The speed of colloidal particles in a colloidal sol at different pH values during electrophoresis are given below :
`{:(pH, 4.20,4.56,5.20,5.65,6.30,7.0),("Speed",+0.50+,0.18,-0.25,-0.65,-0.90,-1.25):}`
`(mums^(-1))`
(opposite signs indicate opposite direction of travel)
The isoelectric point of the colloidal sol will be

Options

A. `4.2`
B. `4.8`
C. `7.0`
D. `5.20`

Explanation

To determine the isoelectric point (IEP) of the colloidal sol based on the given data, we need to analyze the relationship between the pH values and the speed of the colloidal particles during electrophoresis. The IEP is defined as the pH at which the colloidal particles carry no net charge, meaning they do not migrate towards either electrode.

### Step-by-Step Solution:

1. **Understand the Given Data**:
- We have pH values: 4.20, 4.56, 5.20, 5.65, 6.30, 7.0
- Corresponding speeds (in µm/s): +0.50, +0.18, -0.25, -0.65, -0.90, -1.25
- Positive speed indicates movement towards the anode, while negative speed indicates movement towards the cathode.

2. **Identify the Charge Behavior**:
- At pH 4.20, the speed is +0.50 (positive charge).
- At pH 4.56, the speed is +0.18 (still positive charge).
- At pH 5.20, the speed is -0.25 (indicating a switch to negative charge).
- Therefore, we can conclude that the transition from positive to negative charge occurs between pH 4.56 and pH 5.20.

3. **Determine the Isoelectric Point**:
- The IEP is the pH at which the colloidal particles have no net charge. This is typically found between the last pH value with a positive speed and the first pH value with a negative speed.
- Since the transition occurs between pH 4.56 (positive) and pH 5.20 (negative), the IEP must lie between these two values.

4. **Estimate the IEP**:
- The IEP can be estimated as the average of the two pH values:
\[ \text{IEP} = \frac{4.56 + 5.20}{2} = \frac{9.76}{2} = 4.88 \]

5. **Conclusion**:
- The isoelectric point of the colloidal sol is approximately 4.88.