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The initial rate of decomposition of the only reactant X was measured in several

ID: 514326 • Letter: T

Question

The initial rate of decomposition of the only reactant X was measured in several different experiments, all performed at 25 0C. If another experiment was begun with a 0.650 M concentration of X, how long until the concentration of X is 0.0975? Assume this final experiment is also performed at 25 0C under conditions where the reverse reaction is negligible.

Initial concentration (M)            Initial Rate (M/s)

1.50                                           0.042000

1.25                                           0.035000

Explanation / Answer

As the initial concentration increased, the rate has also increased. It can be seen in the table given with two different inital concentrations. So, the reaction is first order with respect to the reactant. Suppose the reaction is:

X --> B

rate = k[X]

k = rate constant

[X] = 1.50 M

rate = 0.042000 M/s

So, k = rate/[X] = 0.042000/1.50 = 0.028000 s-1

The conditions for which the time is to be calculated:

[X] = 0.650 M

After some time, the concentration of X becomes = [X]t = 0.0975 M

rate constant = k = 0.028000 s-1

The equation to be used is:

log [X]/[X]t = kt/2.303

log(0.650/0.0975) = 0.028000*t/2.303

0.824 = 0.028000*t/2.303

t = 67.77 s

Time taken = 67.77 s