Question

Given below are two statements:
Statement (I): Soil Oxygen Diffusion Rate measurement is based on Fick's law
Statement (II): The diffusion coefficient of $\text{O}_2$ is higher than $\text{CO}_2$}
In light of the above statements, choose the most appropriate answer from the options given below.

• A. Both Statement (I) and Statement (II) are correct.
• B. Both Statement (I) and Statement (II) are incorrect.
• C. Statement (I) is correct but Statement (II) is incorrect.
• D. Statement (I) is incorrect but Statement (II) is correct.

Hint:

According to Graham's law, lighter gas molecules diffuse faster.
Since \(\text{O}_2\) (MW = 32) is lighter than \(\text{CO}_2\) (MW = 44), its diffusion coefficient is naturally higher in any gaseous phase.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Soil aeration is primarily governed by the diffusion of gases through the soil pore network.
To quantify the availability of oxygen to plant roots, soil scientists measure the Oxygen Diffusion Rate (ODR).
This measurement represents the rate at which oxygen can replenish the root zone as it is consumed.
The physical principles governing the movement and diffusion rates of different gases like oxygen (\(\text{O}_2\)) and carbon dioxide (\(\text{CO}_2\)) are rooted in transport physics and chemistry laws.

Step 2: Detailed Explanation:
Let us evaluate both statements individually:
Statement (I) is correct:
The measurement and mathematical modeling of the soil Oxygen Diffusion Rate (ODR) is based directly on Fick's first law of diffusion.
Fick's law states that the diffusive flux (\( J \)) of a gas is directly proportional to its concentration or partial pressure gradient:
\[ J = -D \cdot \frac{dc}{dx} \]
Where:
\( D \) is the diffusion coefficient of the gas in the soil medium.
The platinum microelectrode method developed by Lemon and Erickson (1952) measures ODR by simulating a root, where the electric current is limited by the rate at which oxygen diffuses to the electrode surface, a process governed entirely by Fick's law.
Statement (II) is correct:
The diffusion coefficient of a gas in air depends on its molecular mass, as described by Graham's Law of Diffusion.
Graham's law states that the rate of diffusion of a gas is inversely proportional to the square root of its molecular weight (\( M \)):
\[ \text{Rate} \propto \frac{1}{\sqrt{M}} \]
Let us compare the molecular weights of oxygen and carbon dioxide:
Molecular weight of oxygen (\(\text{O}_2\)) = \( 32\text{ g mol}^{-1} \)
Molecular weight of carbon dioxide (\(\text{CO}_2\)) = \( 44\text{ g mol}^{-1} \)
Since oxygen has a lower molecular mass than carbon dioxide, its molecules move faster, resulting in a higher diffusion coefficient.
In air at standard temperature and pressure:
The diffusion coefficient of oxygen (\( D_{\text{O}_2} \)) is approximately \( 0.20\text{ cm}^2\text{ s}^{-1} \).
The diffusion coefficient of carbon dioxide (\( D_{\text{CO}_2} \)) is approximately \( 0.16\text{ cm}^2\text{ s}^{-1} \).
Thus, the diffusion coefficient of \(\text{O}_2\) is higher than that of \(\text{CO}_2\).
Both Statement (I) and Statement (II) are correct.

Step 3: Final Answer:
Therefore, the most appropriate choice is that both Statement (I) and Statement (II) are correct.