Chapter 15: Problem 55
A solution of hydrochloric acid is \(0.059 M \mathrm{HCl}\). What is the hydronium-ion concentration at \(25^{\circ} \mathrm{C} ?\) What is the hydroxide-ion concentration at \(25^{\circ} \mathrm{C} ?\)
Short Answer
Expert verified
[H3O+] = 0.059 M; [OH-] 鈮 1.69 脳 10^-13 M.
Step by step solution
01
Understanding the Problem
We are given the concentration of hydrochloric acid as \(0.059 \ M \ \mathrm{HCl}\). Our goal is to find the concentrations of hydronium ions \([H_3O^+]\) and hydroxide ions \([OH^-]\) in this solution at \(25^{\circ} \mathrm{C}\).
02
Calculate the Hydronium Ion Concentration
Since hydrochloric acid is a strong acid, it completely dissociates in water. Therefore, the concentration of hydronium ions \([H_3O^+]\) is equal to the concentration of the acid. So, \([H_3O^+] = 0.059 \, M\).
03
Use the Ion-Product Constant of Water
At \(25^{\circ} \mathrm{C}\), the ion-product constant of water is \(K_w = 1.0 \times 10^{-14}\). Use this to find \([OH^-]\) using the relationship: \([H_3O^+][OH^-] = K_w\).
04
Find the Hydroxide Ion Concentration
Rearrange the expression to solve for \([OH^-]\): \([OH^-] = \frac{K_w}{[H_3O^+]}\). Substituting the values: \([OH^-] = \frac{1.0 \times 10^{-14}}{0.059}\).
05
Perform the Calculation
Divide the ion-product constant by the hydronium ion concentration: \([OH^-] = \frac{1.0 \times 10^{-14}}{0.059} \approx 1.69 \times 10^{-13} \, M\).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Hydrochloric Acid
Hydrochloric acid, often represented as HCl, is a strong acid commonly found in chemistry labs and various industrial applications. At the molecular level, HCl is a simple diatomic molecule consisting of hydrogen and chlorine atoms. When dissolved in water, hydrochloric acid completely ionizes, meaning every HCl molecule dissociates into a hydrogen ion (H鈦) and a chloride ion (Cl鈦).
This property of complete dissociation makes HCl a strong acid, unlike weak acids that only partially ionize in solution. As a result, in solutions of hydrochloric acid, the concentration of hydrogen ions will be equivalent to the initial concentration of HCl, because there are no undissociated molecules left.
Important points about hydrochloric acid include:
This property of complete dissociation makes HCl a strong acid, unlike weak acids that only partially ionize in solution. As a result, in solutions of hydrochloric acid, the concentration of hydrogen ions will be equivalent to the initial concentration of HCl, because there are no undissociated molecules left.
Important points about hydrochloric acid include:
- It causes its solutions to have a low pH, which indicates high acidity.
- Its complete dissociation makes it useful in various titration processes to determine unknown concentrations of bases or other substances.
- Due to its corrosive nature, appropriate safety measures should be taken when handling this substance.
Hydronium Ion Concentration
The hydronium ion, denoted as (H鈧僌鈦), is the form in which protons (H鈦 ions) typically exist in aqueous solutions. The hydronium ion forms when a hydrogen ion associates with a water molecule (H鈧侽).
For strong acids like hydrochloric acid, the hydronium ion concentration is equal to the concentration of the acid itself, due to complete dissociation. For example, in a 0.059 M HCl solution, the (H鈧僌鈦) concentration is also 0.059 M.
Understanding hydronium ion concentration is crucial in calculating the pH of a solution, a measure of its acidity. The pH is calculated using the formula: \[ pH = -\log [H鈧僌鈦篯 \]. For our example, the pH would be calculated as:\[ pH = -\log(0.059) \].
Key takeaways about hydronium ion concentration include:
For strong acids like hydrochloric acid, the hydronium ion concentration is equal to the concentration of the acid itself, due to complete dissociation. For example, in a 0.059 M HCl solution, the (H鈧僌鈦) concentration is also 0.059 M.
Understanding hydronium ion concentration is crucial in calculating the pH of a solution, a measure of its acidity. The pH is calculated using the formula: \[ pH = -\log [H鈧僌鈦篯 \]. For our example, the pH would be calculated as:\[ pH = -\log(0.059) \].
Key takeaways about hydronium ion concentration include:
- A higher (H鈧僌鈦) concentration implies a more acidic solution.
- The hydronium ion concentration is an essential factor in determining the acidity and pH of solutions.
- Since strong acids fully dissociate, (H鈧僌鈦) concentration can be directly used to compute pH.
Hydroxide Ion Concentration
The hydroxide ion, (OH鈦), is the key component in basic or alkaline solutions. In water, the product of hydronium ion concentration and hydroxide ion concentration remains constant at a given temperature. This product is known as the ion-product constant of water (K_w). At 25掳C, K_w is given as 1.0 脳 10鈦宦光伌.
In the context of a 0.059 M HCl solution, the hydronium ion concentration is 0.059 M, as previously calculated. To find the hydroxide ion concentration, we utilize the relationship:
\[ [H鈧僌鈦篯[OH鈦籡 = K_w \].
Plugging in values, we rearrange to solve for [OH鈦籡:
\[ [OH鈦籡 = \frac{K_w}{[H鈧僌鈦篯} \]
Thus, [OH鈦籡 = \frac{1.0 脳 10鈦宦光伌}{0.059} 鈮 1.69 脳 10鈦宦孤 M.
Important points about hydroxide ion concentration include:
In the context of a 0.059 M HCl solution, the hydronium ion concentration is 0.059 M, as previously calculated. To find the hydroxide ion concentration, we utilize the relationship:
\[ [H鈧僌鈦篯[OH鈦籡 = K_w \].
Plugging in values, we rearrange to solve for [OH鈦籡:
\[ [OH鈦籡 = \frac{K_w}{[H鈧僌鈦篯} \]
Thus, [OH鈦籡 = \frac{1.0 脳 10鈦宦光伌}{0.059} 鈮 1.69 脳 10鈦宦孤 M.
Important points about hydroxide ion concentration include:
- It is inversely related to [H鈧僌鈦篯 due to the K_w equilibrium.
- This relationship is key to understanding the balance of acidity and basicity in a solution.
- Calculating [OH鈦籡 from K_w helps understand the solution's overall chemical nature and pH.