Benzene diazonium chloride, `C_6 H_5 overset(+)(N_2) overset(-)( C) I` , was decomposed in the presence of hypo phosphorous acid and the nitrogen evolved after drying was found to be 36.9 ml at one atmosphere and `27^@ C` . The amount of salt taken must be nearly:

Options

A. 481 mg
B. 240 mg
C. 210 mg
D. 140 mg

Answer

To solve the problem of determining the amount of benzene diazonium chloride salt taken based on the volume of nitrogen evolved, we can follow these steps:

### Step 1: Understand the Reaction
The decomposition of benzene diazonium chloride in the presence of hypophosphorous acid can be represented as follows:
\[ C_6H_5N_2Cl \rightarrow C_6H_6 + N_2 \]
This indicates that one mole of benzene diazonium chloride produces one mole of nitrogen gas (N₂).

### Step 2: Convert Given Volume of Nitrogen to Moles
We are given the volume of nitrogen gas evolved as 36.9 mL at a pressure of 1 atmosphere and a temperature of 27°C. First, we need to convert the volume from mL to liters:
\[ 36.9 \, \text{mL} = 0.0369 \, \text{L} \]

Next, we convert the temperature from Celsius to Kelvin:
\[ T = 27 + 273 = 300 \, \text{K} \]

Now, we can use the Ideal Gas Law to find the number of moles of nitrogen gas:
\[ PV = nRT \]
Where:
- \( P = 1 \, \text{atm} \)
- \( V = 0.0369 \, \text{L} \)
- \( R = 0.0821 \, \text{L atm/(mol K)} \)
- \( T = 300 \, \text{K} \)

Rearranging the equation to solve for \( n \):
\[ n = \frac{PV}{RT} \]

Substituting the values:
\[ n = \frac{(1 \, \text{atm})(0.0369 \, \text{L})}{(0.0821 \, \text{L atm/(mol K)})(300 \, \text{K})} \]

Calculating this gives:
\[ n \approx \frac{0.0369}{24.63} \approx 0.0015 \, \text{mol} = 1.5 \, \text{mmol} \]

### Step 3: Relate Moles of Nitrogen to Moles of Salt
From the reaction, we see that 1 mole of nitrogen gas is produced from 1 mole of benzene diazonium chloride. Therefore, the moles of benzene diazonium chloride (salt) is also 1.5 mmol.

### Step 4: Calculate the Mass of the Salt
To find the mass of the benzene diazonium chloride, we need its molar mass. The molar mass of benzene diazonium chloride (\( C_6H_5N_2Cl \)) is approximately 140.5 g/mol.

Now, we can calculate the mass of the salt:
\[ \text{Mass (in grams)} = \text{moles} \times \text{molar mass} \]
\[ \text{Mass} = 1.5 \, \text{mmol} \times \frac{140.5 \, \text{g}}{1000 \, \text{mmol}} \]
\[ \text{Mass} = 1.5 \times 0.1405 \approx 0.211 \, \text{g} = 211 \, \text{mg} \]

### Step 5: Final Answer
The amount of benzene diazonium chloride salt taken must be nearly 210 mg.