First or second order reaction

I have that $$100$$ mM of K$$_3$$Fe(CN)$$_6$$ is dissolved in equimolar of the organic ion (which I assume is HCN). In the solution Fe(CN)$$_6^{3-}$$ reacts to form Fe(CN)$$_6^{4-}$$.

The formation of Fe(CN)$$_6^{4-}$$ as a function of time is measured in a Na$$_2$$SO$$_4$$ (which does not take part in the reaction) solution of different concentrations.

One of the concentrations of Na$$_2$$SO$$_4$$ = $$0$$ and I want to determine the rate constant from this and:

$$\begin{array}{c|c} t/\pu{min} & \ce{[Fe(CN)_{6}^4-]}/\pu{mM} \\ \hline 10\ & 20.3\\ 20 & 33.7\\ 30\ & 43.3\\ 40\ & 50.4 \\ 50\ & 56\\ 60\ & 60.4 \\ \hline \end{array}$$

I assumed that the reaction would be second order since the reactants are equimolar and so I plotted using the equation:

$$\frac{1}{[A]}= kt + \frac{1}{[A_0]}$$

When I plotted using this I get that the linear equation is: $$−5.78×10^{−4}*x + 0.0463$$

and R$$^2$$ = $$0.771$$.

So I tried using a first order equation and got that the linear equation is: $$0.0204*x + 3.01$$

and R$$^2$$ = $$0.878$$.

Doesn't this mean that my reaction should actually be first order? I don't see how it could be that and would appreciate it if someone could tell me if it is first or second or what I am doing wrong. Thank you!

EDIT

I did plot the curves and now when I look at them I do think that the first order line is a bit curved while the second order is more straight. It is really hard to see and my professor usually looks at the R-value which is why I thought that would help me determine the order here. But does that mean the reaction is second order?

Here are my graphs:

• It is always a good idea to plot data before any curve fitting is done. Perhaps plot your data and see what it may reveal.
– Ed V
Apr 30, 2021 at 13:12
• You could also try doing a similar analysis to check if your points correspond to a first order reaction. Also, what makes you think that your organic ion is HCN? Thinking about the process would get you closer to understanding what's happening here.
– user23638
Apr 30, 2021 at 13:50
• Using $R^2$ is a very, very poor discriminator of the goodness of a fit, basically never use it. Look at fit and see it is curved vs the data, then plot residuals, (calc data-real data)/real data for example and see if they are random, look at size of error in gradient and error in intercept. Apr 30, 2021 at 18:25
• @EdV I have added my plots in my question now but I am still a bit unsure of the order.. May 3, 2021 at 9:25
• I'd be really surprised if either HCl or HCN could be called an organic ion, and I hope you agree with me on this one. The wording of the exercise is a bit weird for sure, but to me it looks like you might want to work assuming pseudo first order conditions.
– user23638
May 3, 2021 at 9:34

Use the 2nd order scheme $$2A \to B$$ with initial amount of $$A=A_0$$ so $$B=A_0-A$$ and B is the product you observe. The rate of change is $$\displaystyle \frac{1}{2}\frac{dA}{dt}=-k_2A^2$$ and I'm not going to use [ ] for concentrations just $$A,\,B,\,A_0$$. Also the 2 in the equation is incorporated into the rate constant just for convenience.
Solving the equation gives $$\displaystyle A=\frac{A_0}{A_0k_2t+1}$$ and so the product follows $$\displaystyle B=\frac{A_0^2k_2t}{A_0k_2t+1}$$. This is shown as the red line in the figure below. I just guessed the rate constant a few time to fit and as you can see the fit is good. You can also linearise this equation by isolating $$A_0k_2t$$.
The first order plot is also shown (grey line) and this is poor. $$B=A_0(1-e^{-kt}$$)