What is the molar mass if diacidic organic Lewis base (B), if 12g of its chloroplatinate salt `(BH_(2)PtCl_(6))` on ignition produced 5g residue of Pt?

Options

A. 52
B. 58
C. 88
D. none of these

Answer

To find the molar mass of the diacidic organic Lewis base (B) from the given information about its chloroplatinate salt \( BH_2PtCl_6 \), we can follow these steps:

### Step 1: Determine the moles of platinum produced
From the problem, we know that 5 g of platinum (Pt) is produced upon ignition of the chloroplatinate salt. The atomic mass of platinum is approximately 195 g/mol.

\[ \text{Moles of Pt} = \frac{\text{mass of Pt}}{\text{molar mass of Pt}} = \frac{5 \, \text{g}}{195 \, \text{g/mol}} \approx 0.0256 \, \text{moles} \]

### Step 2: Relate moles of chloroplatinate salt to moles of platinum
The stoichiometry of the reaction indicates that 1 mole of \( BH_2PtCl_6 \) produces 1 mole of Pt. Therefore, the moles of \( BH_2PtCl_6 \) will also be 0.0256 moles.

\[ \text{Moles of } BH_2PtCl_6 = 0.0256 \, \text{moles} \]

### Step 3: Calculate the molar mass of \( BH_2PtCl_6 \)
We know the mass of the chloroplatinate salt is 12 g. Using the number of moles calculated, we can find the molar mass of \( BH_2PtCl_6 \).

\[ \text{Molar mass of } BH_2PtCl_6 = \frac{\text{mass of } BH_2PtCl_6}{\text{moles of } BH_2PtCl_6} = \frac{12 \, \text{g}}{0.0256 \, \text{moles}} \approx 468.75 \, \text{g/mol} \]

### Step 4: Calculate the molar mass of the organic Lewis base (B)
To find the molar mass of the organic Lewis base (B), we need to subtract the contributions of the other components in the chloroplatinate salt from the total molar mass.

The molar mass of \( BH_2PtCl_6 \) can be expressed as:

\[ \text{Molar mass of } BH_2PtCl_6 = \text{Molar mass of B} + 2 \times \text{molar mass of H} + \text{molar mass of Pt} + 6 \times \text{molar mass of Cl} \]

Substituting the known values:

- Molar mass of H = 1 g/mol
- Molar mass of Pt = 195 g/mol
- Molar mass of Cl = 35.5 g/mol

Calculating the total contribution of H, Pt, and Cl:

\[ \text{Total contribution} = 2 \times 1 + 195 + 6 \times 35.5 = 2 + 195 + 213 = 410 \, \text{g/mol} \]

Now, we can find the molar mass of B:

\[ \text{Molar mass of B} = \text{Molar mass of } BH_2PtCl_6 - \text{Total contribution} \]
\[ \text{Molar mass of B} = 468.75 \, \text{g/mol} - 410 \, \text{g/mol} = 58.75 \, \text{g/mol} \]

### Final Result
The molar mass of the diacidic organic Lewis base (B) is approximately 58 g/mol.

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