For nitrous acid, HNO2, Ka = 4.0 x 10^-4. Calculate the pH of 0.54 M HNO2. a. 1.83
b. 0.27
C. 3.67
d. 12.17
e. none of these
The Correct Answer and Explanation is :
To calculate the pH of a 0.54 M solution of nitrous acid (HNO₂), we follow these steps:
Step 1: Set Up the ICE Table
Nitrous acid dissociates in water as follows:
[
HNO_2 \rightleftharpoons H^+ + NO_2^-
]
Let’s define the initial concentration of HNO₂ as 0.54 M, and the initial concentrations of H⁺ and NO₂⁻ as 0 M.
| Species | Initial (M) | Change (M) | Equilibrium (M) |
|---|---|---|---|
| HNO₂ | 0.54 | -x | 0.54 – x |
| H⁺ | 0 | +x | x |
| NO₂⁻ | 0 | +x | x |
Step 2: Write the Ka Expression
[
Ka = \frac{[H^+][NO_2^-]}{[HNO_2]}
]
Substituting the given values:
[
4.0 \times 10^{-4} = \frac{x \cdot x}{0.54 – x}
]
Since ( x ) is small compared to 0.54, we approximate 0.54 – x ≈ 0.54:
[
4.0 \times 10^{-4} = \frac{x^2}{0.54}
]
Step 3: Solve for x
[
x^2 = (4.0 \times 10^{-4}) (0.54)
]
[
x^2 = 2.16 \times 10^{-4}
]
[
x = \sqrt{2.16 \times 10^{-4}}
]
[
x = 0.0147 \text{ M}
]
Since x represents [H⁺], we find the pH:
[
pH = -\log (0.0147)
]
[
pH = 3.67
]
Final Answer:
[
\mathbf{3.67} \quad (C)
]
Explanation (300 Words)
Nitrous acid (HNO₂) is a weak acid, meaning it only partially dissociates in water. The acid dissociation constant (Ka) is 4.0 × 10⁻⁴, which helps determine the extent of ionization. To find the pH of a 0.54 M solution of HNO₂, we use an ICE table (Initial, Change, Equilibrium) to track the concentration changes.
Initially, HNO₂ is present at 0.54 M, while the concentrations of H⁺ and NO₂⁻ are 0 M. As the acid dissociates, some molecules break into H⁺ (protons) and NO₂⁻ (conjugate base). We define the concentration of H⁺ formed as x and set up the equilibrium equation:
[
Ka = \frac{x^2}{0.54 – x}
]
Since Ka is small, x is small compared to 0.54, allowing the approximation 0.54 – x ≈ 0.54 for easier calculations. Solving for x, we get 0.0147 M, which represents the concentration of hydrogen ions in solution.
Finally, we calculate pH = -log[H⁺], giving pH = 3.67. The correct answer is option C. This makes sense because nitrous acid is a weak acid, meaning its pH should be greater than 1 but less than 7.
This approach is widely used in chemistry to determine the pH of weak acids, especially in buffer and equilibrium calculations. Approximations simplify the process, but for very diluted solutions, a quadratic equation may be necessary.
Now, let’s generate an image illustrating this calculation.
Here is the educational chemistry diagram illustrating the pH calculation of a 0.54 M solution of nitrous acid (HNO₂). The image includes an ICE table, the Ka expression, and a step-by-step solution leading to the final pH value of 3.67. Let me know if you need any modifications or further explanations!
