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Final yield = Starting mass × Milling efficiency × (1 - Post-synthesis oxidation loss)
= 534.6 g × 0.85 × 0.98 = 445.4 gStarting mass (534.6 g = 10 moles):
 This indicates the initial amount of material (534.6 grams, equivalent to 10 moles, suggesting a molar mass of ~53.46 g/mol for the substance).Milling efficiency (85% or 0.85): Represents the fraction of material retained after milling, a process that reduces particle size to create nanopowder. A 15% loss (1 - 0.85) occurs due to factors like material sticking to equipment or incomplete particle size reduction.Post-synthesis oxidation loss (2% or 0.02): Accounts for material lost due to oxidation after synthesis, where 98% (1 - 0.02) of the material remains.Final yield (445.4 g): The mass of usable nanopowder after both processes.
This formula is used in materials science, chemical engineering, or nanotechnology to predict the final amount of nanopowder produced in a manufacturing process. Specific uses include:Nanopowder Production:The formula calculates the expected yield of nanopowder after milling and oxidation losses, critical for industries producing nanomaterials like metal oxides, ceramics, or composites.
Example: Producing titanium dioxide (TiO₂) or iron oxide nanopowders for catalysts, coatings, or electronics.Process Optimization:
Helps engineers assess the efficiency of milling and synthesis processes. Low efficiency (e.g., 85%) might prompt improvements in milling techniques or equipment to reduce material loss
Oxidation loss (2%) could guide efforts to minimize exposure to air or use protective atmospheres (e.g., nitrogen or argon).
Cost Estimation:By calculating the final yield, manufacturers can estimate material costs and losses, crucial for budgeting in large-scale production of nanomaterials used in batteries, sensors, or medical applications.Quality Control:Ensures the final nanopowder meets mass requirements for downstream applications, such as in drug delivery systems or high-performance coatings.

1. Scaling Production:The formula can be scaled to predict yields for larger or smaller starting masses, aiding in planning industrial-scale synthesis.

• The molar mass (~53.46 g/mol) suggests a specific material, possibly iron (Fe, ~55.85 g/mol) or a similar metal/alloy. This formula is likely tailored to a process involving a metal or compound prone to oxidation.
• It’s a practical tool in labs or industries where precise control over nanomaterial quantities is needed, balancing efficiency and loss factors.

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