The ratio of the rate of diffusion of a given element to that of helium at the same pressure is 1.4. The molecular weight of the element is

Options

A. 2
B. 4
C. 8
D. 16

Answer

To solve the problem, 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 Given Information:**
- The ratio of the rate of diffusion of the element (let's call it E) to that of helium (H) is given as 1.4.
- The molar mass of helium (H) is known to be 4 g/mol.

2. **Set Up the Equation Using Graham's Law:**
- According to Graham's law, we can express the relationship as:
\[ \frac{R_E}{R_H} = \sqrt{\frac{M_H}{M_E}} \]
- Where \( R_E \) is the rate of diffusion of element E, \( R_H \) is the rate of diffusion of helium, \( M_H \) is the molar mass of helium, and \( M_E \) is the molar mass of element E.

3. **Substitute the Known Values:**
- We know that:
\[ \frac{R_E}{R_H} = 1.4 \quad \text{and} \quad M_H = 4 \, \text{g/mol} \]
- Substituting these values into the equation gives:
\[ 1.4 = \sqrt{\frac{4}{M_E}} \]

4. **Square Both Sides to Eliminate the Square Root:**
- Squaring both sides results in:
\[ (1.4)^2 = \frac{4}{M_E} \]
- This simplifies to:
\[ 1.96 = \frac{4}{M_E} \]

5. **Rearranging the Equation to Solve for \( M_E \):**
- Rearranging gives:
\[ M_E = \frac{4}{1.96} \]

6. **Calculate the Molar Mass of Element E:**
- Performing the calculation:
\[ M_E \approx 2.04 \, \text{g/mol} \]

7. **Determine the Closest Integer Value:**
- The closest integer value to 2.04 is 2.

8. **Conclusion:**
- Therefore, the molecular weight of the element E is approximately 2 g/mol.

### Final Answer:
The molecular weight of the element is **2 g/mol**.

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