figure on p.2?

13. If Milk of Magnesia (MOM) is typically 0.002 mol of Mg(OH)₂ per gram of suspension, what volume of 0.100 M H₂SO₄ will be required to titrate 0.40 g (12 drops) of MOM? Sketch the expected titration curve, remembering that Mg(OH)₂ is a solid which reacts with sulfuric acid to give ions. How is the equivalence point distinguished?

Equipment & Supplies

Distilled water (The computer measures conductivity in the micromho range, so glassware must be scrupulously clean and only ultrapure distilled water must be used. Deionized water may not work).

Magnetic stirrer & stirbar 0.01 M NaOH, 50 mL

0.01 M H₂SO₄, 50 mL Universal Indicator

0.1 M H2SO4, 25 mL (for MOM) 250, 400 mL Beakers

Milk of Magnesia suspension

Ba(OH)₂·8H₂O, 33 mg (supplied in ten capped, 20 mL vials)

A sulfuric acid solution of unknown concentration (~0.01M)

Procedure

A. Barium Hydroxide and Sulfuric acid

1. Add 200 mL of distilled water and a CLEAN spinbar to a CLEAN beaker and place it on a magnetic stirrer. Immerse the conductivity cell and in the water and measure the conductance with the cursor in any empty cell. If the conductance is not less than 10 microsiemens, your apparatus may be contaminated. If you observe an "out of range" message, this probably means the conductance is 0 (since it is rarely too high to measure) and this is OK.

2. Add 10-15 drops of universal indicator and measure the conductance again. It should not change much, because the indicator is not highly ionized, and the indicator should be yellow in neutral distilled water.

3. With the cursor in the cell designated "mass Ba(OH)₂•8H₂O," add 0.03 (+/- 0.001 g) of Ba(OH)₂•8H₂O to a tared piece of weighing paper on the balance and record the mass. Add the barium hydroxide to the distilled water (with universal indicator), and record the conductance of the solution every 12 seconds as the salt dissolves, with the stirrer operating. The solid has dissolved when the conductance stops increasing.

4. Rinse and fill a burette with 0.010 M H₂SO₄ .

5. Add volumes of about 1 mL of sulfuric acid, measuring the conductance after each, and recording the TOTAL, CUMULATIVE volume as the titration proceeds. Make at least 5 additions of acid AFTER the equivalence point.

View the graph, adding grid lines if you prefer, and enter the volume of H₂SO₄ at the equivalence point, determined from the graph, and its concentration (from the label) in the appropriate cells.

6. Rinse the conductivity electrodes throroughly with distilled water from a wash bottle as you remove them from the solution. Discard the solution.

Do either part B or part C Below:

B. Milk of Magnesia and Sulfuric Acid

1. Shake the Milk of Magnesia well.

2. Draw about 0.5 mL into a disposable Beral pipette

3. Wipe the outside of pipette with a paper towel, place the pipette on the balance and weigh to 0.001g.

4. Add 100mL distilled water to a 400 mL beaker on the stirrer/hotplate.

5. Add a clean spinbar, turn on magnetic stirrer at moderate speed.

6. Record conductance of the distilled water.

7. Add universal indicator and record the conductance.

8. Deliver 2-4 drops of Milk of Magnesia slowly into the water with vigorous stirring, and immediately begin conductivity measurements every 12 seconds for several minutes. When conductance levels off, go on to the next step.

9. Titrate the milk of magnesis suspension with 0.01-0.1 M H₂SO₄. Wait about 10 s after each addition then measure conductance.

C. Sodium hydroxide and Sulfuric Acid.

7. Place a CLEAN 400 mL beaker containing a CLEAN spinbar on the magnetic stirrer, and add 250 mL of distilled water and some universal indicator. Record the conductance.

8. Add 5 mL of 0.010 M H₂SO₄ from your burette to the solution and record the conductivity.

9. Rinse and fill a second burette with 0.010 M NaOH.

10. Titrate the acid in the beaker with NaOH from the burette, following the same procedure as in step 5 above.

Create, Print, and analyze a graph as you did for the first titration. Submit the two graphs, each showing a determination of the equivalence point with the template and sample calculations.

Rinse the NaOH burette with distilled water, then H₂SO₄.

Projects:

I. Conductivity as a Function of Temperature: Measure the conductivity of pure water as it is heated from room temperature to the boiling point, or cooled to the freezing point. The trends you observe indicate that the reaction shown in equation (4) proceeds to a greater or lesser extent depending on temperature, which shouldn’t be too surprising. This means that the pH of pure water changes with temperature.

II. Conductivity of weak acids: See the projects at the end of the experiment “Determination of the Dissociation Constant of a Weak Acid” for ideas about measuring how strong an acid is; that is, how far reactions like (1) or (2) go for different acids. The conductivity of 0.1 M HCl and 0.1 M Acetic acid are very different! Why?

III. Determination of aspirin content of an aspirin tablet: Dissolve an aspirin tablet in about 200 mL of distilled water in a 250 mL volumetric flask, then dilute to the mark. Titrate 100 mL samples with 0.1 M NaOH.

IV. Determine the vanillic acid content of vanilla extract by coductimetric titration.

V. Try a thermometric titration, as described in a Project after the Thermochemistry experiment.