Question

The isotopes of hydrogen are H, D and T. What is the approximate ratio of rate of diffusion of H\(_2\), D\(_2\), and T\(_2\)?

• A. 0.4 : 0.5 : 0.7
• B. 0.7 : 0.5 : 0.4
• C. 0.5 : 0.25 : 0.167
• D. 0.167 : 0.25 : 0.5

Hint:

Rate of diffusion is inversely proportional to the square root of molar mass (Graham’s Law).

Answer 1

The Correct Option is B

According to Graham’s law of diffusion: \[ \text{Rate of diffusion} \propto \frac{1}{\sqrt{\text{Molar mass}}} \] - Molar mass of H\(_2\) = 2
- Molar mass of D\(_2\) = 4
- Molar mass of T\(_2\) = 6
So: \[ \text{Relative rates} \propto \frac{1}{\sqrt{2}} : \frac{1}{\sqrt{4}} : \frac{1}{\sqrt{6}} \approx 0.707 : 0.5 : 0.408 \] Rounded to: \[ \boxed{0.7 : 0.5 : 0.4} \]

Answer 2

The isotopes of hydrogen are H, D and T. What is the approximate ratio of rate of diffusion of H₂, D₂, and T₂?

Step 1: Use Graham’s law of diffusion:
According to Graham’s law, the rate of diffusion (r) of a gas is inversely proportional to the square root of its molar mass (M):
\[ r \propto \frac{1}{\sqrt{M}} \]

Step 2: Determine the molar masses of H₂, D₂, and T₂:
- H₂ = 1 × 2 = 2 g/mol
- D₂ = 2 × 2 = 4 g/mol
- T₂ = 3 × 2 = 6 g/mol

Step 3: Apply Graham’s law for relative rates:
Let the rate of diffusion of H₂ be r_H₂, D₂ be r_D₂, and T₂ be r_T₂:
\[ r_{H_2} : r_{D_2} : r_{T_2} = \frac{1}{\sqrt{2}} : \frac{1}{\sqrt{4}} : \frac{1}{\sqrt{6}} \]
\[ = \frac{1}{1.414} : \frac{1}{2} : \frac{1}{2.45} \]
\[ \approx 0.707 : 0.5 : 0.408 \]
\[ \approx 0.7 : 0.5 : 0.4 \]

Final Answer:
\[ \boxed{0.7 : 0.5 : 0.4} \]