0.8 g of silver salt of a dibasic organic acid on ignition yielded 0.54 g of metallic silver. Molecular weight of the acid is (Ag = 108)

Options

A. 106
B. 108
C. 320
D. 85

Answer

To solve the problem step-by-step, we will follow these steps:

### Step 1: Understand the Reaction
We have a dibasic organic acid (H₂A) that forms a silver salt (Ag₂A). On ignition, this salt yields metallic silver (Ag). The mass of the silver salt is given as 0.8 g, and the mass of the metallic silver produced is 0.54 g.

### Step 2: Determine the Molar Mass of Silver
The atomic mass of silver (Ag) is given as 108 g/mol.

### Step 3: Calculate the Moles of Silver Produced
Using the mass of silver produced, we can calculate the number of moles of silver:
\[ \text{Moles of Ag} = \frac{\text{mass of Ag}}{\text{molar mass of Ag}} = \frac{0.54 \, \text{g}}{108 \, \text{g/mol}} = 0.005 \, \text{mol} \]

### Step 4: Relate Moles of Silver to Moles of Silver Salt
Since the silver salt is Ag₂A, each mole of Ag₂A produces 2 moles of Ag. Therefore, the moles of silver salt (Ag₂A) can be calculated as:
\[ \text{Moles of Ag₂A} = \frac{\text{Moles of Ag}}{2} = \frac{0.005 \, \text{mol}}{2} = 0.0025 \, \text{mol} \]

### Step 5: Calculate the Molar Mass of the Silver Salt
Now we can find the molar mass of the silver salt (Ag₂A) using the mass and moles calculated:
\[ \text{Molar mass of Ag₂A} = \frac{\text{mass of Ag₂A}}{\text{moles of Ag₂A}} = \frac{0.8 \, \text{g}}{0.0025 \, \text{mol}} = 320 \, \text{g/mol} \]

### Step 6: Set Up the Equation for Molar Mass of the Acid
The molar mass of the silver salt (Ag₂A) can be expressed as:
\[ \text{Molar mass of Ag₂A} = 2 \times \text{molar mass of Ag} + \text{molar mass of A} \]
Substituting the values we have:
\[ 320 \, \text{g/mol} = 2 \times 108 \, \text{g/mol} + X \]
Where \(X\) is the molar mass of the anion A.

### Step 7: Solve for the Molar Mass of A
Calculating the equation:
\[ 320 = 216 + X \]
\[ X = 320 - 216 = 104 \, \text{g/mol} \]

### Step 8: Calculate the Molar Mass of the Dibasic Acid (H₂A)
The molar mass of the dibasic acid (H₂A) is given by:
\[ \text{Molar mass of H₂A} = 2 \times 1 + X = 2 + 104 = 106 \, \text{g/mol} \]

### Final Answer
The molecular weight of the dibasic organic acid (H₂A) is **106 g/mol**.

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