# Concentrated sulfuric acid (98.12 g.mol-1) has a density of 1.5 g/cm3 and is 60 % H2SO4 per mass. The rest is water. How many H+ ions are there in a 45ml concentrated sulfuric acid solution?

Mar 30, 2017

There are approx. $5 \times {10}^{23}$ individual hydronium ions.......

#### Explanation:

We need to find (i) $\left[{H}_{2} S {O}_{4}\right]$, the concentration with respect to $\text{sulfuric acid}$.

And so we start with a $1 \cdot c {m}^{3}$ volume, which has a mass of $1.5 \cdot g$, of which 60% by mass is the acid, i.e. $0.90 \cdot g$ with respect to sulfuric acid.

And so $\text{concentration}$ $=$ $\text{moles"/"volume}$ $=$ $\frac{\frac{0.90 \cdot g}{98.08 \cdot g \cdot m o {l}^{-} 1}}{1.0 \times {10}^{-} 3 \cdot L}$

$= 9.18 \cdot m o l \cdot {L}^{-} 1$ WITH RESPECT TO ${H}_{2} S {O}_{4} \left(a q\right)$.

And thus (ii) in a $45 \cdot m L$ volume, there are $45 \times {10}^{-} 3 L \times 9.18 \cdot m o l \cdot {L}^{-} 1 = 0.413 \cdot m o l$ with respect to ${H}_{2} S {O}_{4}$.

Given that the acid is DIPROTIC, there are thus $0.826 \cdot m o l$ with respect to ${H}_{3} {O}^{+}$ or ${H}^{+}$.

To get the number of ${H}_{3} {O}^{+}$ ions, we multiply this quantity by the $\text{Avocado number}$, i.e.

$0.826 \cdot m o l \times 6.022 \times {10}^{23} \cdot m o {l}^{-} 1 = 4.97 \times {10}^{23}$ hydronium ions.