The reaction between iron (III) ions and thiocyanate ions, SCN$^-$, is an equilibrium reaction:

Fe$^{3+}$ (aq) $+$ SCN$^-$ (aq) $\ce{<=>}$ FeSCN$^{2+}$ (aq)

When $20$cm$^3$ of $1.0\times10^{-3}$ mol dm$^{-3}$ Fe(NO$_3$)$_3$ (aq) is mixed with $20$cm$^3$ of $1.0\times10^{-3}$ mol dm$^{-3}$ KSCN (aq), the concentration of FeSCN$^{2+}$ (aq) at equilibrium is $8.0 \times 10^{-3}$ mol dm$^{-3}$. What is $K_{c}$ for the equilibrium system?

The question also includes a hint, saying that,

After mixing, the concentration of each reactant is half, because the volume of solution is doubled.

My attempts to solve this question are as follows:

The initial number of moles of Fe$^{3+}$ and SCN$^- $$= 1\times 10^{-3}\times20\times10^{-3}=2\times10^{-5}$mol

At equilibrium, the concentration of Fe$^{3+}$ and SCN$^-$$ = \displaystyle\frac{2\times10^{-5}}{20\times10^{-3}} - (8\times10^{-3})=1\times10^{-3} - (8\times10^{-3}) $mol dm$^{-3}$

I have obtained a negative value for the concentration Fe$^{3+}$ and SCN$^-$, so I think I have made some wrong calculations somewhere. I am confused about the volume and concentrations of Fe$^{3+}$ and SCN$^-$.

Could you tell me where I made a mistake?

  • 2
    $\begingroup$ You don't not to write that cumbersome codes, your first equation is \ce{Fe^{3+}(aq) + SCN-(aq) <=> FeSCN^{2+}(aq)} $\endgroup$ – Zenix May 21 at 14:31
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    $\begingroup$ I didn't see your calculations, but, concentration of $\ce{FeSCN^{2+}}$ is too high to be true. $\endgroup$ – Zenix May 21 at 14:39
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    $\begingroup$ I think there's a typo: $\ce{[FeSCN^2+]}$ can't be higher than $\ce{[Fe^3+]}$ or $\ce{[SCN^-]}$. I think it should be $8 \times 10^{-5}$ $\endgroup$ – Aniruddha Deb May 21 at 15:22
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    $\begingroup$ I find following your logic pretty hard since you are randomly omitting units. The measured quantity consists of a number and a unit, and you are not allowed to omit either of them. Also, your markup is indeed pretty cumbersome; please visit this page, this page and this one on how to format your future posts better with MathJax and Markdown. $\endgroup$ – andselisk May 21 at 15:30
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    $\begingroup$ The $\ce{[FeSCN^2-]}$ at equilibrium should be $\lt 5.0 \times 10^{-4}$. $\endgroup$ – Mathew Mahindaratne May 21 at 15:53

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