Growth processes

• The rate of a slow enzyme-catalysed reaction depends on the temperature of its solution. It activates at 20 degrees, at a rate of zero mol/l/hr and deactivates at 80 degrees. For each degree increase in temperature between 20 and 60 degrees the rate of reaction increase by 0.1 mol/l/hr and for each degree increment between 60 and 80 the rate reduces by 0.2 mol/l/hr. If the solution if prepared at a temperature of 20 degrees how, in principle can applying a constant heat to the solution minimise the time taken for 10 mol of this chemical to have catalysed? What additional information or data would you need to be able to provide a numerical answer to this question?
  • By applying a constant heat source to 100 litres of solution, how quickly can you cause 1000 mol to catalyse? [you might want to experiement by drawing up a table for different rates of heating]
  • Consider an alternative problem: if the solution is prepared at boiling point: at what rate must 1 litre be cooled to end up with exactly 3 mol having been catalysed?
    [Hint: how does a total relate to a rate of reaction graph?]
  • What aspects of your approach to this question would work if the rate doubled for every 2 degrees between 20 and 60 and halved for every degree between 60 and 80? What aspects would not work, and what mathematics would you need to use to solve this more realistic version of the problem?
• These four graphs can be used to represent growth rates of certain organisms. How many possibilities can you suggest for each one? Can you suggest organisms which grow according to a qualitatively different type of graph?

The graphs are all without scale. For any possibility you suggest, what would be a sensible scale for the axes?

• An evolutionary scientist suggests that at some distant point 350 million years ago in the past one of his ancestors was an early form of fish. Try to estimate the number of generations that link the scientist to the fish. To make your estimation, you will need to fill in sensible values in the table below
  

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