Debye-Huckel Onsager equation for strong electrolytes:
`wedge=wedge_(o)-Asqrt(c)`
Which of the following equality holds?

Options

A. `wedge=wedge_(o)` as `C to sqrt(A)`
B. `wedge=wedge_(o)` as `Cto oo`
C. `wedge=wedge_(o)` as `C to 0`
D. `wedge=wedge_(o)` as `C to 1`

Explanation

To solve the problem regarding the Debye-Huckel Onsager equation for strong electrolytes, we need to analyze the given equation:

\[ \lambda = \lambda_0 - A\sqrt{c} \]

where:
- \(\lambda\) is the molar conductivity,
- \(\lambda_0\) is the molar conductivity at infinite dilution,
- \(A\) is a constant,
- \(c\) is the concentration of the electrolyte.

### Step-by-Step Solution:

1. **Understanding the Equation**:
The equation describes how the molar conductivity (\(\lambda\)) of a strong electrolyte decreases as the concentration (\(c\)) increases. At infinite dilution (where \(c\) approaches zero), the molar conductivity approaches a maximum value (\(\lambda_0\)).

2. **Setting Concentration to Zero**:
To find the relationship between \(\lambda\) and \(\lambda_0\), we can analyze the behavior of the equation as the concentration \(c\) approaches zero:
\[ \lambda = \lambda_0 - A\sqrt{0} \]
Simplifying this gives:
\[ \lambda = \lambda_0 - 0 \]
Therefore:
\[ \lambda = \lambda_0 \]

3. **Interpreting the Result**:
This result indicates that at infinite dilution (or when the concentration is zero), the molar conductivity equals the molar conductivity at infinite dilution, \(\lambda_0\).

4. **Identifying the Correct Option**:
Based on our analysis, the equality that holds true is:
\[ \lambda = \lambda_0 \quad \text{as} \quad c \to 0 \]

5. **Conclusion**:
Thus, the correct answer to the question is that the equality holds when \(c\) approaches zero.

### Final Answer:
The equality that holds is:
\[ \lambda = \lambda_0 \quad \text{as} \quad c \to 0 \]