A particular chemical reaction experiment requires that there is at least 50 gra

Question

A particular chemical reaction experiment requires that there is at least 50 grams of a certain key ingredient in the reacting mix. This compound is being used up at a rate proportional to its amount. When the reaction is initiated with 350 grams, in 20 minutes the amount present is down to 75 grams.

a. Define the variables and set up the initial value problem that would predict the amount of the compound remaining after t minutes into the reaction. Solve the problem and determine how long this reaction would run.

b. in the next stage of the experiment, the reaction is initiated in the same way, but this compounded is steadily injected into the reaction mix at the rate of 10 grams a minute. Use the proportionality constant you already found above, and set up the differential equation that would model how this reaction would proceed. Wilthout solving the equation, determine the amount of the compound at which the reaction stabilizes (the amount stops changing).

c. What is the minimum steady injection rate that would guarantee that the reaction stabilizes with at least 50 grams of the compound always present in the mix?

Explanation / Answer

since the rate of the reaction is directly proportional to the concentration of the compound this seems a first order reaction

so the reaction will proceed for infinit time.

differential equation , dx/dt = k[compound]

after t minutes the compound remaining = (2.303/k) log 50/ 50-x

x is the concentration after time t min.

50 is taken as standard initial value of the concentration of the compound

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