Chapter 15: Problem 70
What is the pH of \(5.00 \times 10^{-4} \mathrm{MH}_{2} \mathrm{SO}_{4} ?\)
Short Answer
Expert verified
Answer: The pH of the 5.00 x 10^-4 M H鈧係O鈧 solution is approximately 3.30.
Step by step solution
01
Calculate the initial concentration of H鈦 ions from the first dissociation of H鈧係O鈧
The first step in calculating the pH of a solution of H鈧係O鈧 is to determine the initial concentration of H鈦 ions formed when one mole of acid dissociates into ions. The dissociation equation for H鈧係O鈧 is:
\[
\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{H}^{+} + \mathrm{HSO}_{4}^{-}
\]
The provided concentration is \(5.00 \times 10^{-4} \mathrm{M}\), and since every 1 mole of H鈧係O鈧 will produce 1 mole of H鈦 ions, the initial concentration of H鈦 ions will be equal to the concentration of H鈧係O鈧. Therefore, the concentration of H鈦 ions is:
\[
\mathrm{[H^{+}]}_1 = 5.00 \times 10^{-4} \mathrm{M}
\]
02
Calculate the concentration of H鈦 ions from the second dissociation of HSO鈧勨伝
In the second step, we need to take into account that the HSO鈧勨伝 ion can further dissociate to form an additional H鈦 ion. The dissociation equation for HSO鈧勨伝 is:
\[
\mathrm{HSO}_{4}^{-} \rightarrow \mathrm{H}^{+} + \mathrm{SO}_{4}^{2-}
\]
However, this reaction does not proceed completely as in the first step. The equilibrium constant for this dissociation, K鈧, is \(1.2 \times 10^{-2}\). To find the concentration of H鈦 ions formed from this step, we can use an ICE (Initial, Change, Equilibrium) table.
03
Calculate the total concentration of H鈦 ions
Since \(K_2\) is relatively small compared to the concentration of H鈦 ions in step 1, the equilibrium concentration of H鈦 ions formed from the HSO鈧勨伝 dissociation will be negligible as it will have limited effect on the pH calculation. Thus, the total concentration of H鈦 ions in the solution will remain the same as after the first dissociation:
\[
\mathrm{[H^{+}]}_{\text{total}} \approx \mathrm{[H^{+}]}_1 = 5.00 \times 10^{-4} \mathrm{M}
\]
04
Calculate the pH of the solution
Now that we have determined the total concentration of H鈦 ions in the solution, we can calculate the pH using the pH definition:
\[
\mathrm{pH} = -\log \mathrm{[H^{+}]}
\]
Plugging in the H鈦 ion concentration:
\[
\mathrm{pH} = -\log (5.00 \times 10^{-4})
\]
Calculating the pH:
\[
\mathrm{pH} \approx 3.30
\]
So, the pH of the \(5.00 \times 10^{-4} \mathrm{MH}_{2} \mathrm{SO}_{4}\) solution is approximately 3.30.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Acid Dissociation
Acid dissociation refers to the process in which a compound breaks apart in water, releasing ions. For sulfuric acid, H鈧係O鈧, dissociation is a critical step in determining the concentration of hydrogen ions (H鈦) and subsequently the pH of the solution.
In a sequential process, sulfuric acid undergoes two dissociation reactions. The initial dissociation is nearly complete, where H鈧係O鈧 splits into a hydrogen ion and bisulfate ion (HSO鈧勨伝):
The second dissociation is less complete. Here, the bisulfate ion can further release a hydrogen ion:
In a sequential process, sulfuric acid undergoes two dissociation reactions. The initial dissociation is nearly complete, where H鈧係O鈧 splits into a hydrogen ion and bisulfate ion (HSO鈧勨伝):
- H鈧係O鈧 鈫 H鈦 + HSO鈧勨伝
The second dissociation is less complete. Here, the bisulfate ion can further release a hydrogen ion:
- HSO鈧勨伝 鈬 H鈦 + SO鈧劼测伝
Equilibrium Constant
The equilibrium constant, represented as K, showcases how far a reaction proceeds before reaching a state of equilibrium. For sulfuric acid, the second dissociation step, where HSO鈧勨伝 ionizes into H鈦 and SO鈧劼测伝, is characterized by its equilibrium constant, known as K鈧.
The value of K鈧, being 1.2 x 10鈦宦, indicates that this ionization is not complete and some bisulfate ions remain undissociated in solution. A smaller K value demonstrates a tendency of the reaction to prefer the reactants over the products at equilibrium.
In practical terms, because K鈧 is relatively small in comparison to the concentration of H鈦 ions from the first dissociation, its role in calculating the pH of diluted sulfuric acid solutions becomes less significant. Hence, the total hydrogen ion concentration from this step is effectively negligible when determining the pH.
The value of K鈧, being 1.2 x 10鈦宦, indicates that this ionization is not complete and some bisulfate ions remain undissociated in solution. A smaller K value demonstrates a tendency of the reaction to prefer the reactants over the products at equilibrium.
In practical terms, because K鈧 is relatively small in comparison to the concentration of H鈦 ions from the first dissociation, its role in calculating the pH of diluted sulfuric acid solutions becomes less significant. Hence, the total hydrogen ion concentration from this step is effectively negligible when determining the pH.
Sulfuric Acid
Sulfuric acid (H鈧係O鈧) is a strong diprotic acid, meaning it can release two protons (H鈦) per molecule. Its strength lies in the first dissociation, which is virtually complete:
Sulfuric acid finds its application in various industries due to its reactivity and ability to ionize completely during its first ionization. The second dissociation, though less complete, still plays a role in chemical reactions where additional H鈦 ions are utilized in the reaction mechanism.
Understanding these characteristics is crucial, especially in contexts where the acid's concentration significantly affects the pH level and the chemical behavior of the solution.
- H鈧係O鈧 鈫 H鈦 + HSO鈧勨伝
Sulfuric acid finds its application in various industries due to its reactivity and ability to ionize completely during its first ionization. The second dissociation, though less complete, still plays a role in chemical reactions where additional H鈦 ions are utilized in the reaction mechanism.
Understanding these characteristics is crucial, especially in contexts where the acid's concentration significantly affects the pH level and the chemical behavior of the solution.
ICE Table
ICE tables, standing for Initial, Change, and Equilibrium, are systematic strategies to keep track of concentrations during reactions reaching equilibrium.
For the dissociation of HSO鈧勨伝 in sulfuric acid, the ICE table allows us to calculate the concentration changes and establish the final equilibrium concentrations:
For the dissociation of HSO鈧勨伝 in sulfuric acid, the ICE table allows us to calculate the concentration changes and establish the final equilibrium concentrations:
- Initial: Start with initial concentrations before any reaction occurs.
- Change: Account for the changes in concentrations as the system progresses towards equilibrium.
- Equilibrium: Determine the concentrations once the reaction reaches equilibrium.