Chemical reactions: In a second-order reaction, one molecule of a substance A collides with one molecule of a substance B to produce a new substance, the product. If t denotes time and x = x(t)...

Chemical reactions: In a second-order reaction, one molecule of a substance A collides with one molecule of a substance B to produce a new substance, the product. If t denotes time and x = x(t) denotes the concentration of the product, then its rate of change dx dt is called the rate of reaction. Suppose the initial concentration of A is a and the initial concentration of B is b. Then, assuming a constant temperature, x satisfies the equation of change

for some constant k. This is because the rate of reaction is proportional both to the amount of A that remains untransformed and to the amount of B that remains untransformed. Here we study a reaction between isobutyl bromide and sodium ethoxide in which k = 0.0055, a = 51, and b = 76. The concentrations are in moles per cubic meter, and time is in seconds.10

a. Write the equation of change for the reaction between isobutyl bromide and sodium ethoxide.

b. Make a graph of dx dt versus x. Include a span of x = 0 to x = 100.

c. Explain what can be expected to happen to the concentration of the product if the initial concentration of the product is 0.