The sodium salt of an acid dye contains 7% of sodium. What is the minimum molar mass of the dye?

Options

A. 336.5
B. 286.5
C. 300.6
D. 306.5

Explanation

To find the minimum molar mass of the dye, we can follow these steps:

### Step 1: Define the mass of the dye
Let the mass of the sodium salt of the dye be \( W \) grams.

### Step 2: Determine the mass of the anion
Since the dye is an acid dye, it will have an anionic part. When the dye releases a hydrogen ion (H+), the mass of the anion can be expressed as:
\[ \text{Mass of anion} = W - 1 \text{ grams} \]
Here, we subtract 1 gram for the hydrogen ion.

### Step 3: Calculate the total mass of the sodium salt
The sodium salt of the dye consists of the mass of the anion plus the mass of sodium (Na). The mass of sodium is 23 grams. Therefore, the total mass of the sodium salt can be expressed as:
\[ \text{Mass of sodium salt} = (W - 1) + 23 = W + 22 \text{ grams} \]

### Step 4: Set up the equation for sodium percentage
We know that the sodium salt contains 7% sodium by mass. This can be expressed as:
\[ \frac{\text{Mass of sodium}}{\text{Total mass of sodium salt}} \times 100 = 7 \]
Substituting the known values:
\[ \frac{23}{W + 22} \times 100 = 7 \]

### Step 5: Solve the equation
To eliminate the percentage, we can rewrite the equation:
\[ 23 \times 100 = 7 \times (W + 22) \]
This simplifies to:
\[ 2300 = 7W + 154 \]
Now, isolate \( W \):
\[ 2300 - 154 = 7W \]
\[ 2146 = 7W \]
\[ W = \frac{2146}{7} \approx 306.57 \text{ grams} \]

### Step 6: Conclusion
The minimum molar mass of the dye is approximately:
\[ \text{Minimum molar mass of the dye} \approx 306.57 \text{ grams} \]