Calculate the ionic mobility of colloidal particles in arsenic colloidal solution, if zeta potential is `0.045 V` (Dielectric
constant = 81, Viscosity of liquid` = 1.008` centipoise)

Answer

To calculate the ionic mobility of colloidal particles in an arsenic colloidal solution, we will use the given data and the formula for ionic mobility. Here are the steps to solve the problem:

### Step-by-Step Solution:

**Step 1: Write down the given data.**
- Zeta potential (ζ) = 0.045 V
- Dielectric constant (ε) = 81
- Viscosity (η) = 1.008 centipoise

**Step 2: Convert viscosity from centipoise to SI units.**
- 1 centipoise = 0.001 Pa·s
- Therefore, η = 1.008 centipoise = 1.008 × 0.001 Pa·s = 0.001008 Pa·s

**Step 3: Write the formula for ionic mobility (U).**
The formula for ionic mobility is given by:
\[ U = \frac{2 \cdot ζ \cdot ε}{3 \cdot η} \]

**Step 4: Substitute the values into the formula.**
Now, substituting the values into the formula:
\[ U = \frac{2 \cdot 0.045 \cdot 81}{3 \cdot 0.001008} \]

**Step 5: Perform the calculations.**
First, calculate the numerator:
\[ 2 \cdot 0.045 \cdot 81 = 7.290 \]

Next, calculate the denominator:
\[ 3 \cdot 0.001008 = 0.003024 \]

Now, divide the numerator by the denominator:
\[ U = \frac{7.290}{0.003024} \approx 2412.5 \, \text{cm}^2/\text{V·s} \]

**Step 6: Round the answer to two decimal places.**
Thus, the ionic mobility \( U \) is approximately:
\[ U \approx 2412.5 \, \text{cm}^2/\text{V·s} \]

### Final Answer:
The ionic mobility of colloidal particles in the arsenic colloidal solution is approximately **2412.5 cm²/V·s**.

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