FYKOS Year 27 Series 6 Problem 4 — insatiable spider · FYKOS 27 #27.6.4
Physics · mechanics
Problem
In a dark corner there lurks a spider that has just caught a fly and is slowly devouring it. Assume that the consumption follows such an equation:
A+B⇌k−1k1AB⟶k2C+B,
where A is fly substrate, B are the digestive compounds (there is always enough of themu) and C is the product of digestion. AB denotes the unstable intermediate product. The reaction is of the first order, in other words the speed is directly proportional to the concentration of the said substance. Determine how long will take the spider to digest the fly and begin hunting again, if its receptors will tell it that it is hungry once the substrate reaches 10 % of the original value.
Tip Use the approximation of the stationary state of intermediate product.