Vernier Software & Technology

# Titration of a Diprotic Acid: Identifying an Unknown

## Introduction

A diprotic acid is an acid that yields two H+ ions per acid molecule. Examples of diprotic acids are sulfuric acid, H2SO4, and carbonic acid, H2CO3. A diprotic acid dissociates in water in two stages:

${\text{(1) }}{{\text{H}}_{\text{2}}}{\text{X(aq)}} \leftrightarrow {{\text{H}}^{\text{ + }}}{\text{(aq) + H}}{{\text{X}}^{\text{ - }}}{\text{(aq)}}$ ${\text{(2) H}}{{\text{X}}^{\text{ - }}}{\text{(aq)}} \leftrightarrow {{\text{H}}^{\text{ + }}}{\text{(aq) + }}{{\text{X}}^{{\text{2 - }}}}{\text{(aq)}}$

Because of the successive dissociations, titration curves of diprotic acids have two equivalence points, as shown in Figure 1. The equations for the acid-base reactions occurring between a diprotic acid, H2X, and sodium hydroxide base, NaOH, are from the beginning to the first equivalence point:

${\text{(3) }}{{\text{H}}_{\text{2}}}{\text{X + NaOH}} \leftrightarrow {\text{NaHX + }}{{\text{H}}_{\text{2}}}{\text{O}}$

from the first to the second equivalence point:

${\text{(4) NaHX + NaOH}} \leftrightarrow {\text{N}}{{\text{a}}_{\text{2}}}{\text{X + }}{{\text{H}}_{\text{2}}}{\text{O}}$

from the beginning of the reaction through the second equivalence point (net reaction):

${\text{(5) }}{{\text{H}}_{\text{2}}}{\text{X + 2 NaOH}} \leftrightarrow {\text{N}}{{\text{a}}_{\text{2}}}{\text{X + 2 }}{{\text{H}}_{\text{2}}}{\text{O}}$

At the first equivalence point, all H+ ions from the first dissociation have reacted with NaOH base. At the second equivalence point, all H+ ions from both reactions have reacted (twice as many as at the first equivalence point). Therefore, the volume of NaOH added at the second equivalence point is exactly twice that of the first equivalence point (see Equations 3 and 5).

The primary purpose of this experiment is to identify an unknown diprotic acid by finding its molecular weight. A diprotic acid is titrated with NaOH solution of known concentration. Molecular weight (or molar mass) is found in g/mole of the diprotic acid. Weighing the original sample of acid will tell you its mass in grams. Moles can be determined from the volume of NaOH titrant needed to reach the first equivalence point. The volume and the concentration of NaOH titrant are used to calculate moles of NaOH. Moles of unknown acid equal moles of NaOH at the first equivalence point (see Equation 3). Once grams and moles of the diprotic acid are known, molecular weight can be calculated, in g/mole. Molecular weight determination is a common way of identifying an unknown substance in chemistry.

You may use either the first or second equivalence point to calculate molecular weight. The first is somewhat easier, because moles of NaOH are equal to moles of H2X (see Equation 3). If the second equivalence point is more clearly defined on the titration curve, however, simply divide its NaOH volume by 2 to confirm the first equivalence point; or from Equation 5, use the ratio:

${\text{1 mol }}{{\text{H}}_{\text{2}}}{\text{X / 2 mol NaOH}}$

## Objectives

In this experiment, you will identify an unknown diprotic acid by finding its molecular weight.

## Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

### Option 2

You may also need an interface and software for data collection. What do I need for data collection?

## Chemistry with Vernier

See other experiments from the lab book.

 1 Endothermic and Exothermic Reactions 2 Freezing and Melting of Water 3 Another Look at Freezing Temperature 4 Heat of Fusion of Ice 5 Find the Relationship: An Exercise in Graphing Analysis 6 Boyle's Law: Pressure-Volume Relationship in Gases 7 Pressure-Temperature Relationship in Gases 8 Fractional Distillation 9 Evaporation and Intermolecular Attractions 10 Vapor Pressure of Liquids 11 Determining the Concentration of a Solution: Beer's Law 12 Effect of Temperature on Solubility of a Salt 13 Properties of Solutions: Electrolytes and Non-Electrolytes 14 Conductivity of Solutions: The Effect of Concentration 15 Using Freezing Point Depression to Find Molecular Weight 16 Energy Content of Foods 17 Energy Content of Fuels 18 Additivity of Heats of Reaction: Hess's Law 19 Heat of Combustion: Magnesium 20 Chemical Equilibrium: Finding a Constant, Kc 21 Household Acids and Bases 22 Acid Rain 23 Titration Curves of Strong and Weak Acids and Bases 24 Acid-Base Titration 25 Titration of a Diprotic Acid: Identifying an Unknown 26 Using Conductivity to Find an Equivalence Point 27 Acid Dissociation Constant, Ka 28 Establishing a Table of Reduction Potentials: Micro-Voltaic Cells 29 Lead Storage Batteries 30 Rate Law Determination of the Crystal Violet Reaction 31 Time-Release Vitamin C Tablets 32 The Buffer in Lemonade 33 Determining the Free Chlorine Content of Swimming Pool Water 34 Determining the Quantity of Iron in a Vitamin Tablet 35 Determining the Phosphoric Acid Content in Soft Drinks 36 Microscale Acid-Base Titration

### Experiment 25 from Chemistry with Vernier Lab Book

#### Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.