$\require{mhchem}$
Acid-Base Titration
===
## Introduction
Titration is a volumetric technique used to determine the concentration of an unknown solution by reacting it with a solution of known concentration. There are many types of titrations. In this experiment, we will be performing an acid-base titration. Our solution of known concentration, or **titrant**, will be an aqueous sodium hydroxide. Our unknown, or **titrand**, will be a solid acid. You will prepare a solution of this unknown by weighing out a known quantity, dissolving it in water and then adding a small amount of indicator solution. The sodium hydroxide will be added quantitatively from a buret into a flask containing the unknown solution. The titration is complete when the indicator changes color. Since both the concentration of sodium hydroxide and the volume of sodium hydroxide are known quantities, we can determine the number of moles of sodium hydroxide required to fully react with the unknown acid. We can then use stoichiometry to determine the moles of unknown acid. Dividing the mass of unknown acid by the moles of acid will allow us to determine the formula mass of the acid and predict its identity.
### Standardizing Sodium Hydroxide
The accuracy of a titration is limited by the degree of accuracy to which the titrant’s concentration is known i.e. we must know very accurately the titrant’s concentration. However, the chemical properties of sodium hydroxide make it is nearly impossible to prepare a solution of known concentration.
1. Sodium hydroxide is hygroscopic, it absorbs water from the air.
2. Sodium hydroxide is also reactive. Sodium hydroxide pellets react with carbon dioxide in the air to form a layer of sodium carbonate around them. Once in solution, sodium hydroxide will continue to react with dissolved air causing the concentration to drift over time.
3. Extremely pure sodium hydroxide (>99.9 mass%) is expensive and difficult to source
4. Sodium hydroxide has low formula mass (39.997 ). The error due to weighing sodium hydroxide is amplified when you divide by the formula mass to determine the number of moles.
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**Figure 1: KHP, a common acidic primary standard**
In order to get around these limitations, we will first need to **standardize** our sodium hydroxide. Standardization is when you titrate with a solution prepared from a primary (1º) standard. Primary standards are chemicals that do not have any of the limitations of sodium hydroxide. The are non-hygroscopic, they are only moderately reactive, they are very pure, and they have high formula masses $\left( M^w = 204.22 \, \frac{\textsf{g}}{\textsf{mol}} \, \textsf{for KHP} \right)$. In this experiment, we will be standardizing our sodium with potassium hydrogen phthalate (KHP). KHP is a common primary standard used in acid-base titrations.
Once the actual concentration of NaOH is determined, it too can be used as a standard to determine other unknown solutions. In this case, the NaOH is the secondary (2º) standard.
### Indicators
Titrations are performed in order to determine the point at which a stoichiometric equivalent of the titrant has reacted with the titrand. In other words, we want to find the point when we have added enough moles of titrant to react with all of the moles of titrand. Adding additional titrant after this point will only result in excess being present in the reaction mixture. The point at which a stoichiometric equivalence has been reached is called the **equivalence point.** In practice, the equivalence point of an acid-base titration can only be determined by carefully measuring the pH of the reaction mixture as the titration proceeds.
An alternate approach is to use a chemical indicator. Indicators are chemical additives that change color at a specific pH. Indicators must be carefully chosen to ensure that they will change color near the expected equivalence point. Luckily, there are many known acid-base indicators whose chemistry is well understood. Using an indicator can yield accurate results, however, there will always be some error associated with their use. This is because it is not possible to choose an indicator that changes color precisely at the equivalence point. The point at which the indicator changes color is known as the **endpoint**. Figure 2 shows a titration curve. This is a graph of volume of titrant added vs. pH. The difference between the titration volumes of the equivalence point and the endpoint is the error associated with using an indicator.
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<img src="https://doc.chemnotes.org/uploads/3a1704c5-b99f-4716-928a-8c491798d6a4.png" alt="Image of an acid-base titration curve, Titrant volume added vs. pH. The curve is a sigmoid with the equivalence point marked at the inflection point. An arbitrary line has been drawn to represent a theoretical endpoint." style="zoom: 100%;" />
</center>
**Figure 2: Example Titration Curve**
#### Sample Problem 1
A student weighs out 0.236 g of KHP (204.22 ) and dissolves it in a minimal amount of water inside a flask. The sample is titrated with 25.60 ml of sodium hydroxide to a phenolphthalein endpoint. What is the concentration of the sodium hydroxide solution?
First, we need to write a balanced equation for the titration reaction.
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We can see from the reaction that there is a one to one ratio between sodium hydroxide and KHP. Next, we need to calculate the number of moles of KHP present in solution.
$$
0.236 \, \textsf{g KHP} \left(\frac{1 \, \textsf{mole KHP}}{204.22 \, \textsf{g KHP}} \right) = 0.00116 \, \textsf{mole KHP}
$$
Now, we can multiply by the one to one stoichiometric ratio to determine the number of moles of sodium hydroxide that was reacted during the titration.
$$
0.00116 \, \textsf{mole KHP} \left(\frac{1 \, \textsf{mole} \, \ce{NaOH}}{1 \, \textsf{mole KHP}} \right) = 0.0464 \, \textsf{M} \, \ce{NaOH}
$$
We can now calculate the concentration of sodium hydroxide by dividing by the volume we added in liters.
$$
\left( \frac{0.00116 \, \textsf{moles} \, \ce{NaOH}}{25.60 \, \textsf{ml}} \right) \left( \frac{1000 \, \textsf{ml}}{1 \, \textsf{L}} \right) = 0.0464 \, \textsf{M} \, \ce{NaOH}
$$
### Sample Problem 2
A student weighs out 0.347 g of unknown solid acid and dissolves it in a minimal amount of water inside a flask. The student titrates the sample with the standardized sodium hydroxide solution from problem 1 to a phenolphthalein endpoint. If it takes 15.87 ml to titrate the sample, what are some possible formula masses of the acid?
First, we will need to calculate the number of moles of sodium hydroxide used to titrate the sample
$$
15.87 \, \textsf{ml} \left( \frac{1 \, \textsf{L}}{1000 \, \textsf{ml}} \right) \left( \frac{0.0464 \, \textsf{moles} \, \ce{NaOH}}{1 \, \textsf{L}} \right) = 7.36 \times 10^{-4} \, \textsf{moles} \, \ce{NaOH}
$$
Since we don’t know the identity of the unknown acid, we will have to consider a few possibilities. If we have a monoprotic acid, we would have a one to one stoichiometric ratio. If we have a diprotic acid, we would have a one to two stoichiometric ratio. If we had a triprotic acid, we would have a one to three stoichiometric ratio.
**Monoprotic**
$$
\ce{HA + NaOH -> NaA + H2O}
$$
$$
7.36 \times 10^{-4} \hspace{2mm} \textsf{moles} \, \ce{NaOH} \left( \frac{1 \, \textsf{mole Acid}}{1 \, \textsf{mole} \, \ce{NaOH}} \right) = 7.36 \times 10^{-4} \hspace{2mm} \textsf{moles Acid}
$$
**Diprotic**
$$
\ce{H2A + 2NaOH -> Na2A + 2H2O}
$$
$$
7.36 \times 10^{-4} \hspace{2mm} \textsf{moles} \, \ce{NaOH} \left( \frac{1 \, \textsf{mole Acid}}{2 \, \textsf{mole} \, \ce{NaOH}} \right) = 3.68 \times 10^{-4} \hspace{2mm} \textsf{moles Acid}
$$
**Triprotic**
$$
\ce{H3A + 3NaOH -> Na3A + 3H2O}
$$
$$
7.36 \times 10^{-4} \hspace{2mm} \textsf{moles} \, \ce{NaOH} \left( \frac{1 \, \textsf{mole Acid}}{3 \, \textsf{mole} \, \ce{NaOH}} \right) = 2.45 \times 10^{-4} \hspace{2mm} \textsf{moles Acid}
$$
To calculate the formula masses possible for our unknown acids, we will need to divide the mass of our acid sample by all of the possible number of moles for our three cases.
**Monoprotic**
$$
\frac{0.347 \, \textsf{g Acid}}{7.36 \times 10^{-4} \, \textsf{moles Acid}} = 471 \, \frac{\textsf{g}}{\textsf{mole}}
$$
**Diprotic**
$$
\frac{0.347 \, \textsf{g Acid}}{3.68 \times 10^{-4} \, \textsf{moles Acid}} = 943 \, \frac{\textsf{g}}{\textsf{mole}}
$$
**Triprotic**
$$
\frac{0.347 \, \textsf{g Acid}}{2.45 \times 10^{-4} \, \textsf{moles Acid}} = 1420 \, \frac{\textsf{g}}{\textsf{mole}}
$$
Without more information, it is impossible for us to know the actual formula mass of the unknown acid. In our experiment, you will be asked to calculate the formula masses for all three cases based on your experimental measurements. You will then be asked to predict the acids identity by comparing your experimentally determined formula masses to a list of possible candidates.
## Materials
- Buret
- Erlenmeyer Flask
- Sodium Hydroxide
- Phenolphthalein
- Balance
- KHP
- Unknown Acid
## Procedures
### Part A: Standardization of Sodium Hydroxide
1. Inspect your titration apparatus. Make sure you have identified all of the required items and understand which positions coorespond to a *closed* or *open* stopcock valve.
<img src="https://doc.chemnotes.org/uploads/4e4a71cb-58b6-4b0f-b280-55fb673765f1.png" alt="img" style="zoom:10%;" />
**Figure 3: Titration Apparatus**
1. Weigh out approximately 0.25 g of KHP $\left( M^w = 204.22 \, \frac{\textsf{g}}{\textsf{mol}} \, \right)$ directly into the 250-ml Erlenmeyer flask. Record mass used on the data sheet.
1. Add approximately 100 ml of deionized water to the flask and completely dissolve the solid.
1. Add 2–3 drops of phenolphthalein to the Erlenmeyer flask. This is the 1º standard solution.
1. Rinse buret with about 5 ml of NaOH before you begin prepping the buret. Make sure you cover all the inside and through the tip.
1. Fill your buret with sodium hydroxide and record your initial volume.
1. Titrate the solution using the NaOH in your buret until the endpoint is reached. The phenolphthalein endpoint is the first faint pink color which persists for 30 seconds. Titrating past the faint pink will introduce experimental error.
1. Calculate your sodium hydroxide concentration. Average this value with the other student groups. Use this average sodium hydroxide value to calculate the formula mass of the unknown acid in Part B.
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### Part B: Determining the Formula Mass of an Unknown Acid
1. Weigh out 0.200 – 0.250 g of the unknown acid into a clean Erlenmeyer flask. Record mass used on the data sheet.
2. Add approximately 100 ml of water and 2 – 3 drops of phenolphthalein to the flask. Make certain that your unknown dissolves completely before titrating.
3. Titrate with NaOH until a faint pink color persists for 30 seconds.
4. Repeat steps 1 through 3.
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## Data Sheet
{%pdf https://public.chemnotes.org/lab/sheets/titration.pdf %}