3. A certain chemical reaction problem involving the law of mass action leads to the following equation: 1 (80-x)(60-x) da = k fdt, where k is a constant, and r(t) is the number of kg of reaction product that is present after t minutes, if we start with 80 kg and 60 kg of two reacting substances that follow this law. (a) Integrate on each side, using an appropriate method of integration, to get an equation relating a function of ar to a function of t. (b) Solve your equation from part (a) to get a specific exponential formula for r(t), using the initial condition z(0) = 0. (c) How much reaction product r(t) is present after 15 minutes, assuming that (10) Explain. <= 20?

3. A certain chemical reaction problem involving the law of mass action leads to the following equation: 1 (80-x)(60-x) da = k fdt, where k is a constant, and r(t) is the number of kg of reaction product that is present after t minutes, if we start with 80 kg and 60 kg of two reacting substances that follow this law. (a) Integrate on each side, using an appropriate method of integration, to get an equation relating a function of ar to a function of t. (b) Solve your equation from part (a) to get a specific exponential formula for r(t), using the initial condition z(0) = 0. (c) How much reaction product r(t) is present after 15 minutes, assuming that (10) Explain. <= 20?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

3. A certain chemical reaction problem involving the law of mass action leads to the following
equation:
1
√(80-2) (60 - 2)
k fdt,
dx = k
where k is a constant, and z(t) is the number of kg of reaction product that is present after
t minutes, if we start with 80 kg and 60 kg of two reacting substances that follow this law.
(a) Integrate on each side, using an appropriate method of integration, to get an equation
relating a function of a to a function of t.
(b) Solve your equation from part (a) to get a specific exponential formula for r(t), using
the initial condition z(0) = 0.
(c) How much reaction product r(t) is present after 15 minutes, assuming that z(10) = 20?
Explain.

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