Which of the following expressions correctly repesents the equivalent conductance at infinte dilution of `Al_(2)(SO_(4))_(3)`. Given that `Lambda_(Al^(3+))^(@)` and `Lambda_(SO_(4)^(2-))^(@)` are the equivalent conductance at infinte dilution of the respective ions?

Options

A. `Lambda_(Al^(3+))^(@)+Lambda_(SO_(4)^(2-))`
B. `(Lambda_(Al^(3+))^(@)+Lambda_(SO_(4)^(2-)))xx6`
C. `(1)/(3)Lambda_(Al^(3+))^(@)+(1)/(2)Lambda_(SO_(4)^(2-))^(@)`
D. `2Lambda_(Al^(3+))^(@)+3Lambda_(SO_(4)^(2-))^(@)`

Answer

To find the equivalent conductance at infinite dilution of \( Al_2(SO_4)_3 \), we need to consider how the compound dissociates in solution and the contributions of its ions to the overall conductance.

### Step-by-Step Solution:

1. **Identify the Dissociation of the Compound:**
The dissociation of \( Al_2(SO_4)_3 \) in water can be represented as:
\[ Al_2(SO_4)_3 \rightarrow 2Al^{3+} + 3SO_4^{2-} \]

2. **Understand Equivalent Conductance:**
The equivalent conductance (\( \Lambda \)) at infinite dilution is the sum of the contributions from each ion in solution. For a given ion, it is denoted as \( \Lambda^0 \) (at infinite dilution).

3. **Write the Expression for Equivalent Conductance:**
The equivalent conductance at infinite dilution for \( Al_2(SO_4)_3 \) can be expressed as:
\[ \Lambda_{Al_2(SO_4)_3}^0 = 2\Lambda_{Al^{3+}}^0 + 3\Lambda_{SO_4^{2-}}^0 \]
However, since we are looking for the equivalent conductance, we only consider the contributions of the ions without multiplying by their stoichiometric coefficients.

4. **Final Expression:**
Therefore, the equivalent conductance at infinite dilution of \( Al_2(SO_4)_3 \) is given by:
\[ \Lambda_{Al_2(SO_4)_3}^0 = 2\Lambda_{Al^{3+}}^0 + 3\Lambda_{SO_4^{2-}}^0 \]

### Conclusion:
The correct expression representing the equivalent conductance at infinite dilution of \( Al_2(SO_4)_3 \) is:
\[ \Lambda_{Al_2(SO_4)_3}^0 = 2\Lambda_{Al^{3+}}^0 + 3\Lambda_{SO_4^{2-}}^0 \]