Question

What is the concentration of \(\mathrm{OH}^{-}\)in each of the following solutions? (a) \(0.0010 \mathrm{M} \mathrm{KOH}\) (b) \(0.0050 \mathrm{M} \mathrm{NaOH}\) (c) \(0.0010 \mathrm{MHCl}\)

Short answer

(a) The concentration of OH- in 0.0010 M KOH is 0.0010 M (b) The concentration of OH- in 0.0050 M NaOH is 0.0050 M. (c) The concentration of OH- in 0.0010 M HCl is 1 * 10^-7 M

Step-by-step solution

Analyze KOH Solution

In a solution, Potassium hydroxide (KOH) dissociates into K+ and OH- ions. Being a strong base, it completely ionizes, so the concentration of OH-, or [OH-], is the same as initially given KOH concentration. Therefore, [OH-] = 0.0010 M.

Analyze NaOH Solution

Similarly to KOH, Sodium hydroxide (NaOH) also dissociates into Na+ and OH- ions. It is also a strong base and completely ionizes in solution. Therefore, the [OH-] is the same as the initially given NaOH concentration. Hence, [OH-] = 0.0050 M.

Analyze HCl Solution

Hydrochloric Acid (HCl) is an acid and will completely ionize in solution to form H+ ions and Cl- ions. As an acid, it does not produce OH- ions. Instead, the OH concentration depends on the water's self-ionization, which is 1 * 10^-7 M at 25°C. Thus, [OH-] = 1 * 10^-7 M.

Key concepts

Acid-Base Chemistry

Acid-base chemistry revolves around substances that donate or accept protons (H+ ions). Acids, like hydrochloric acid (HCl), donate protons, while bases, such as potassium hydroxide (KOH) and sodium hydroxide (NaOH), accept them. When these substances dissolve in water, they undergo a process known as ionization. Acids release H+ ions whereas bases release hydroxide ions (OH-) into the solution.

The strength of an acid or base depends on its ability to ionize in water. Strong acids and bases, like HCl, KOH, and NaOH mentioned in the exercise, ionize completely, meaning every molecule of the substance dissociates into ions. In contrast, weak acids and bases only partially ionize, leading to an equilibrium between the ionized and the non-ionized form in the solution.

In the given examples, KOH and NaOH are strong bases, so the concentration of hydroxide ions in the solution ([OH-]) is equivalent to the concentration of the base itself. For HCl, a strong acid, the situation is different. It does not produce hydroxide ions; instead, it increases the concentration of H+ ions.

Molarity

Molarity is a measure of concentration used in chemistry to express the amount of a solute in a given volume of solution. It is defined as the number of moles of solute per liter of solution. The unit for molarity is moles per liter (M). In the context of our exercise, molarity gives us the concentration of the strong base or acid in the solution.

For example, when we say a solution is 0.0010 M KOH, it means there are 0.0010 moles of potassium hydroxide dissolved in every liter of the solution. Given that KOH and NaOH are strong bases that completely ionize in solution, the molarity of the base directly translates to the molarity of hydroxide ions released. Therefore, determining [OH-] for these bases is a simple and direct process.

It's crucial to remember that molarity can change with the volume of the solution; it's not just the amount of solute that matters, but the ratio of solute to solution volume.

Strong Base Ionization

Strong base ionization is a fundamental concept in acid-base chemistry which captures the ability of strong bases to completely dissociate into their constituent ions in an aqueous solution. Ionization is the process that increases the concentration of ions in the solution, which for bases includes hydroxide ions (OH-).

Complete Ionization

When we talk about strong bases such as KOH or NaOH, complete ionization is implied. This means that every molecule of the strong base breaks apart to release hydroxide ions into the solution. For instance, KOH dissociates into K+ and OH- ions. As there are no remaining KOH molecules in the solution, the original concentration of the base (measured in molarity) is also the concentration of hydroxide ions.

Calculating Hydroxide Ion Concentration

The hydroxide ion concentration is vital for understanding the pH level and basicity of the solution. In a 0.0050 M NaOH solution, since the NaOH fully ionizes, the [OH-] is also 0.0050 M. Note that this is specific to strong bases; if we were dealing with a weak base, the concentration of OH- would be less than the concentration of the base due to incomplete ionization.

Understanding these concepts is key to analyzing solutions and predicting their behaviors in various chemical reactions and processes.