Differential Equations: differential equations – #27232


Question: At t = 0, 1 mole of chemical A and 1 mole of chemical B are dissolved in a liter of water. Eventually, these chemicals will combine to produce 1 mole of chemical C. However, the reaction does not take place immediately. At any point in time, the rate at which chemical. C is produced is proportional to the product of the remaining number of moles of chemical A times the remaining number of moles of chemical B. Assume that at t = 0, there is no chemical C present at all, but by t = 1 minute, a half mole of chemical C has been produced. Let x(t) be the number of moles of chemical C in the solution after t minutes. Write an appropriate differential that determines x(t) and solve it. Determine all constants present in your solution.





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