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A solution is \(0.25 \mathrm{M} \mathrm{KOH}\). What are the concentrations of \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{OH}^{-}\) in this solution?

Short Answer

Expert verified
[OH鈦籡 is 0.25 M and [H鈧僌鈦篯 is 4.0 脳 10鈦宦光伌 M.

Step by step solution

01

Understanding the Relationship between KOH and OH鈦

Potassium hydroxide (KOH) is a strong base and dissociates completely in water. This means that the concentration of OH鈦 ions in the solution is equal to the concentration of KOH. Therefore, \[[\text{OH}^-] = 0.25 \text{ M}.\]
02

Using Ion Product of Water

We know that the ion product of water (\( K_w \) ) at 25掳C is \( 1.0 \times 10^{-14} \). For any aqueous solution:\[[\text{H}_3\text{O}^+][\text{OH}^-] = 1.0 \times 10^{-14}\]Since the \([\text{OH}^-]\) is 0.25 M, we can solve for \([\text{H}_3\text{O}^+]\).
03

Calculating the Concentration of H鈧僌鈦

Substitute \([\text{OH}^-] = 0.25 \text{ M}\) into the ion product of water equation:\[[\text{H}_3\text{O}^+](0.25) = 1.0 \times 10^{-14}\]Solving for \([\text{H}_3\text{O}^+]\), we get:\[[\text{H}_3\text{O}^+] = \frac{1.0 \times 10^{-14}}{0.25} = 4.0 \times 10^{-14} \text{ M}.\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Strong Base
Strong bases are substances that completely dissociate into their ions in solution. They release hydroxide ions (OH鈦) into the water, which significantly increases the solution's pH level, making it more basic. KOH, or potassium hydroxide, is a classic example of a strong base.
What makes a base 'strong' is its ability to fully ionize in water. Therefore, for every mole of KOH dissolved in water, one mole of OH鈦 ions is produced. This concept is crucial because it allows for the straightforward calculation of hydroxide ion concentration just by knowing the concentration of the strong base.
In a solution of KOH, since it completely dissociates, the concentration of OH鈦 is precisely the same as the concentration of the KOH originally added. This is a cornerstone principle when dealing with strong bases.
Ion Product of Water
The ion product of water, represented as \( K_w \), is a critical equilibrium constant in chemical reactions involving aqueous solutions. At 25掳C, it has a consistent value of \( 1.0 \times 10^{-14} \). This value arises from the self-ionization of water, where water partially dissociates into hydronium ions (H鈧僌鈦) and hydroxide ions (OH鈦).
The formula for the ion product of water is: \[[\text{H}_3\text{O}^+][\text{OH}^-] = 1.0 \times 10^{-14}\]This equation is always valid for any aqueous solution at room temperature. It serves as a relationship between the concentrations of H鈧僌鈦 and OH鈦 in the solution, allowing you to calculate one if the other is known.
Understanding this relationship aids in determining the acidity or basicity of a solution, providing the foundation for many aspects of chemistry related to reactions in water.
Hydroxide Ions
Hydroxide ions (OH鈦) are negatively charged and are one of the key contributors to a solution's pH level. They are produced when substances, especially strong bases like KOH, dissolve in water. In a typical strong base like KOH, each molecule of the base will fully dissociate to provide one hydroxide ion.
The presence of hydroxide ions is what characterizes a solution as being basic, as opposed to acidic solutions which are characterized by a higher concentration of hydronium ions. In the exercise provided, since KOH fully dissociates, the concentration of OH鈦 equals the concentration of KOH, which was given as 0.25 M.
Knowing the concentration of hydroxide ions is essential for understanding the process of neutralization, where these ions react with hydronium ions to form water, thereby shifting the pH towards a neutral value.
Hydronium Ion Concentration
Hydronium ions (H鈧僌鈦) are pivotal in understanding the acidity of a solution. They are formed when a proton (H鈦) associates with a water molecule. In neutral water at 25掳C, the concentration of H鈧僌鈦 is equal to that of OH鈦, resulting in a neutral pH.The concentration of hydronium ions in a solution changes significantly when strong acids or bases are present. For a strong base like KOH, the concentration of H鈧僌鈦 is very low compared to that of OH鈦. Using the ion product of water \([\text{H}_3\text{O}^+][\text{OH}^-] = 1.0 \times 10^{-14}\), you can calculate the concentration of H鈧僌鈦 if OH鈦 is known.
In the given exercise, OH鈦 concentration was 0.25 M, and using the ion product constant of water, we determined the H鈧僌鈦 concentration as \(4.0 \times 10^{-14} \text{ M}\). This low concentration indicates a highly basic solution, as expected from a strong base like KOH.

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