The Correct Answer and Explanation is :
Explanation of Diffusion Rate Calculations
The rate of diffusion is calculated using the formula:
[
\text{Rate} \, (\text{mm/hr}) = \left( \frac{\text{Diameter} \, (\text{mm})}{\text{Time} \, (\text{min})} \right) \times 60
]
This equation helps determine how fast diffusion occurs for different crystal counts at various time intervals.
Step-by-Step Calculation:
1. For 1 Crystal:
- At 10 minutes: ( \left( \frac{19}{10} \right) \times 60 = 114.0 ) mm/hr
- At 20 minutes: ( \left( \frac{23}{20} \right) \times 60 = 69.0 ) mm/hr
- At 30 minutes: ( \left( \frac{27}{30} \right) \times 60 = 54.0 ) mm/hr
2. For 3 Crystals:
- At 10 minutes: ( \left( \frac{13}{10} \right) \times 60 = 78.0 ) mm/hr
- At 20 minutes: ( \left( \frac{16}{20} \right) \times 60 = 48.0 ) mm/hr
- At 30 minutes: ( \left( \frac{16}{30} \right) \times 60 = 32.0 ) mm/hr
3. For 6 Crystals:
- At 10 minutes: ( \left( \frac{20}{10} \right) \times 60 = 120.0 ) mm/hr
- At 20 minutes: ( \left( \frac{29}{20} \right) \times 60 = 87.0 ) mm/hr
- At 30 minutes: ( \left( \frac{37}{30} \right) \times 60 = 74.0 ) mm/hr
Interpretation:
- The rate of diffusion is highest in the early time intervals and gradually decreases.
- Increasing the number of crystals leads to a higher initial diffusion rate, likely due to increased concentration gradients.
- Over time, the rate of diffusion slows down as the system reaches equilibrium.
Now, I will generate an image to visualize these diffusion rates.
Here is the visual representation of the diffusion rates over time for different crystal counts. The graph shows that diffusion rates are initially high but decrease over time as equilibrium is approached. Additionally, increasing the number of crystals results in higher diffusion rates initially, likely due to greater concentration gradients. Let me know if you need further analysis!