`0.607g` of silver salt of tribasic organic acid was quantitatively reduced to `0.37g` of pure `Ag`. What is the mol. Wt. of the acid ?

Options

A. 207
B. 210
C. 531
D. 324

Answer

To find the molecular weight of the tribasic organic acid from the given data, we can follow these steps:

### Step 1: Calculate the moles of silver obtained
Given:
- Mass of silver obtained = 0.37 g
- Atomic weight of silver (Ag) = 108 g/mol

Using the formula for moles:
\[ \text{Number of moles of Ag} = \frac{\text{Mass of Ag}}{\text{Atomic weight of Ag}} = \frac{0.37 \, \text{g}}{108 \, \text{g/mol}} \approx 0.00343 \, \text{moles} \]

### Step 2: Relate moles of silver to moles of silver salt
Since the silver salt is a tribasic salt (Ag₃A), it releases 3 moles of Ag for every mole of the salt. Therefore, the moles of silver salt (Ag₃A) can be calculated as:
\[ \text{Number of moles of Ag₃A} = \frac{\text{Number of moles of Ag}}{3} = \frac{0.00343}{3} \approx 0.00114 \, \text{moles} \]

### Step 3: Calculate the molecular weight of the silver salt
Given:
- Mass of silver salt = 0.607 g

Using the formula for molecular weight:
\[ \text{Molecular weight of Ag₃A} = \frac{\text{Mass of Ag₃A}}{\text{Number of moles of Ag₃A}} = \frac{0.607 \, \text{g}}{0.00114 \, \text{moles}} \approx 532.46 \, \text{g/mol} \]

### Step 4: Calculate the molecular weight of the organic acid
The molecular weight of the organic acid (H₃A) can be calculated using the molecular weight of the silver salt and the weights of the silver and hydrogen atoms:
\[ \text{Molecular weight of H₃A} = \text{Molecular weight of Ag₃A} - 3 \times \text{Atomic weight of Ag} + 3 \times \text{Atomic weight of H} \]
Substituting the values:
- Atomic weight of Ag = 108 g/mol
- Atomic weight of H = 1.008 g/mol

\[ \text{Molecular weight of H₃A} = 532.46 - (3 \times 108) + (3 \times 1.008) \]
\[ = 532.46 - 324 + 3.024 \approx 211.484 \, \text{g/mol} \]

### Final Answer
The molecular weight of the tribasic organic acid is approximately **211.48 g/mol**, which can be rounded to **210 g/mol**.

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