State whether each of the following statements is true or false. Justify your answer in each case. (a) Sulfuric acid is a monoprotic acid. (b) \(\mathrm{HCl}\) is a weak acid. (c) Methanol is a base.

We will first determine if this statement is true or false by understanding the definition of a monoprotic acid and verifying if sulfuric acid fits that definition. A monoprotic acid is an acid that donates one proton (\(\mathrm{H^+}\)) per molecule upon being dissolved in water. Sulfuric acid (\(\mathrm{H_2SO_4}\)), on the other hand, has two hydrogen atoms that can be donated as protons when dissolved in water. Thus, the statement is False. Sulfuric acid is not a monoprotic acid; it is a diprotic acid because it can donate two protons per molecule in a solution.

Now, we will examine the second statement by understanding the distinction between weak and strong acids and determining if hydrochloric acid (\(\mathrm{HCl}\)) belongs to the weak acid group. A weak acid is an acid that does not dissociate completely in water, meaning not all acid molecules lose their hydrogen ions (\(\mathrm{H^+}\)) when dissolved in water, leaving a significant amount of un-dissociated acid molecules in the solution. Strong acids, on the other hand, dissociate completely in water, with essentially all the acid molecules losing their hydrogen ions. Hydrochloric acid is a strong acid, which is characterized by its complete dissociation in water: \[\mathrm{HCl \rightarrow H^+ + Cl^{-}}\] Thus, the statement is False. \(\mathrm{HCl}\) is not a weak acid; it is a strong acid due to its complete dissociation in water.

Lastly, let's analyze the third statement and determine if methanol is a base. A base is a substance that can accept a proton (\(\mathrm{H^+}\)), typically releasing a hydroxide ion (\(\mathrm{OH^{-}}\)) in water. Methanol (\(\mathrm{CH_3OH}\)) is an alcohol, specifically the simplest one. In an aqueous solution, methanol does not readily act as a proton acceptor, neither does it release a hydroxide ion. Instead, methanol can act as a solvent or a reactant in various chemical reactions, but it does not possess the characteristics of a base. Thus, the statement is False. Methanol is not a base; it is an alcohol that does not exhibit the proton-accepting behavior of bases.