Question

A zero-order reaction has a constant rate of 2.40×10−4 M/s. If after 35.0 seconds the concentration has dropped to 3.50×10−2 M, what was the initial concentration? Express your answer with the appropriate units. Learning Goal: To understand how to use integrated rate laws to solve for concentration. A car starts at mile marker 145 on a highway and drives at 55 mi/hr in the direction of decreasing marker numbers. What mile marker will the car reach after 2 hours? This problem can easily be solved by calculating how far the car travels and subtracting that distance from the starting marker of 145. 55 mi/hr×2 hr=110 miles traveled milemarker 145−110 miles=milemarker 35 If we were to write a formula for this calculation, we might express it as follows: milemarker=milemarker0−(speed×time) where milemarker is the current milemarker and milemarker0 is the initial milemarker. Similarly, the integrated rate law for a zero-order reaction is expressed as follows: [A]=[A]0−rate×time or [A]=[A]0− kt since rate= k[A]0=k A zero-order reaction (Figure 1)proceeds uniformly over time. In other words, the rate does not change as the reactant concentration changes. In contrast, first-order reaction rates (Figure 2) do change over time as the reactant concentration changes. Because the rate of a first-order reaction is nonuniform, its integrated rate law is slightly more complicated than that of a zero-order reaction. The integrated rate law for a first-order reaction is expressed as follows: [A]=[A]0e−kt where k is the rate constant for this reaction. The integrated rate law for a second-order reaction is expressed as follows: 1[A]= kt+1[A]0 where k is the rate constant for this reaction.

Answer 1

Initial concentration = 0.0434 M

Explanation

The integrated zero order rate law is given as

[A] = [A]_o - (k) * (t)

where

[A]_o is the initial concentration

[A] = final concentration = 3.50 x 10^-2 M

k = rate constant = 2.40 x 10^-4 M/s

t = time = 35.0 s

[A]_o = [A] + (k) * (t)

[A]_o = (3.50 x 10^-2 M) + (2.40 x 10^-4 M/s) * (35.0 s)

[A]_o = (3.50 x 10^-2 M) + (8.40 x 10^-3 M)

[A]_o = 0.0434 M