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# AcidBase: Titrations

### Skills to develop

• Calculate the pH and plot it during a titration of a strong acid by a strong base.
• Calculate the pH and plot it when a weak acid is titrated by a strong base

# Titrations

The process of obtaining quantitative information of a sample using a fast chemical reaction by reacting with a certain volume of reactant whose concentration is known is called titration. When an acid-base reaction is used, the process is called acid-base titration. When a redox reaction is used, the process is called a redox titration. Titration is also called volumetric analysis, which is type of quantitative chemical analysis.

In freshman chemistry, we treat titration this way. A titration is a technique where a solution of known concentration is used to determine the concentration of an unknown solution. Typically, the titrant (the known solution) is added from a buret to a known quantity of the analyte (the unknown solution) until the reaction is complete. Knowing the volume of titrant added allows the determination of the concentration of the unknown. Often, an indicator is used to usually signal the end of the reaction, the endpoint.

In hospital and medical labs, automated titration equipments are used. The following sites have some information regarding the automated titrator:

For acid-base titration, a modern lab will usually monitor titration with a pH meter which is interfaced to a computer, so that you will be able to plot the pH or other physical quantities versus the volume that is added.

In this module we simulate this experiment graphically without using chemicals. A program that simulates titrations of strong acids and strong bases is very easy, because the calculation of pH in this experiment is very simple.

## Titration Curve

The plot of pH as a function of titrant added is called a titration curve. Let us take a look of a titration process:

Base
[H+]pH
0 1.0 0.0
1.0 9/11 0.087
2.0 8/12 0.176
5.0 5/15 0.477
Half-equivalent point
8.0 2/18 0.954
9.0 1/19 1.279
9.3 0.7/19.3 1.440
9.5 0.5/19.5 1.591
9.7 0.3/19.7 1.817
9.8 0.2/19.8 2.0
9.9 0.1/19.9 2.300
9.95 0.05/19.95 2.60
10 H2O=H++OH- pH = 7
NaCl neutral salt
Base
[OH-]pH
10.05 0.05/20.05 11.397
10.10 0.5/20.1 11.697
11.0 1/21 12.678
15.0 5/25 13.301
20.0 20/3013.924
Example 1

Evaluate [H+] and pH in the titration of 10.0 mL 1.0 M HCl solution with 1.0 M NaOH solution, and plot the titration curve.

Solution
The amount of acid present = Va*Ca
= 10.0 mL * 1.0 mol/1000 mL
= 10 mmol (mili-mole)

The amount of base NaOH added = Vb*Cb

The amount of acid left = Va*Ca - Vb*Cb

The concentration of acid and thus [H+]
= [Va*Ca - Vb*Cb] / (Va + Vb)

With the above formulation, we can built a table for various values as shown on the right.

Working to learn
Plot the titration curve on a graph based on the data.

At equivalent point, why is pH=7? What formula is used to calculate pH?

Why does pH change rapidly at the equivalent point?

Sketch titration curves when the concentrations of both acids and bases are 0.10, 0.0010 and 0.000010 M? What can you conclude from these sketches?

What are [Na+] and [Cl-] at the following points: initially (before any base is added), half-equivalent point; equivalent point, after 10.5 mL NaOH is added, after 20.0 mL NaOH is added?

Well, when you have acquired the skill to calculate the pH at any point during titration, you may write a simulation program to plot the titration curve. Calculations for strong-acid_strong-base titration are simple, but when weak acid or base are involved, the calculations are somewhat more complicated. However, we are interested in this area and some simulation programs are available on the internet.

Yue-Ling Wong has given a Java interactive titration simulation. His website is rather fun to play with and it is nicely done. In fact, the design of Wong's Java interactive simulation is very much like the design of the DOS CACT version.

Using a computer we are able to simulate the titrations of weak acids and strong bases, or strong acids and weak bases. Calculation of pH in the titration of weak acids with weak bases is more difficult. However, let the complexity bother you no more, since you can simply have fun testing the computer model.

In a titration experiment, the amount to add from the buret depends on the condition at the time. At the start, you may add large amount before observing much pH change, but when the titration is at its end or equivalent point, you would like to ad the titrant slowly. In the simulation, you control the rate of titration.

While trying the Java simulation of titration, please answer the following questions.

• Identify the buffer area on the titration curve.

• In the titration of weak acids, why does the pH change quickly at the beginning?

### Confidence Building Questions

• What are the pH of solutions of 10, 1.0, 0.10, 0.010 and 0.0010 M HCl?

Answer pH=-1, 0, 1, 2, and 3
Consider...

No calculators should be used.

• What are [H+] and the pH at the half equivalent point when a solution of 1.0 M HCl is titrated by a 1.0 NaOH solution?

Consider...

Do not forget the dilution factor.

• What are [Na+] at the half equivalent point when a solution of 1.0 M HCl is titrated by a 1.0 NaOH solution?

Consider...

• What are [H+] and the pH at the equivalent point when a solution of 1.0 M HCl is titrated by a 1.0 NaOH solution?

Consider...

This is only a theoretical value.

• What are [Na+] and [Cl-] at the equivalent point when a solution of 1.0 M HCl is titrated by a 1.0 NaOH solution?

Answer [Ca+] = [Cl-] = 0.5
Consider...

Note that [H+] is balanced by [OH-], amd [Na+] is balanced by [Cl-].
Most students usually forget the salt resulting from the titration.

• What are [H+] and the pH of 1.0 M acetic acid solution? Ka = 1.8e-5

Consider...

The approximation [H+]=(C Ka)1/2 can be used.

• What is the pH of the above solution when half of the acid is neutralized by NaOH in the titration?

Consider...

Do you know why pH = pKa in this case? At this point, the solution is a very good buffer.

• What is the pH of the end point or equivalent point when 1.0 M acetic acid is titrated by 1.0 M NaOH solution?

Consider...

Justfy the following formula for this condition. [OH-]=(Kw/Ka*C)1/2

What is the pH of a 0.5 M sodium acetate solution?

• A 0.10 M acetic acid solution is titrated with a 0.10 M NaOH solution to the equivalent point. What is the concentration of the acetate ion?