# Titrimetry, Alkalinity, and Water Hardness


## Titrimetry

Q1. In an acid-base titration, what is the chemical reaction that is occurring and how would you determine the endpoint, when all of the unknown had reacted with the titrant?

You need some indicator to identify when the endpoint occurs. For an acid-base titration, you can have change in solution color due to acid/base indicator, or you can determine the endpoint by measuring pH as a function of added titrant. The inflection point of this graph will be at the endpoint.

Q2. What might be the difference between using an acid-base indicator and a pH electrode in measuring the endpoint for an acid-base titration?

The indicator changes in the pH range of the indicator, therefore you have to select the correct acid-base indicator. The pH electrode consistently allows pH to be measured, and requires a titration curve be prepared in order to determine the endpoint. An acid/base indicator is much quicker-but you need to know the pH of the endpoint. Following the titration with a pH electrode can give you additional information, such as something about how the solution is buffered, and the pH of the endpoint.

## Alkalinity or Acid Neutralizing Capacity (ANC)

Resources:

Rounds, S.A., 2006, Alkalinity and acid neutralizing capacity (ver. 3.0): U.S. Geological Survey Techniques of Water-Resources Investigations, book 9, chap A6, sec 6.6, July 2006, accessed [June 25, 2012], from http://water.usgs.gov/owq/FieldManual/Chapter6/section6.6/ .

Q1. How is ANC different than the pH of a solution?

pH is simply a measure related to the amount of H+ in solution. ANC deals with how much acid can be neutralized, therefore it relates to the buffer capacity of the system. The greater the ANC, the less likely that body of water will be affected by acidic inputs.

Q2. What are some likely chemical species present in natural water that would neutralize an added acid?

Carbonate species (HCO3-, CO32- ) and partially deprotonated natural organic acids (humic acid, fulvic acids) can both act to buffer natural water systems.

Q3. How could particles filtered out of a water sample neutralize an acid?

Filtering a water sample will remove suspended particles, and natural organic acids can form micelle-like aggregates that are large enough to be filtered, particularly in the presence of metal ions. Therefore filtering can remove some of the deprotonated organic acids.

Q4. If pKa1 of carbonic acid is 6.352 and pKa2 is 10.329, what carbonate species would primarily be present at pH 7.0? As you adjust the pH to around 4.5, how would the dominant species change?

At pH 7.0, since this is a little more basic than the pKa1 of carbonic acid, the primary species would be the HCO3-. As you adjust the pH to 4.5 you will continue to protonate this species, causing the dominant carbonate species to be the carbonic acid.

Q5. For most surface water samples, the method calls for a sample volume of either 50 mL or 100 mL?

Will either use volumetric pipet or some graduated cylinders that are rated TD (to deliver).

Q6. The analysis requires a known concentration of H2SO4, usually 0.1600N or lower. How would you prepare and standardize this titrant

This concentration can either be purchased directly, or prepared by diluting from a more concentrated solution. Since H2SO4 has two H+, the normality of the acid solution is twice the molarity of the acid solution. The USGS Field Manual has the directions for preparing and standardizing this solution in section 6.6.2

Q7. Sketch an approximate plot of how the pH of a solution of calcium carbonate (a representative weak base) would change as it is titrated with a strong acid. Where is the endpoint of the titration on this plot?

This would be a diprotic acid titration curve with two equivalence points.

The endpoints can be determined by the inflection point method. This works if the sample has a high enough ANC to allow for an accurate determination of the inflection point.

In samples with low alkalinity, such as the salmon rivers in Maine, the ANC can be calculated using a Gran Method rather than an inflection point.

ANC data analysis:

1. In Excel enter sample name, volume and pH values between 4.5 and 3.5 with their corresponding titrant volumes added (Vi).
2. Calculate Gran F for each pH.

Gran F = (Sample Volume + Vi) x 10(4-pH)

3. Perform a data regression to calculate the ANC (milliEQ/L) and R2 using Gran F as the X axis and Vi as the Y axis.

The R2 value should be greater than or equal to 0.990.

ANC (milliEQ/L) = (Acid Normality X Regression Constant X 1000)/ Sample Volume. A sample plot is presented in the Excel sheet (ANC_samplegranplots) with this learning module)

Alkalinity data analysis:

Alkalinity is a related parameter calculated in mg/L CaCO3 using the equation:

$T_{alk} = \left(\dfrac{V_B * N_{H_2SO_4}}{V_S}\right)\left(\dfrac{1\: mole\: CaCO_3}{2\: eq\: H^+}\right)(MW_{CaCO_3})\nonumber$

$$T_{alk}$$ : Total alkalinity (mg/L CaCO3)

$$V_B$$ : Total titrant volume required to reach bicarbonate equivalence point (L)

$$N_{H_2SO_4}$$ : Normality of sulfuric acid (eq/L)

$$V_S$$ : Sample volume titrated (L)

$$MW_{CaCO_3}$$ : Molecular weight of calcium carbonate (1.00087 x 105 mg/mol)

This analysis makes the assumption that there are low concentrations of other titratable species such as ammonia, silicic acid, or borate.

If you have measured the concentration of other common cations and anions, you can usually calculate a mass balance once you have calculated alkalinity.

## Water Hardness

Q1. How can you ensure that the four carboxylic acid sites are deprotonated to ensure the ability to bind with Ca2+ and Mg2+?

You need to have the solution pH above the pKa4 for EDTA.

Q2. What metals would EDTA likely form stable complexes with in most water samples? How selective is this process?

In most water samples the common cations EDTA would complex with would be Ca2+, Mg2+, and in some samples Al3+, or iron species (Fe2+, Fe3+)

Q3. The endpoint of a titration is determined using an indicator. What would be the general features of an indicator that could be used to determine the endpoint of a water hardness titration?

The indicator would need to have some aspect where it changes color when a cation is bonded to it. There is a class of indicators that change color as a metal binds to the indicator. For EPA method 130.2 Eriochrome Black T (EBT) is used to determine total water hardness. In the case of EBT, the indicator is wine-red in the presence of metal ions and blue when the indicator does not have a metal bound to it.

Q4. When the EBT is added to your sample, what color would you expect the indicator?

You would expect the indicator to be a wine-red color, as the EBT would have the cations in the water sample to bind to it. (Do note that EBT does degrade when in solution, and thus can only be stored for a couple of weeks before a new indicator solution needs to be prepared.)

As you titrate the solution with EDTA, the EDTA binds with the metal and once it has complexed all of the cations in solution, the EBT will change color as it is not complexed.

Q5.  How might raising the pH potentially cause metals to precipitate?

Metals that are not Group 1 metals will precipitate as the hydroxide if the pH is raised high enough.

Q6. The chart below lists the solubility product constants of the hydroxide complexes of several common cations in water. Which metal would precipitate last as its hydroxide complex? This is the metal then available for titration using the HB indicator after you adjusted the solution pH to 12.0.

Cation

Equilibrium

Ksp

Al3+

$$\ce{Al(OH)3 (s) ↔ Al^3+ (aq) + 3 OH- (aq)}$$

4.6 x 10-33

Ca2+

$$\ce{Ca(OH)2 (s) ↔ Ca^2+ (aq) + 2 OH- (aq)}$$

6.5 x 10-6

Fe2+

$$\ce{Fe(OH)2 (s) ↔ Fe^2+ (aq) + 2 OH- (aq)}$$

8 x 10-16

Fe3+

$$\ce{Fe(OH)3 (s) ↔ Fe^3+ (aq) + 3 OH- (aq)}$$

1.6 x 10-39

Mg2+

$$\ce{Mg(OH)2 (s) ↔ Mg^2+ (aq) + 2 OH- (aq)}$$

7.1 x 10-12

Raising the pH above pH 12 will precipitate all of the cations except for Ca2+. This process masks the other ions by precipitating them out. After filtering the sample, titration with EDTA is performed. Thus Ca2+ is the only species dissolved in solution, and when this solution is titrated with EDTA, the EDTA will only complex with the Ca2+. Thus the titration at pH 12 with HB as the indicator will determine just the Ca2+.

Q7. If you have measured the total water hardness using EBT as the endpoint and the concentration of the Ca2+ using HB as the endpoint, how could you determine the concentration of Mg2+

Since the concentration of the Al3+ and the iron species are usually very low to negligible, the Mg2+ can be determined by taking the difference in results between the titration with the EBT and the HB analyses.

Q8. Have you made any assumptions in performing up this calculation?

The assumption that the concentrations of Al3+ and the iron species are usually very low to negligible compared to either the calcium or magnesium.

Q9. The concentration of the titrant needs to be known when performing a titration. This concentration is determined by standardizing the titrant. How could you standardize the EDTA solution?

The EDTA is standardized by titrating it was a solution of known Ca2+ concentration. EBT is usually used as the indicator.

Experimental analysis:

The common procedure for this analysis is:

Solutions needed:

• 0.00250 M EDTA solution
• Eriochrome Black T indicator solution (0.1 g in 25 mL of methanol)
• Ammonium Buffer (pH 10): dissolve 67.6 g NH4Cl in 572 mL of NH4+ and dilute to 1 liter with distilled water.
• Hydroxynaphthol blue indicator (solid)
• 50% NaOH

Waste information:

• Neutralize the solutions to between pH 5 and 8, then flush down the drain.

The volume of your sample will depend upon the hardness of the water. Generally a 50.00 mL sample of freshwater is reasonable. Add 3.0 mL of ammonium buffer and 6 drops Eriochrome black T indicator. Titrate with EDTA solution and note when the color changes from wine red to blue. You may want to practice finding the end-point several times using tap water. If the water is rather hard, you may have to increase the EDTA concentration, or you can decrease the sample volume. Save a solution at the endpoint to compare for the titration of your sample.

The water hardness results are usually reported with units of ppm CaCO3, which you calculate using the following equation:

Calculation of Water Hardness

$\dfrac{(V_{EDTA})(C_{EDTA})\left(\dfrac{1\: mmole\: M^{n+}}{1\: mmole\: EDTA}\right)\left(\dfrac{1\: mmole\: CaCO_3}{1\: mmole\: M^{n+}}\right)\left(\dfrac{100.09\: mg\: CaCO_3}{1\: mmole\: CaCO_3}\right)}{(V_{sample})} = ppm\: CaCO_3\nonumber$

Where:

(VEDTA) is the corrected titration volume of EDTA standard titrated (in liters)

(CEDTA) is the concentration of the EDTA standard (in mM)

(VSample) is the volume of the water sample (in liters)

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