In a study of the decomposition of the compound XX via the reaction X(g)⇌Y(g)+Z(g)X(g)⇌Y(g)+Z(g)

the following concentration-time data were collected:

Time (min)(min) [X](M)[X](M)
0 0.467
1 0.267
2 0.187
3 0.144
4 0.117
5 0.099
6 0.085
7 0.075

Given that the rate constant for the decomposition of hypothetical compound XX is is 1.60 M^−1⋅min^−1. Calculate the concentration of XX after 18.0 minmin .

( About ) 0.03232 M

Explanation:

Based on the units for this reaction it should be a second order reaction, and hence you would apply the integrated rate law equation "1 / [X] = kt + 1 / []"

This formula would be true for the following information -

{ = the initial concentration of X, k = rate constant, [ X ] = the concentration after a certain time ( which is what you need to determine ), and t = time in minutes }

________

Therefore, all we have left to do is plug in the known values. The initial concentration of X is 0.467 at a time of 0 minutes, as you can tell from the given data. This is not relevant to the time needed in the formula, as we need to calculate the concentration of X after 18 minutes ( time = 18 minutes ). And of course k, the rate constant = 1.6

1 / [X] = ( 1.6 )( 18 minutes ) + 1 / ( 0.467 ) - Now let's solve for X

1 / [X] = 28.8 + 1 / ( 0.467 ),

1 / [X] = 28.8 + 2.1413...,

1 / [X] = 31,

[X] = 1 / 31 = ( About ) 0.03232 M

Now for this last bit here you probably are wondering why 1 / 31 is not 0.03232, rather 0.032258... Well, I did approximate one of the numbers along the way ( 2.1413... ) and took the precise value into account on my own and solved a bit more accurately. So that is your solution! The concentration of X after 18 minutes is about 0.03232 M