Chapter 16: Problem 38
Calculate the \(\mathrm{pH}\) of an aqueous solution at \(25^{\circ} \mathrm{C}\) that is (a) \(0.12 \mathrm{M}\) in \(\mathrm{HCl}\), (b) \(2.4 \mathrm{M}\) in \(\mathrm{HNO}_{3}\), and (c) \(3.2 \times 10^{-4} \mathrm{M}\) in \(\mathrm{HClO}_{4}\).
Short Answer
Expert verified
(a) pH 鈮 0.92; (b) pH 鈮 -0.38; (c) pH 鈮 3.5.
Step by step solution
01
Understanding Strong Acids
Hydrochloric acid (HCl), nitric acid (HNO鈧), and perchloric acid (HClO鈧) are all strong acids. This means they dissociate completely in water. For strong acids, the concentration of hydrogen ions [H鈦篯 is equal to the concentration of the acid.
02
Calculating pH for 0.12 M HCl
Since HCl is a strong acid and dissociates completely, [H鈦篯 = [HCl] = 0.12 M. The pH is calculated using the formula: \[\text{pH} = -\log [\text{H}^+]\]Substitute [H鈦篯 with 0.12:\[\text{pH} = -\log(0.12) \approx 0.92\]
03
Calculating pH for 2.4 M HNO鈧
Similarly, for HNO鈧, [H鈦篯 = [HNO鈧僝 = 2.4 M. Calculate the pH:\[\text{pH} = -\log(2.4) \approx -0.38\]Since negative pH values are possible with strong concentrations, this result is reasonable.
04
Calculating pH for 3.2 x 10鈦烩伌 M HClO鈧
For HClO鈧, [H鈦篯 = [HClO鈧刔 = 3.2 \times 10^{-4} M. Calculate the pH:\[\text{pH} = -\log(3.2 \times 10^{-4}) \approx 3.5\]
05
Interpreting Results
For a strong acid, the lower the concentration, the higher the pH. Even for strong acids, at very low concentrations, pH can be greater than zero. This is reflected in the fact that 3.2 x 10鈦烩伌 M HClO鈧 results in a pH of about 3.5.
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with 91影视!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Strong Acids
When we talk about strong acids, we refer to acids that completely dissociate in water, releasing all their hydrogen ions. Three prominent strong acids that often appear in chemistry studies are hydrochloric acid (HCl), nitric acid (HNO鈧), and perchloric acid (HClO鈧).
These acids are characterized by their ability to completely ionize in an aqueous solution. This means that when you dissolve a strong acid in water, you can assume that its concentration is equal to the concentration of hydrogen ions \([\text{H}^+]\).
Understanding this property simplifies the calculation of pH, making it straightforward: we use the initial concentration of the acid to determine that of the hydrogen ions directly.
These acids are characterized by their ability to completely ionize in an aqueous solution. This means that when you dissolve a strong acid in water, you can assume that its concentration is equal to the concentration of hydrogen ions \([\text{H}^+]\).
Understanding this property simplifies the calculation of pH, making it straightforward: we use the initial concentration of the acid to determine that of the hydrogen ions directly.
Hydrogen Ion Concentration
Hydrogen ion concentration, represented as \([\text{H}^+]\), is a crucial factor in determining the acidity of a solution. For strong acids, calculating \([\text{H}^+]\) becomes a simple task since the acid dissociates completely.
This means the concentration of hydrogen ions is equal to the concentration of the acid itself. For example, if you have a 0.12 M solution of HCl, the hydrogen ion concentration is also 0.12 M.
Measuring \([\text{H}^+]\) lets us calculate the pH by using the formula \(\text{pH} = -\log [\text{H}^+]\). This logarithmic measure gives us an easy-to-understand scale of acidity.
This means the concentration of hydrogen ions is equal to the concentration of the acid itself. For example, if you have a 0.12 M solution of HCl, the hydrogen ion concentration is also 0.12 M.
Measuring \([\text{H}^+]\) lets us calculate the pH by using the formula \(\text{pH} = -\log [\text{H}^+]\). This logarithmic measure gives us an easy-to-understand scale of acidity.
HCl Dissociation
Hydrochloric acid (HCl) is a prototypical strong acid, demonstrating the concept of complete dissociation. When HCl dissolves in water, it splits entirely into hydrogen ions and chloride ions.
The chemical equation for this process is:
Thus, the pH can be calculated as:
The chemical equation for this process is:
- \(\text{HCl} \rightarrow \text{H}^+ + \text{Cl}^-\)
Thus, the pH can be calculated as:
- \(\text{pH} = -\log(0.12) \approx 0.92\)
HNO鈧 Dissociation
Nitric acid (HNO鈧) shares the behavior of strong acids by also fully dissociating in water. In this scenario, it separates into hydrogen and nitrate ions.
The dissociation equation is:
The calculation of the pH follows:
The dissociation equation is:
- \(\text{HNO}_3 \rightarrow \text{H}^+ + \text{NO}_3^-\)
The calculation of the pH follows:
- \(\text{pH} = -\log(2.4) \approx -0.38\)
HClO鈧 Dissociation
Perchloric acid (HClO鈧) is another example of a strong acid, dissociating entirely in aqueous solutions into hydrogen ions and perchlorate ions.
The dissociation process can be represented by the equation:
This results in a pH calculation:
The dissociation process can be represented by the equation:
- \(\text{HClO}_4 \rightarrow \text{H}^+ + \text{ClO}_4^-\)
This results in a pH calculation:
- \(\text{pH} = -\log(3.2 \times 10^{-4}) \approx 3.5\)