1. Many chemical reactions are the result of the interaction of two molecules that undergo a change to produce a new product. The rate of the reaction typically depends on the concentrations of the two kinds of molecules. If a is the amount of substance A and b is the amount of substance B at time 0, and if x is the amount of product at time t, then the rate of formation of x may be given by dx the differential equation = k(a - x)(b - x), or k, where k is a constant for the (a - x)(b - x) dt t = dx dt = 1 = reaction. Integrate both sides of this equation to obtain a relation between x and t. Do this for both a = b and ab. Assume in each case that x = 0 when t = 0. 2. Find the area of the region between the curve y = e¯¯ and the x-axis.
1. Many chemical reactions are the result of the interaction of two molecules that undergo a change to produce a new product. The rate of the reaction typically depends on the concentrations of the two kinds of molecules. If a is the amount of substance A and b is the amount of substance B at time 0, and if x is the amount of product at time t, then the rate of formation of x may be given by dx the differential equation = k(a - x)(b - x), or k, where k is a constant for the (a - x)(b - x) dt t = dx dt = 1 = reaction. Integrate both sides of this equation to obtain a relation between x and t. Do this for both a = b and ab. Assume in each case that x = 0 when t = 0. 2. Find the area of the region between the curve y = e¯¯ and the x-axis.
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Transcribed Image Text:1. Many chemical reactions are the result of the interaction of two molecules that undergo a change to
produce a new product. The rate of the reaction typically depends on the concentrations of the two
kinds of molecules. If a is the amount of substance A and b is the amount of substance B at time
0, and if x is the amount of product at time t, then the rate of formation of x may be given by
dx
the differential equation = k(a - x)(b - x), or
k, where k is a constant for the
(a - x)(b - x) dt
t =
dx
dt
=
1
=
reaction. Integrate both sides of this equation to obtain a relation between x and t. Do this for both
a = b and ab. Assume in each case that x = 0 when t = 0.
2. Find the area of the region between the curve y = e¯¯ and the x-axis.
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