`[H^(+)]` =`sqrt((K_(w)K_(a))/C)` is suitable for
`[H^(+)]` =`sqrt((K_(w)K_(a))/C)` is suitable for
A
`NaCl,NH_(4)Cl`
B
`CH_(3)COONa,NaCN`
C
`CH_(3)COONa,(NH_(4))_(2)SO_(4)`
D
`CH_(3)COONH_(4),(NH_(4))_(2)CO_(3)`
Text Solution
AI Generated Solution
The correct Answer is:
To determine the conditions under which the equation \([H^+] = \sqrt{\frac{K_w K_a}{C}}\) is valid, we need to analyze the salts provided in the options and their corresponding acid-base properties.
### Step-by-Step Solution:
1. **Understanding the Equation**:
The equation \([H^+] = \sqrt{\frac{K_w K_a}{C}}\) relates the concentration of hydrogen ions \([H^+]\) to the ion product of water \(K_w\), the dissociation constant of a weak acid \(K_a\), and the concentration \(C\) of the salt solution.
2. **Analyzing the Options**:
We need to evaluate each option to see if it can lead to the condition described by the equation.
3. **Option A: NaCl and Ammonium Chloride**:
- NaCl is formed from a strong acid (HCl) and a strong base (NaOH).
- Ammonium chloride is formed from a strong acid (HCl) and a weak base (NH₄OH).
- Since one salt is from a strong acid and strong base, and the other from a strong acid and weak base, they will not yield the same \([H^+]\). Thus, this option is **not suitable**.
4. **Option B: CH₃COONa and NaCN**:
- CH₃COONa is formed from a weak acid (acetic acid) and a strong base (NaOH).
- NaCN is formed from a weak acid (HCN) and a strong base (NaOH).
- Both salts are derived from weak acids and strong bases, which means they will have similar hydrolysis behavior. Therefore, this option is **suitable**.
5. **Option C: CH₃COONa and (NH₄)₂SO₄**:
- CH₃COONa is from a weak acid and a strong base.
- (NH₄)₂SO₄ is formed from a strong acid (H₂SO₄) and a weak base (NH₄OH).
- Since one is a weak acid-strong base salt and the other is a weak base-strong acid salt, they will not yield the same \([H^+]\). Thus, this option is **not suitable**.
6. **Option D: CH₃CONH₃ and Ammonium Carbonate**:
- CH₃CONH₃ (ammonium acetate) is formed from a weak acid (acetic acid) and a weak base (NH₄OH).
- Ammonium carbonate is formed from a weak acid (H₂CO₃) and a weak base (NH₄OH).
- Both salts are derived from weak acids and weak bases, but they do not match the form of the equation provided. Thus, this option is **not suitable**.
7. **Conclusion**:
After analyzing all options, the only suitable option for the equation \([H^+] = \sqrt{\frac{K_w K_a}{C}}\) is **Option B: CH₃COONa and NaCN**.
### Final Answer:
**Option B: CH₃COONa and NaCN** is suitable for the equation \([H^+] = \sqrt{\frac{K_w K_a}{C}}\).
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