The sodium salt of methyi orange has `7%` sodium. What is the minimum molecular weight of the compound? :

Options

A. `420`
B. `375`
C. `329`
D. `295`

Explanation

To find the minimum molecular weight of the sodium salt of methyl orange, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
We know that the sodium salt of methyl orange contains 7% sodium by mass.

2. **Define the Variables**:
Let \( M \) be the molecular weight (or molar mass) of the sodium salt of methyl orange.

3. **Set Up the Percentage Equation**:
The percentage of sodium in the compound can be expressed as:
\[ \text{Percentage of Sodium} = \frac{\text{mass of Sodium}}{\text{molecular weight of the compound}} \times 100 \]
Given that the percentage of sodium is 7%, we can write:
\[ 7 = \frac{\text{mass of Sodium}}{M} \times 100 \]

4. **Express Mass of Sodium**:
Rearranging the equation gives us:
\[ \frac{\text{mass of Sodium}}{M} = \frac{7}{100} \]
This implies:
\[ \text{mass of Sodium} = 0.07M \]

5. **Determine the Mass of Sodium in One Mole**:
The atomic mass of sodium (Na) is approximately 23 grams. Therefore, in one mole of the compound, the mass of sodium is:
\[ 0.07M = 23 \text{ grams} \]

6. **Solve for M**:
Now, we can solve for \( M \):
\[ M = \frac{23}{0.07} \]
\[ M = 329 \text{ grams per mole} \]

7. **Conclusion**:
The minimum molecular weight of the sodium salt of methyl orange is \( 329 \text{ g/mol} \).

### Final Answer:
The minimum molecular weight of the sodium salt of methyl orange is \( 329 \text{ g/mol} \).

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