Acid-base titration process illustrating the addition of a standard solution to an unknown solution until neutralization occurs, indicated by a color change.

Problem Description:

The image describes the process of acid-base titration, which is a common laboratory technique used to determine the concentration (molarity) of an unknown acid or base solution. The key components and steps are outlined in the text and diagram provided.

Key Concepts from the Image:

1. Titration: A process where a measured volume of a standard solution (of known molarity) is added to a solution of unknown molarity until neutralization occurs.
2. Standard Solution: A solution with a known concentration (molarity).
3. Unknown Solution: A solution whose concentration (molarity) is to be determined.
4. Indicator: A substance added to the flask that changes color when the endpoint of the titration (neutralization) is reached.

Objective:

The goal of the titration is to determine the molarity of the unknown solution using the known molarity of the standard solution and the volume of the standard solution required to reach the endpoint.

Solution Explanation:

#### Step-by-Step Process of Acid-Base Titration:
1. Prepare the Solutions:
- Take a known volume of the unknown solution and place it in an Erlenmeyer flask.
- Add a few drops of an appropriate indicator to the flask. The choice of indicator depends on the type of titration (e.g., phenolphthalein for strong acid–strong base titrations).

2. Set Up the Titration:
- Place the standard solution in a burette, which allows precise measurement of the volume added.
- Ensure the burette is properly calibrated and filled with the standard solution.

3. Add the Standard Solution Gradually:
- Slowly add the standard solution from the burette into the flask containing the unknown solution while continuously stirring the mixture.
- Observe the color change of the indicator. The color change indicates the point at which the reaction between the acid and base is complete (neutralization).

4. Determine the Endpoint:
- The endpoint is reached when the indicator changes color permanently. This signifies that the number of moles of hydrogen ions (\(H^+\)) equals the number of moles of hydroxide ions (\(OH^-\)).

5. Record the Volume of Standard Solution Used:
- Note the initial and final readings of the burette to calculate the exact volume of the standard solution added.

6. Calculate the Molarity of the Unknown Solution:
- Use the balanced chemical equation for the reaction to relate the moles of the standard solution to the moles of the unknown solution.
- The relationship is given by the equation:
\[
M_1 V_1 = M_2 V_2
\]
where:
- \(M_1\) is the molarity of the standard solution.
- \(V_1\) is the volume of the standard solution used.
- \(M_2\) is the molarity of the unknown solution (to be determined).
- \(V_2\) is the volume of the unknown solution.

- Rearrange the equation to solve for \(M_2\):
\[
M_2 = \frac{M_1 V_1}{V_2}
\]

#### Example Calculation:
Suppose:
- The molarity of the standard solution (\(M_1\)) is 0.1 M.
- The volume of the standard solution used (\(V_1\)) is 25.0 mL.
- The volume of the unknown solution (\(V_2\)) is 20.0 mL.

Using the formula:
\[
M_2 = \frac{M_1 V_1}{V_2} = \frac{(0.1 \, \text{M}) \times (25.0 \, \text{mL})}{20.0 \, \text{mL}} = \frac{2.5}{20.0} = 0.125 \, \text{M}
\]

Thus, the molarity of the unknown solution is 0.125 M.

Final Answer:

\[
\boxed{M_2 = \frac{M_1 V_1}{V_2}}
\]

This formula is the key to solving any acid-base titration problem, provided the volumes and molarities are known.