Calculate the relative rates of diffusion of `""^235UF_6 and ""^238UF_6` in gaseous form (F= 19).

Explanation

To calculate the relative rates of diffusion of `^235UF_6` and `^238UF_6`, we will use Graham's Law of Effusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.

### Step-by-Step Solution:

1. **Identify the Molar Mass of Each Compound**:
- For `^235UF_6`:
- Molar mass of uranium-235 (U) = 235 g/mol
- Molar mass of fluorine (F) = 19 g/mol
- Since there are 6 fluorine atoms in `UF_6`, the total mass of fluorine = 6 × 19 = 114 g/mol.
- Therefore, the molar mass of `^235UF_6` = 235 + 114 = 349 g/mol.

- For `^238UF_6`:
- Molar mass of uranium-238 (U) = 238 g/mol
- Total mass of fluorine remains the same = 114 g/mol.
- Therefore, the molar mass of `^238UF_6` = 238 + 114 = 352 g/mol.

2. **Apply Graham's Law**:
- According to Graham's law, the relative rates of diffusion (R) can be expressed as:
\[ \frac{R_1}{R_2} = \sqrt{\frac{M_2}{M_1}} \]
- Where:
- \( R_1 \) is the rate of diffusion of `^235UF_6`
- \( R_2 \) is the rate of diffusion of `^238UF_6`
- \( M_1 \) is the molar mass of `^235UF_6` (349 g/mol)
- \( M_2 \) is the molar mass of `^238UF_6` (352 g/mol)

3. **Calculate the Relative Rates of Diffusion**:
- Substitute the values into the equation:
\[ \frac{R_1}{R_2} = \sqrt{\frac{352}{349}} \]
- Calculate the square root:
\[ \frac{R_1}{R_2} = \sqrt{1.0086} \approx 1.0043 \]

4. **Express the Final Result**:
- Thus, the relative rates of diffusion can be expressed as:
\[ R_1 : R_2 \approx 1.0043 : 1 \]

### Final Answer:
The relative rates of diffusion of `^235UF_6` to `^238UF_6` is approximately **1.0043 : 1**.

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