If a solution of sulfuric acid (H2SO4) has a concentration of 2.1E-4M, what is the concentration of its hydronium ion?

First, let's look at this question using 2.1 x `~10^-^4` M HCl instead of `~H_2SO_4`. HCl is a strong acid. This means that it will disassociate completely in water: 

   `~HCl` + `~H_2O` -> `~H_3O^+` + `~Cl^-`

Therefore, all of the hydrogen ions in HCl will be converted into hydronium ions (`~H_3O^+` ). Since there is a 1:1 ratio of HCl used and `~H_3O^+` produced, the concentration of HCl and the concentration of `~H_3O^+` will be the same, 2.1 x `10^-^4` M.

Now, let's look at what happens when we use 2.1 x `~10^-^4 M` `~H_2SO_4`. `~H_2SO_4` is also a strong acid and will disassociate completely in water; however, `~H_2SO_4` has two H atoms instead of just one. This means that we will need to react two molecules of `~H_2O` with every one molecule of `~H_2SO_4` :

   `~H_2SO_4` + `~2H_2O`  -> `~2H_3O^+` + `~SO_4^2^-`

Since this reaction results in the production of two `~H_3O^+` molecules for every one `~H_2SO_4` molecules, the concentration of hydronium ions (`~H_3O^+` ) will be twice the concentration of the `~H_2SO_4` .

   2  x (2.1 x `~10^-^4` M) = 4.2 x `~10^-^4` M `~H_3O^+` .