Differentiation and chemical reaction
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In an autocatalytic chemical reaction, the product formed is a catalyst for the reaction. If Q sub zero is the amount of the original substance, and x is the amount of catalyst formed, the rate of the chemical reaction is
dQ/dx = kx(qsubzero - x)
For what value of x will the rate of the chemical reaction be greatest?
Answer: x = Qsubzero/2
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Solution Summary
This shows how to determine the maximum rate of a chemical reaction.
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For a certain autocatalytic reaction the differential equation is
where Q is the amount of the substance, Q0 is the original amount of the substance, t is time, k is the rate constant, and x is the amount of the catalyst formed.
We want the value of x at ...
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