If the specific conductance of `1 M H_(2)SO_(4)` solution is `26xx10^(-2)S cm^(2)`, then the equivalent conductivity would be

Options

A. `1.3xx10^(2)S cm^(-1)`
B. `1.6 xx 10^(2) S cm^(-2)`
C. `13 S cm^(2)mol^(-1)`
D. `1.3xx10^(3) S cm^(2) mol^(-1)`

Explanation

To solve the question regarding the equivalent conductivity of a 1 M \( H_2SO_4 \) solution with a specific conductance of \( 26 \times 10^{-2} \, S \, cm^{-1} \), we can follow these steps:

### Step 1: Determine Normality
Since sulfuric acid (\( H_2SO_4 \)) is a dibasic acid, its normality (N) can be calculated using the formula:
\[ \text{Normality} = \text{Molarity} \times \text{Basicity} \]
Given that the molarity is 1 M and the basicity of \( H_2SO_4 \) is 2:
\[ \text{Normality} = 1 \, M \times 2 = 2 \, N \]

### Step 2: Use the Formula for Equivalent Conductivity
The equivalent conductivity (\( \Lambda_{eq} \)) can be calculated using the formula:
\[ \Lambda_{eq} = \frac{\kappa}{N} \]
where \( \kappa \) is the specific conductance and \( N \) is the normality.

### Step 3: Convert Units
Since the specific conductance is given in \( S \, cm^{-1} \), we need to convert normality from equivalents per liter to equivalents per cubic centimeter.
\[ N = 2 \, N = 2 \, \text{equivalents per liter} = \frac{2}{1000} \, \text{equivalents per cm}^3 \]

### Step 4: Substitute Values
Now we can substitute the values into the formula:
\[ \Lambda_{eq} = \frac{26 \times 10^{-2} \, S \, cm^{-1}}{2 \, N} \]
\[ \Lambda_{eq} = \frac{26 \times 10^{-2}}{2} \, S \, cm^{-1} = 13 \times 10^{-2} \, S \, cm^{-1} \]

### Step 5: Convert to Equivalent Conductivity
To express this in terms of equivalent conductivity, we multiply by 1000 (to convert from \( S \, cm^{-1} \) to \( S \, cm^2 \, equivalent^{-1} \)):
\[ \Lambda_{eq} = 13 \times 10^{-2} \times 1000 \, S \, cm^2 \, equivalent^{-1} = 1.3 \times 10^{2} \, S \, cm^2 \, equivalent^{-1} \]

### Final Answer
Thus, the equivalent conductivity of the \( 1 M \, H_2SO_4 \) solution is:
\[ \Lambda_{eq} = 1.3 \times 10^{2} \, S \, cm^2 \, equivalent^{-1} \]

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