State whether the following sentences are true $(T)$ or false $(F)$.
$(a)$ Concentration of pure water is $1.0 \ mol \ L^{-1}$.
$(b)$ Concentration of pure water is $55.5 \ mol \ L^{-1}$.

(B) The density of pure water is approximately $1.0 \ g \ mL^{-1}$ or $1000 \ g \ L^{-1}$.
The molar mass of water $(H_2O)$ is $2 \times 1.008 + 16.00 = 18.016 \ g \ mol^{-1}$,which is approximately $18 \ g \ mol^{-1}$.
Concentration (Molarity) $= \frac{\text{Mass of solute in } g \ L^{-1}}{\text{Molar mass of solute in } g \ mol^{-1}}$.
Concentration of water $= \frac{1000 \ g \ L^{-1}}{18 \ g \ mol^{-1}} \approx 55.5 \ mol \ L^{-1}$.
Therefore,statement $(a)$ is False $(F)$ and statement $(b)$ is True $(T)$.