The hydrogen ion concentration of a $10^{-8}\text{M}$ $\text{HCl}$ aqueous solution at $298\text{K}$ ($K_w=10^{-14}$) is :

For very dilute acids ($10^{-8}\text{M}$), the autoionization of water cannot be neglected. Let the $[{\text{H}}^{+}]$ contributed by water be $x$. Total $[{\text{H}}^{+}]=10^{-8}+x$ and $[{\text{OH}}^{-}]=x$.Using $K_w=[{\text{H}}^{+}][{\text{OH}}^{-}]=(10^{-8}+x)(x)=10^{-14}$.Solving this quadratic equation yields $x\approx 0.95\times 10^{-7}$.Total $[{\text{H}}^{+}]=10^{-8}+0.95\times 10^{-7}\approx 1.05\times 10^{-7}\text{M}$.