1. **State the problem:** We want to find the formula used to calculate 3.7 tons of HF produced per year from the salt flux trial data. 2. **Given data:** - Metal processed by Melter 1: 42636 tons - Metal processed by Melter 2: 48659 tons - Total hours in a year: 8760 (not directly needed here) - Fluoride content in salt: 2.2% (by weight) - Maximum salt per ton of aluminum: 100 lbs/ton - Atomic weights: Fluoride (F) = 18.999, Hydrogen (H) = 1, HF molecular weight = 20.006 3. **Formula used:** The total HF produced per year is calculated by: $$\text{HF tons/year} = \frac{\text{Total metal processed (tons)} \times \text{Salt per ton (lbs/ton)} \times \text{Fluoride fraction} \times \text{Molecular weight of HF}}{\text{Atomic weight of F} \times 2000}$$ Explanation: - Total metal processed = 42636 + 48659 = 91295 tons - Salt per ton = 100 lbs - Fluoride fraction = 2.2% = 0.022 - The factor 2000 converts pounds to tons (2000 lbs = 1 ton) - The ratio molecular weight of HF to atomic weight of F accounts for converting fluoride mass to HF mass 4. **Intermediate calculations:** $$\text{HF tons/year} = \frac{91295 \times 100 \times 0.022 \times 20.006}{18.999 \times 2000}$$ 5. **Simplify step-by-step:** Calculate numerator: $$91295 \times 100 = 9,129,500$$ $$9,129,500 \times 0.022 = 200,849$$ $$200,849 \times 20.006 = 4,017,180.9$$ Calculate denominator: $$18.999 \times 2000 = 37,998$$ 6. **Divide numerator by denominator:** $$\frac{4,017,180.9}{37,998} \approx 105.7 \text{ tons of HF}$$ 7. **Adjusting for actual HF production:** The problem states 3.7 tons of HF per year, so likely the salt usage or fluoride fraction is adjusted or only a portion of salt is converted to HF. **Summary:** The formula to calculate HF tons per year is: $$\text{HF tons/year} = \frac{(\text{Metal processed in tons}) \times (\text{Salt per ton in lbs}) \times (\text{Fluoride fraction}) \times (\text{Molecular weight of HF})}{(\text{Atomic weight of F}) \times 2000}$$ This formula converts the fluoride content in salt to HF mass produced per year.