Question

In \(0.10 \mathrm{M} \quad \mathrm{CH}_{3} \mathrm{NH}_{2}(\mathrm{aq}), \quad\) (a) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=0.10 \mathrm{M}\) (b) \(\left[\mathrm{OH}^{-}\right]=0.10 \mathrm{M} ;(\mathrm{c}) \mathrm{pH}<7 ;(\mathrm{d}) \mathrm{pH}<13\).

Short answer

Only the statement in case (d) (\(\mathrm{pH}<13\)) is true in the case of \(0.10 \, \mathrm{M}\) \( \mathrm{CH}_{3} \mathrm{NH}_{2} (\mathrm{aq}) \, \) solution. Statements in case (a), (b) and (c) are not true.

Step-by-step solution

Analyze Case (a)

In the case (a), it is given that \([H_3O^{+}]=0.10 M\). In an aqueous solution of methylamine, there would not be any hydronium ions (\(H_3O^{+}\)) as it is a base and does not have any acidic properties. Hence, \([H_3O^{+}]\) cannot be equal to 0.10 M. This statement is not true.

Analyze Case (b)

In the case (b), it is given that \([OH^{-}]=0.10\, M\). Methylamine being a weak base will yield lower concentration of \(OH^-\) ions, certainly much lower than the initial concentration of methylamine itself. Hence, \([OH^{-}]\) cannot be equal to 0.10M. This statement is also not true.

Analyze Case (c)

In the case (c), it is stated \(\mathrm{pH}<7\). This is a characteristic of an acidic solution. However, methylamine is a base and not an acid, so the statement is not true in this case either.

Analyze Case (d)

Finally in the case (d), it is stated \(\mathrm{pH}<13\). A solution with \(\mathrm{pH}\) value less than 14 but more than 7 is a basic solution. This one is the only accurate statement related to the solution of methylamine, since it is a weak base and its \(\mathrm{pH}\) value is expected to be greater than 7 and less than 13.

Key concepts

pH Scale

The pH scale is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. It ranges from 0 to 14, with 7 being neutral. pH values less than 7 indicate an acidic solution, while values greater than 7 denote a basic or alkaline solution. The pH scale is calculated using the formula \( pH = -\log[H_3O^+] \), where \( [H_3O^+] \) is the concentration of hydronium ions in moles per liter. A low pH corresponds to high hydronium ion concentration and vice versa.

When it comes to determining the pH of weak bases such as methylamine \( (CH_3NH_2) \), it is important to remember that they partially dissociate in water. This partial dissociation leads to a lower hydronium ion concentration and thus a pH value above 7. The exercise mentioned previously erred in stating that the pH of a methylamine solution would be less than 7, as that would imply the solution is acidic, which is not the case for a weak base.

Weak Bases

Weak bases are substances that partially accept protons when dissolved in water. Unlike strong bases, which dissociate completely, weak bases do not fully ionize in solution. Their incomplete ionization results in a less concentrated \( [OH^-] \) than the initial concentration of the base itself. This concept is crucial when dealing with weak bases in aqueous solutions, as it will influence the solutions' pH and \( [OH^-] \) values.

For instance, methylamine in water will not produce an \( [OH^-] \) of 0.10M as initially stated in the exercise. The exercise improvement advice would be to consider the dissociation constant (Kb) of the weak base to calculate the expected concentration of hydroxide ions in the solution.

Hydroxide Ion Concentration

Hydroxide ion concentration, represented as \( [OH^-] \), is a measure of how many hydroxide ions are present in a solution. It is a key factor in determining the solution's basicity. For strong bases, the \( [OH^-] \) typically equals the concentration of the base. However, for weak bases, the concentration of hydroxide ions produced will be less than the concentration of the base due to partial dissociation.

In the context of the exercise, the given concentration of \( [OH^-] \) at 0.10M is incorrect because methylamine will not completely dissociate. Instead, we need to use the base dissociation constant (Kb) and an equilibrium calculation to find the actual hydroxide ion concentration. This approach will lead to a more accurate determination of the solution’s pH.

Acidic and Basic Properties

Acidic and basic properties in chemical solutions define whether a substance is an acid or a base. Acids are proton donors and increase the hydronium ion concentration in a solution, thereby lowering the pH. Bases, on the other hand, are proton acceptors. They increase the hydroxide ion concentration and raise the pH of the solution above 7.

In aqueous solutions, bases can be classified as strong or weak based on their ability to accept protons. Strong bases fully dissociate, while weak bases, like methylamine, only partially dissociate. As seen in the exercise, mistakenly attributing acidic properties, such as a pH less than 7, to a weak base overlooks the fundamental concept that bases increase pH. Understanding the nature of acidic and basic properties helps to correct such misconceptions.