How to Calculate Reaction Rate for Pseudo-First Order Kinetics?

[ThirdEyeBlind]

Homework Statement

2A + 2B -> C +D
where rate = k [A] ^2
[A]_0 = .000443 M
_0 = 1.69 M
A plot of ln [A] vs time has a slope of -9.87. What will the rate of this reaction be when [A]==1.412 M?

Homework Equations

The Attempt at a Solution

From given information, this is pseudo-first order. So slope=-k so k = 9.87 but this is pseudo-order so k'= 9.87

rate= k' [A]
k' = k ^2 --> k = k' / ^2 and I plug in the values for k' and = 1.412 and I get the wrong answer. The answer should be 9.73 M/s

 

[nate808]

.

The correct approach to solving this problem would be to first calculate the value of k using the given initial concentrations of [A] and :

k = slope / 0^2 = -9.87 / (1.69 M)^2 = -3.38 M^-2 s^-1

Then, use this value of k to calculate the rate at [A] = = 1.412 M:

rate = k [A] ^2 = (-3.38 M^-2 s^-1) (1.412 M) (1.412 M)^2 = -8.56 M/s

Note that the units of the rate are in M/s, not M^-1 s^-1 as in your attempt. Also, the given answer of 9.73 M/s may be rounded to the nearest hundredth.