# Titration of sulfuric acid with sodium hydroxide

$55.0~\mathrm{mL}$ of $0.250~\mathrm{M}~\ce{NaOH}$ is used to titrate $35.0~\mathrm{ml}$ of $\ce{H2SO4}$. What is the molarity of $\ce{H2SO4}$?

I know that the equation for this reaction is: $$\ce{H2SO4 + 2NaOH <=> Na2SO4 + 2H2O}$$

I know that I have to use $$i_\mathrm a\cdot M_\mathrm a\cdot V_\mathrm a = i_\mathrm b\cdot M_\mathrm b\cdot V_\mathrm b$$ formula where $i$ is the number of ions, $M_\mathrm a$ and $M_\mathrm b$ are the molarities (of the acid and base, respectively), and $V_\mathrm a$ and $V_\mathrm b$ are the volumes of the acid and base (in milliliters).

I starting doing this problem and got up to this point:

$$i\cdot M_\mathrm a\cdot 35~\mathrm{ml} = 2\cdot 0.250~\mathrm{M}\cdot 55~\mathrm{ml}$$

So my question is: What should I put for the number of ions on the left hand side? Is it three or two?

• You're almost right. $i_a$ is the number of $H^+$ ions and $i_b$ is the number of $OH^-$ ions. – LDC3 May 4 '14 at 21:17

That is one way of doing it.

In reality, this is a stoichiometric question where you are trying to find the molarity of an unknown polyprotic acid by titrating it with a strong base (woo-hoo!) of known molarity. I prefer using this method as it is easier to see the relationship between the units as well as use chain-ink conversion which most people are familiar with.

We know that

$$\text{M} = \frac{\text{mol}}{\text{L}}$$

Therefore,

$$55 \ \text{mL} \ \ce{ NaOH} * \frac{250 \ \text{mmol} \ \ce{NaOH}}{1000 \ \text{mL} \ \ce{NaOH}} * \frac{1 \ \text{mmol} \ \ce{H2SO4}}{2 \ \text{mmol} \ \ce{NaOH}} * \frac{1}{ 35 \ \text{mL} \ \ce{H2SO4}} =$$

Which equals

$$0.19643 \ \frac{\text{mol}}{\text{L}}$$

• In reality you would do this experiment probably with conductometry or for sulphate it is even better to do it via gravimetry via $$\ce{BaCl2 + H2SO4 -> BaSO4 v + 2 'HCl'}.$$ It should also be noted, that the second protolysis of suphuric acid does not behave like a strong acid. The equilibrium $$\ce{HSO4- (aq) + {}^{-}OH <=> H2O + SO4^{2-} (aq)}$$ is not fully on the right side. There is a significant amount of undissociated hydrogensulphate ions left (at pH=7). – Martin - マーチン May 5 '14 at 4:03