December 2015 - January 2016

# Acid-base titrations with citric acid: part 2

##

David Cash PhD, Mohawk College (retired), Hamilton ON

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## Introduction

Part 1 of this article was published in Chem 13 News in November 2014. This second part presents three titration exercises of increasing sophistication, suitable for students with some titration experience. Citric acid and sodium hydroxide are used for all three presented titrations. Refer to Part 1 for the background information and the titration method. The reaction

3 NaOH (aq) + H3C6H5O7 (aq) → Na3C6H5O7 (aq) + 3 H2O

goes to completion and is suitable for analytical titrations. Part 1 is posted online at the Chem 13 News magazine website.

This first titration, A, described below provides the method to standardize a sodium hydroxide solution, providing a less expensive alternative to the commonly-used potassium hydrogen phthalate in acid/base titrations. The second titration, B, determines the purity and type, — anhydrous or monohydrate — of an unknown citric acid. The third titration, C, has citric acid monohydrate as an unknown carboxylic acid to be determined by titration.

## A. Standardization of a sodium hydroxide solution

Citric acid can be used as a lower-cost alternative reagent to potassium hydrogen phthalate1 (KHP) for standardizing 0.1 M NaOH solutions. High-purity solid citric acid costs about

US$15 per 100 g while high-purity KHP costs about double for the same amount.2 Solid citric acid is not a primary standard substance. It cannot be oven-dried, and the purity level is not as high as that of KHP. Its neutralization equivalent, NE (Note 1), is lower, only about 70 g per mol of NaOH, relative to 204 g per mol of NaOH for KHP, and therefore the uncertainties in mass measurements are proportionally greater. An accuracy of about 1% is the best one can do. But the lower mass required is a cost advantage to the economy-minded teacher; since one needs only 35% as much solid citric acid by mass as solid KHP for the experiment; the cost advantage is almost 6-fold. The relatively lower accuracy should not be a problem for secondary school and general chemistry courses.

To try out this standardization experiment, a high-purity solid citric acid sample was used to prepare a citric acid solution (target: 0.033 M) (Note 2). Repeated 5 mL portions of this solution were measured out using a graduated cylinder (Note 3) and were titrated against an ‘unknown’ NaOH solution, which was actually a 0.1000 M solution of NaOH of highly accurate concentration prepared from an ampoule.3 The experiment was carried out exactly as students would be instructed to perform the standardization.

### Titration data (gravimetric titration)

- Citric acid monohydrate, 99-102%; free-flowing, colourless (white) crystals; 210.1 g/mol; Caledon Labs 20094
- Sample: 3.68 g in 500 mL water (volumetric flask); 0.0350 M;
- Titration mass of NaOH (g) (6 repeats): 5.27, 5.18, 5.28, 5.29, 5.32, 5.27
- Mean 5.29 g; Range 5.32 g - 5.18 g = 0.14 g (2.6% of mean);
- Calculated NaOH molarity: 0.0992 M — shown below

### Calculation of the molarity of a sodium hydroxide solution

In the equations here and in the rest of the article, substance labels, where obvious, are omitted for simplicity. Note that the mass of the NaOH solution in g units has been used as a volume in mL units with little error because the density of a 0.125 M NaOH solution at 20 oC is 1.0039 g/mL (CRC Handbook).

[NaOH]=0.0350 M × 0.00500 L × (3 mol)/(1 mol) × 1/(0.00529 L)

= 0.0992 M

The relatively small percentage range of the titration results is encouraging, given that the sample volumes were measured by a graduated cylinder. The experimental result of 0.0992 M is in very good agreement with the known value 0.1000 M for the molarity of the NaOH solution. The error is less than 1%. This gives me confidence in the accuracy, the precision and the validity of the analysis method for student use. The Caledon Labs sample checks out as high purity citric acid monohydrate.

## B. Analysis of a solid citric acid of unknown type and purity

High-purity, more costly citric acid purchased from a chemical supplier is usually specified as to its type, anhydrous or monohydrate, and a purity level is often stated.2,4 Citric acid of lesser cost may have no specification at all.5 This is an exercise to determine either or both of the purity level and the molar mass and hence the type of a sample of unspecified solid citric acid. A solution of sodium hydroxide of known molarity is required; the NaOH solution used here was 0.1000 M. This exercise may be performed as a stand-alone experiment, or may be combined with Exercise A as a longer, two-part experiment.

The low cost unspecified type citric acid sample for this trial experiment was purchased from Fibre Garden,5 a vendor specializing in fibres and dyestuffs. Citric acid is employed as a non-volatile, non-odorous substitute for vinegar in the acid dyeing of wool fibres. It was packaged in a wide-mouth polymer container, similar to a food storage container. Although very inexpensive, this solid citric acid would not be easy to use or store unless transferred to a bottle with a screw-on lid. Other sources of unspecified citric acid include some chemical supply houses and vendors selling citric acid for use in food preparation (pickling).

### Titration data (gravimetric titration)

- Formula and purity of the solid citric acid sample are unknown; free-flowing, colourless (white) crystals; Fibre Garden 20145
- Sample: 3.29 g in 500 mL water (volumetric flask);
- Titration mass of 0.1000 M NaOH (g) (6 repeats, using 5 mL samples of citric acid solution): 5.05, 5.08, 5.09, 5.09, 5.06, 5.13
- Mean 5.08 g, Range 5.13 g – 5.05 g = 0.08 g (1.6% of mean);
- Calculated citric acid molarity; 0.0339 M;
- Calculated percentage as anhydrous citric acid: 99.1%;
- Calculated molar mass as citric acid: 194.1 g/mol.

The calculation is essentially the same as for the previous exercise, but reversed. Once the molarity of the citric acid (CA) solution has been calculated, the percent purity or the experimental molar mass or both may be calculated as shown below.

### Calculation of the percent purity and the molar mass of an unspecified citric acid sample

Molarity of CA=0.1000 M × 0.00508 L × (1 mol)/(3 mol) × 1/(0.00500 L)= 0.0339 M

Mass of CA (g)= 0.0339 mol/L× 0.500 L × 192.1 g/mol=3.26 g

Percent Purity of CA= (3.26 g)/(3.29 g)× 100%=99.1%

Experimental Molar Mass CA (g)=

3.29 g × (1 L)/(0.0339 mol)× 1/(0.500 L)=194.1 g/mol

The value 194.1 g/mol is just slightly more than 1% above the molar mass of anhydrous citric acid. Allowing for an uncertainty range in the experimental results of a couple of percent due to the method, it seems reasonable to conclude that the Fibre Garden solid is good quality anhydrous citric acid.

## C. Neutralization equivalent of an unknown carboxylic acid

Your students may find it interesting to determine the identity of an unknown carboxylic acid by titration analysis and calculations. This experiment is based on a classic method for the characterization of an organic carboxylic acid (Note 4). The students will determine by experiment the neutralization equivalent (NE) of an unknown acid (Note 1). Either or both forms of citric acid are ideal unknowns.

The unknown sample can be given to the students as a solid or as a solution of known concentration in g/L units, shortening the time required for the experiment. Table 1 gives a list of acids and their data that can be given to the students as possible identities for their unknown acid. (Note 5)

### Calculation of a neutralization equivalent

The titration data in A and B above may be used as examples. Calculate the mass of each acid in a 5 mL sample, and divide by the number of moles of sodium hydroxide neutralized. The calculation for the A data for the Caledon Labs sample is shown; the calculation method for the B data for the Fibre Garden sample is identical:

Mass of sample in 5 mL= (3.68 g)/(500 mL) × 5.00 mL= 0.0368 g

mol NaOH neutralized= 0.00529 L × 0.1000 mol/L

= 0.000529 mol

Experimental NE of sample= (0.0368 g)/0.000529 = 69.6 g

Note: In the above calculations, the value of 3.68 g citric acid was the amount added to 500 mL to make the sample solution. These values can be given to the students. The 0.00529 L was determined as the average of the titration mass of sodium hydroxide in titration A, where 1 mL was assumed to equal 1 gram based on density.

The experimental value of NE for the Caledon Labs sample in A above is 69.6 g and that for the Fibre Garden sample in B above is 64.8 g. Students performing this experiment for a citric acid monohydrate sample should be able to identify it as citric acid monohydrate from the data in Table 1. Those having an anhydrous citric acid sample might find it difficult to choose between oxalic acid dihydrate and anhydrous citric acid from the data in Table 1.

#### Table 1: Possible unknown carboxylic acid identities data

Acid name | Molar mass (g/mol) | NE (g)
Malonic acid | 104.06 | 52.03
Succinic Acid | 118.1 | 59.05
Oxalic acid dihydrate | 126.07 | 63.04
Anhydrous citric acid | 192.12 | 64.03
Malic acid | 134.1 | 67.05
Citric acid monohydrate | 210.14 | 70.05
Adipic acid | 146.14 | 73.1
Tartaric acid | 150.1 | 75.05
Lactic acid | 90.08 | 90.08

### Questions for students

Create a table listing all of the acids above in the first column. Add and fill in columns with: IUPAC names; sources; uses; safety hazards.

Citric acid is a tri-carboxylic acid. The three Ka values are:

7.1 × 10-4; 1.7 × 10-5, 6.4 × 10-6 (CRC Handbook). Assuming that only the first acid dissociation constant1 is important, calculate the expected pH of a 0.0333 M citric acid solution. Answer: pH = 2.34. he observed pH of this solution is 2.2.6 Account for the discrepancy.

An experiment determines the NE of an acid to be 82.0 g. What is the molar mass of the acid? Explain your answer.

Note 1. The neutralization equivalent or NE of a carboxylic acid is defined as the mass in g units of the acid required to neutralize one mole of a strong alkali such as sodium hydroxide. The theoretical NE value is the molar mass in g units divided by the number of carboxylic acid groups in the molecule.

Note 2. Since citric acid is a tri-carboxylic acid a solution of 0.0333 M citric acid is equivalent on a volume to volume basis to a 0.1000 M NaOH solution. In chemical industry this citric acid solution may be referred to as 0.1000 N (Normal) citric acid.6

Note 3. Graduated cylinders are marked TC (to contain) and are not intended to deliver (TD) specific volumes of solution. However, for introductory students, convenience and simplicity are arguably more important than high precision.

Note 4. The neutralization equivalent of an unknown acid, purified by recrystallization, can be determined accurately and with precision by an analyst having a 4-place balance with as little as 0.100 g of solid. Prior to modern instrumental techniques, this method gave valuable evidence as to the molar mass of natural and synthetic organic substances and/or their degradation products. (See Question 3.)

Note 5: These aliphatic carboxylic acids are all of low hazard rating. Stay away from aromatic carboxylic acids, which are all very corrosive to mucous membranes, especially as airborne dusts. If you want to rotate to a different acid unknown each year, or use more than one unknown, the following acids are reasonably priced and are sufficiently soluble in water: malonic acid; oxalic acid dihydrate; malic acid; adipic acid; DL-tartaric acid.1,2

## Acknowledgements

The author thanks Randy Travis, technologist, of the Department of Chemical, Environmental, and Biotechnology of Mohawk College, for his invaluable help.

## References

1. https://www.wikipedia.org/ for: citric acid; potassium hydrogen phthalate (KHP); malonic acid; succinic acid; oxalic acid dihydrate; malic acid; adipic acid; tartaric acid; lactic acid; acid dissociation constant (Ka).
2. http://www.sigmaaldrich.com/chemistry.html for: citric acid (99%); citric acid monohydrate (98%); potassium hydrogen phthalate; malonic acid; oxalic acid dihydrate; malic acid; adipic acid; DL-tartaric acid.
3. Sigma-Aldrich for 0.1000 M NaOH ampoules: http://www.sigmaaldrich.com/.Caledon Labs for citric acid monohydrate: http://caledonlabs.com/home.php .Fibre Garden for citric acid (unspecified type or % purity): http://www.fibregarden.ca/shopfg/index.php?main_page=product_info&cPath=1_135_139&products_id=658.

   Engineering Toolbox: Acids — pH values: http://www.engineeringtoolbox.com/acids-ph-d_401.html

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