(Solution) - The article Lead Dissolution from Lead Smelter Slags Using Magnesium -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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The article "Lead Dissolution from Lead Smelter Slags Using Magnesium Chloride Solutions" (A. Xenidis, T. Lillis, and I. Hallikia, The AusIMM Proceedings, 1999:37-44) discusses an investigation of leaching rates of lead in solutions of magnesium chloride. The data in the following table (read from a graph) present the percentage of lead that has been extracted at various times (in minutes).

a. The article suggests fitting a quadratic model y = ?0 +?1t +?2t2 +? to these data. Fit this model, and compute the standard deviations of the coefficients.
b. The reaction rate at time t is given by the derivative dy/dt = ?1 +2?2t. Estimate the time at which the reaction rate will be equal to 0.05.
c. The reaction rate at t = 0 is equal to ?1. Find a 95% confidence interval for the reaction rate at t = 0.
d. Can you conclude that the reaction rate is decreasing with time? Explain.