Titrations

Titration is the procedure of identifying the quantity (moles or concentration) of a compound (which is called the analyte) using a well known reaction. In order to titrate a substance, there must be a reaction it participates in, and the end point of that reaction must be identifiable. Also, the quantity of the other reactants (the titrants) must be known. Acid-base reactions and redox reactions are most often used for titration.

Acid-base titrations are commonly used because they are simple and their end points can be easily detected using an indicator or a $\text{pH}$ meter. For example, suppose we have a $50 \text{ mL}$ hydrochloric acid solution whose concentration we do not know of. We want to know its molar concentration (let it be $x$). So, we prepare a $0.1\text{ M}$ sodium hydroxide solution, and slowly mix it into the acid solution: $$\text{HCl}+\text{NaOH}\rightarrow\text{NaCl}+\text{H}_2\text{O}.$$ The acid-base reaction equation above implies that the equivalence point is when the number of moles of $\text{NaOH}$ added equals the number of moles of $\text{HCl}.$ In this case the end point (or equivalence point) would be the point at which $\text{pH}=7,$ so we slowly add $\text{NaOH}$ until the $\text{pH}$ meter reads $7.$ If the $\text{pH}$ is $7$ when $50 \text{ mL}$ of $\text{NaOH}$ has been added, then we have $$\begin{aligned} (\text{\# of moles of NaOH added})&=50\text{ mL}\times0.1\text{ M}=5\text{ mmol} &\qquad(1)\\ (\text{\# of moles of HCl})&=50\text{ mL}\times x\text{ M}=50x\text{ mmol}, &\qquad(2) \end{aligned}$$ where $(1)$ must equal $(2).$ Thus now we know that the initial molar concentration $x$ of the hydrochloric acid solution was $x=0.1\text{ M}.$

$\hspace{5cm}$ Imgur

Titration can also be done by using a well known redox reaction. In some cases the equivalence point can be detected using the bare eye for reactions involving color changes. For reactions that do not, a redox indicator or potentiometer may be used.

The oxidation of $\text{Fe}^{2+}$ using potassium permanganate is a well known redox reaction. Below is the reaction equation: $$5\text{Fe}^{2+}(aq)+\text{MnO}_4^{-}(aq)+8\text{H}^+(aq)\rightarrow5\text{Fe}^{3+}(aq)+\text{Mn}^{2+}(aq)+4\text{H}_2\text{O}(l).$$ Note that $5$ moles of $\text{Fe}^{2+}$ is oxidized to become $\text{Fe}^{3+}$ while one mole of permanganate is reduced to form $\text{Mn}^{2+}.$ Thus the ferrous ion and permanganate ion react with a $5:1$ ratio. The use of permanaganate is very handy, due to the fact that its solution is bright purple, making it a good indicator. Suppose we have $10 \text{ mL}$ of $0.1\text{ M}$ potassium permanganate solution, and we want to know the concentration $x$ of $\text{Fe}^{2+}$ in another solution. We slowly add the ferrous solution (which is colorless) to the permanganate solution, until the purple color disappears. If the color disappeared when $5 \text{ mL}$ of ferrous solution was added, then we have $$\begin{aligned} (\text{\# of moles of Fe}^{2+}\text{ added})&=5\text{ mL}\times x\text{ M}=5x\text{ mmol} &\qquad(1)\\ (\text{\# of moles of permanganate})&=10\text{ mL}\times0.1\text{ M}=1\text{ mmol}. &\qquad(2) \end{aligned}$$ Since the ratio $(1):(2)$ must equal $5:1,$ it must be true that $x=0.1\text{ M}.$