[edwards]

Hi, I'm marking some work and know that to get kinetic info on a first order reaction a plot of Ln[A]t-Ln[A]o or Ln[A] against time will have a gradient of -k. But a couple of the students have plotted Ln[A]o-Ln[A]t against time and got a gradient of k. This seems wrong to me, but as my maths is not the best I wanted advice on whether it can be done this way.  (using the logic below)


Ln[A]t-Ln[A]o=-kt
-Ln[A]t-Ln[A]o = kt
Ln[A]o-Ln[A]t = kt

Any help would be appreciated

[juanrga]

Hi, I'm marking some work and know that to get kinetic info on a first order reaction a plot of Ln[A]t-Ln[A]o or Ln[A] against time will have a gradient of -k. But a couple of the students have plotted Ln[A]o-Ln[A]t against time and got a gradient of k. This seems wrong to me, but as my maths is not the best I wanted advice on whether it can be done this way.  (using the logic below)


Ln[A]t-Ln[A]o=-kt
-Ln[A]t-Ln[A]o = kt
Ln[A]o-Ln[A]t = kt

Any help would be appreciated

First the correct term is slope, not gradient (a gradient is a vector).

Second if -k is the slope of the line with equation

Ln[A] = Ln[A]₀ - kt

then the slope will be -k for the line

Ln[A] - Ln[A]₀ = - kt

and the slope will be k for the line

Ln[A]₀ - Ln[A] = kt

One line will look as \ and the other will look as / The first slope will be negative and the second positive, but in both cases you obtain the same value of k.

If I say you that Z=5 and W=1, which is the value of T using the equation (Z - W = T)? And using the equation (W - Z = -T)?