Question

(a) What is a strong base? (b) A solution is labeled \(0.035 \mathrm{M} \mathrm{Sr}(\mathrm{O} \mathrm{H})_{2}\). What is \(\left[\mathrm{OH}^{-}\right]\) for the solution? (c) Is the following statement true or false? Because \(\mathrm{Mg}(\mathrm{OH})_{2}\) is not very soluble, it cannot be a strong base. Explain.

Short answer

(a) A strong base is a substance that dissociates completely in an aqueous solution, releasing a hydroxide ion (OH-) for every molecule or ion of the base, resulting in a high pH value. (b) The concentration of OH- ions in the 0.035 M Sr(OH)2 solution is 0.070 M. (c) The statement is true; Mg(OH)2 is not a strong base because it does not dissociate completely, even if it is sparingly soluble. The strength of a base is defined by complete dissociation, not solubility.

Step-by-step solution

(a) Definition of a strong base

A strong base is a substance that dissociates completely in an aqueous solution, releasing a hydroxide ion (OH-) for every molecule or ion of the base. In other words, a strong base has a 100% ionization or dissociation rate, resulting in a high concentration of hydroxide ions (OH-) in the solution, which leads to a high pH value.

(b) Calculating [OH-] in a 0.035 M Sr(OH)2 solution

Given the concentration of a Sr(OH)2 solution as 0.035 M, we need to determine the concentration of OH- ions. Strontium hydroxide, Sr(OH)2, is a strong base, so it will dissociate completely in the solution. The equation for the dissociation of Sr(OH)2 is: \[ \mathrm{Sr}(\mathrm{O} \mathrm{H})_{2} \rightarrow \mathrm{Sr}^{2+} + 2\mathrm{OH}^- \] From the equation, one mole of Sr(OH)2 will produce 2 moles of OH- ions. Therefore, the concentration of OH- ions in the solution can be calculated as follows: \[ [\mathrm{OH}^-] = 2 \times [\mathrm{Sr(OH)_2}] \] Now, substituting the given concentration of Sr(OH)2: \[ [\mathrm{OH}^-] = 2 \times 0.035\,\mathrm{M} \]

(b) [OH-] concentration

Calculate the concentration of OH- ions: \[ [\mathrm{OH}^-] = 0.070\,\mathrm{M} \] So, the concentration of OH- ions in the 0.035 M Sr(OH)2 solution is 0.070 M.

(c) Statement analysis: Mg(OH)2 solubility and strength as a base

The statement is: "Because Mg(OH)2 is not very soluble, it cannot be a strong base." We need to determine if this statement is true or false and provide an explanation. The strength of a base depends on its ability to dissociate completely in a solution to form hydroxide ions. Mg(OH)2 is a sparingly soluble base, meaning it does not dissolve completely in water. When it does dissolve, it partially dissociates into Mg2+ and OH- ions. However, its low solubility does not necessarily determine its strength as a base. A strong base is defined by complete dissociation, not solubility. Since Mg(OH)2 does not dissociate completely in water, it is considered to be a weak base.

(c) Statement evaluation

The statement is true; Mg(OH)2 is not a strong base because it does not dissociate completely, even if it is sparingly soluble. The low solubility in itself is not what defines the strength of a base, but it does have an indirect effect since the weak dissociation results in a lower hydroxide ion concentration in the solution, and thus, a weak base.

Key concepts

Base Dissociation

Understanding base dissociation is crucial when dealing with bases in chemistry. This process refers to the separation of a base into its component ions in a solution. For example, when a base like sodium hydroxide (NaOH) dissolves in water, it disassociates into a sodium ion (Na⁺) and a hydroxide ion (OH^-).

This dissociation is complete in strong bases, meaning they release all of their hydroxide ions into the solution. The dissociation equation for a strong base like NaOH is represented as:
\[ \mathrm{NaOH} \rightarrow \mathrm{Na}^+ + \mathrm{OH}^- \]
Such complete disassociation makes the solution highly alkaline, which is why these bases are considered 'strong'. It's the hydroxide ions that are particularly important as they are responsible for the basic nature of the solution.

Hydroxide Ion Concentration

The hydroxide ion concentration, often represented as \( [\mathrm{OH}^-] \), is a measure of how many hydroxide ions are present in a solution. It's a critical factor in determining the pH of a solution, which tells us how acidic or basic a solution is. For strong bases, this concentration is directly proportional to the strength of the base, since they dissociate fully in solution.

For a given concentration of a strong base, one can calculate the concentration of hydroxide ions by considering the stoichiometry of the dissociation reaction. The higher the hydroxide ion concentration, the more basic the solution, and therefore the higher the pH.

Solubility and Base Strength

Many students often confuse solubility with base strength, but they are two distinct concepts. Solubility refers to how well a substance can dissolve in a solvent like water. Base strength, on the other hand, is determined by how completely a base dissociates to produce hydroxide ions.

Just because a base doesn't dissolve well in water doesn't mean it's not a strong base. Conversely, a highly soluble base might not be a strong one if it doesn't fully dissociate.

The Case of Magnesium Hydroxide

Take magnesium hydroxide, Mg(OH)₂, for instance. It has low solubility in water, meaning only a small amount will dissolve. When it does dissolve, it doesn't disassociate completely, producing relatively few hydroxide ions. Thus, despite its low solubility, it's considered a weak base due to its partial dissociation.

Weak vs Strong Bases

The difference between weak and strong bases lies in their ability to dissociate in solution. A strong base, like potassium hydroxide (KOH), dissociates completely in water, producing a high concentration of hydroxide ions. This results in a high pH level of the solution. On the other hand, a weak base, such as ammonia (NH₃), only partially dissociates, leading to fewer hydroxide ions and a lower pH.

A base's strength is important in many chemical reactions, such as titrations, where knowing the complete dissociation of the strong base ensures accurate calculations for determining an unknown concentration of an acid.