The Question is from neet-botany plant-physiology diffusion, and it was created by the author Mr. NARESH KUMAR K

Question

The diffusion coefficient of a gas is inversely proportional to the square root of its molar mass.  If gas A has a molar mass four times that of gas B, under identical conditions, the diffusion rate of gas A will be:

Mr. NARESH KUMAR K · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
 **Primary Concept**: Graham's Law of Diffusion
 **Related Topics**: Kinetic Theory of Gases, Molar Mass, Diffusion Rate
 **Prerequisites**: Understanding of proportionality and square roots.
## SOLUTION PATHWAY
**Given Information**:
  * Gas A has a molar mass four times that of gas B: $M_A = 4M_B$
  * Diffusion coefficient is inversely proportional to the square root of molar mass.
**Method & Steps**:
 1. State Graham's Law of Diffusion:
  Reasoning: Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.  Mathematically:
  Formula/Rule: $\frac{Rate_A}{Rate_B} = \sqrt{\frac{M_B}{M_A}}$
 2. Substitute the given information into Graham's Law:
  Working: We are given that $M_A = 4M_B$. Substituting this into the formula:
  $\frac{Rate_A}{Rate_B} = \sqrt{\frac{M_B}{4M_B}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$
  Key Point: This shows that the rate of diffusion of gas A is half the rate of diffusion of gas B.
 3. Interpret the Result:
  Result: $Rate_A = \frac{1}{2} Rate_B$
  Verification: The result is consistent with the inverse square root relationship; a larger molar mass leads to a slower diffusion rate.
 ## OPTION ANALYSIS
A ✓: Half that of gas B. This is the correct answer derived from Graham's Law.
B :x: Twice that of gas B. This would be true if the diffusion coefficient were directly proportional to the square root of molar mass.
C :x: Four times that of gas B. This implies a direct proportionality to the molar mass, not the square root.
D :x: One-fourth that of gas B. This is the inverse of the correct relationship.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing direct and inverse proportionality: Remember that an inverse relationship means as one quantity increases, the other decreases.
  2.Incorrectly handling the square root: Ensure you understand how to simplify square roots, particularly involving fractions.
 **Quick Tips**:
  1.Visualize the relationship: Imagine a heavier molecule moving slower than a lighter molecule.
  2.Remember the formula:  $\frac{Rate_A}{Rate_B} = \sqrt{\frac{M_B}{M_A}}$

Mr. NARESH KUMAR K · Answer

Twice that of gas B

Mr. NARESH KUMAR K · Answer

The correct Option is "Half that of gas B"

Mr. NARESH KUMAR K · Answer

Four times that of gas B

Mr. NARESH KUMAR K · Answer

One-fourth that of gas B

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