The rate of
a certain chemical reaction is directly proportional to the square of the
concentration of chemical A present and inversely proportional to the
concentration of chemical B present.If
the concentration of chemical B is increased by 100 percent, which of the
following is closest to the percent change in the concentration of chemical A
required to keep the reaction rate unchanged?
Solution: Let r be the rate of the reaction, x be the concentration of A, and y be the concentration of B. From the given information, we have r = kx^2/y, where k is a constant. Let the original value of x be a and that of y be b. We then have r = ka^2/b.
If b is increased 100%, then the new y is 2b. Substituting it into the equation, we have r = kx^2/2b.
r remain constant. Then ka^2/b = kx^2/2b. This gives x = (sqrt 2)a = 1.4142 . . . a, which shows that a must increase about 40%.