A solution of sulfuric acid is known to have a hydroxide ion concentration of 5.03 x 10-13 M. What would the hydrogen ion concentration be for this...

The product of the hydrogen ion and hydroxide ion concentrations in aqueous solution is a constant, 1.00 X 10-14. 

Dividing this constant by the hydroxide ion concentration will give the hydrogen ion concentration:

`[H+] = (1.00x10^(-14))/([OH-]) = (1.00x10^(-14))/(5.03x10^(-13)) = 1.99x10^(-2)`

Choice b is therefore the correct answer, reported to two significant figures. 

A solution that contains more hydrogen ions than hydroxide ions, as this one does, is acidic. If a solution contains more hydroxide than hydrogen ions it's basic. If [H+] = [OH-] the solution is neutral and the concentration of both H+ and OH- will be 1.00 X 10E-7.

The constant used here, 1.00 X 10-14, also written as Kw, is the equilibrium constant for the auto-ionization of water:

`H_2O_((l)) -> H^+_(aq) + OH^-_(aq)`

The equilibrium constant expression for this reaction is :

`K_w = [H+][OH-]`

The concentration of water is not included in the expression because it's a pure liquid and so its concentration remains relatively constant.