`^^_(m(NH_4OH))^@` is equal to ....

Options

A. `^^_(m(NH_4OH))^@ + ^^_(m(NH_4Cl))^@ - ^^_(HCl)^@`
B. `^^_(m(NH_4Cl))^@ + ^^_(m(NH_4OH))^@ - ^^_(HCl)^@`
C. `^^_(m(NH_4Cl))^@ + ^^_(m(NaCl))^@ - ^^_(NaOH)^@`
D. `^^_(m(NaOH))^@ + ^^_(m(NaCl))^@ - ^^_(NH_4Cl)^@`

Answer

To solve the problem of finding the limiting molar conductivity of ammonium hydroxide (NH₄OH), we can follow these steps:

### Step 1: Understand the Concept of Limiting Molar Conductivity
Limiting molar conductivity (λ₀) is the conductivity of an electrolyte solution when it is infinitely diluted. It is the sum of the contributions from the individual ions produced when the electrolyte dissociates.

### Step 2: Write the Dissociation Equation
Ammonium hydroxide (NH₄OH) dissociates in water as follows:
\[ \text{NH}_4\text{OH} \rightleftharpoons \text{NH}_4^+ + \text{OH}^- \]

### Step 3: Express Limiting Molar Conductivity
The limiting molar conductivity of NH₄OH can be expressed as:
\[ \lambda_m^{\text{NH}_4\text{OH}} = \lambda_m^{\text{NH}_4^+} + \lambda_m^{\text{OH}^-} \]
Where:
- \( \lambda_m^{\text{NH}_4^+} \) is the limiting molar conductivity of the ammonium ion.
- \( \lambda_m^{\text{OH}^-} \) is the limiting molar conductivity of the hydroxide ion.

### Step 4: Identify the Limiting Molar Conductivities of the Ions
We need to know the values of \( \lambda_m^{\text{NH}_4^+} \) and \( \lambda_m^{\text{OH}^-} \). These values can typically be found in tables of molar conductivities:
- \( \lambda_m^{\text{NH}_4^+} \) (for ammonium ion)
- \( \lambda_m^{\text{OH}^-} \) (for hydroxide ion)

### Step 5: Calculate the Limiting Molar Conductivity of NH₄OH
Once we have the values for \( \lambda_m^{\text{NH}_4^+} \) and \( \lambda_m^{\text{OH}^-} \), we can substitute them into the equation from Step 3 to find the limiting molar conductivity of NH₄OH:
\[ \lambda_m^{\text{NH}_4\text{OH}} = \lambda_m^{\text{NH}_4^+} + \lambda_m^{\text{OH}^-} \]

### Step 6: Conclusion
The final answer will be the sum of the individual molar conductivities of the ions.