To find the organic halide (A) in this problem, we will follow these steps:
### Step 1: Calculate the depression in melting point (ΔT)
The melting point of pure camphor is given as 179°C, and the melting point of the mixture is 167°C. Thus, the depression in melting point (ΔT) is:
\[
\Delta T = T_{\text{pure}} - T_{\text{mixture}} = 179°C - 167°C = 12°C
\]
### Step 2: Use the depression of melting point to find the molality (m)
The formula for depression in melting point is given by:
\[
\Delta T = K_f \cdot m
\]
Where:
- \( K_f \) is the cryoscopic constant (given as 40).
- \( m \) is the molality.
Rearranging the formula to find molality:
\[
m = \frac{\Delta T}{K_f} = \frac{12}{40} = 0.3 \, \text{mol/kg}
\]
### Step 3: Calculate the number of moles of the solute (A)
We have 2.0 g of camphor, which is 0.002 kg. Using the formula for molality:
\[
m = \frac{\text{moles of solute}}{\text{kg of solvent}}
\]
Rearranging gives:
\[
\text{moles of solute} = m \cdot \text{kg of solvent} = 0.3 \cdot 0.002 = 0.0006 \, \text{moles}
\]
### Step 4: Calculate the molar mass of the organic halide (A)
We know the mass of the organic halide (A) is 0.0852 g. To find the molar mass (M):
\[
M = \frac{\text{mass}}{\text{moles}} = \frac{0.0852 \, \text{g}}{0.0006 \, \text{mol}} = 142 \, \text{g/mol}
\]
### Step 5: Analyze the gas (B) produced when A is heated with sodium
The problem states that compound A when heated with sodium produces a gas (B). The volume of gas B is 280 mL at STP, and its weight is 0.375 g.
### Step 6: Calculate the molar mass of gas (B)
At STP, 1 mole of gas occupies 22.4 L (or 22400 mL). Therefore, we can find the number of moles of gas B:
\[
\text{moles of B} = \frac{280 \, \text{mL}}{22400 \, \text{mL/mol}} = 0.0125 \, \text{mol}
\]
Now, using the mass of gas B to find its molar mass:
\[
\text{Molar mass of B} = \frac{0.375 \, \text{g}}{0.0125 \, \text{mol}} = 30 \, \text{g/mol}
\]
### Step 7: Establish the relationship between A and B
The gas produced (B) has a molar mass of 30 g/mol. Assuming B is an alkane, we can represent it as \( C_nH_{2n+2} \). From the molar mass, we can deduce:
\[
12n + 2 = 30 \implies n = 2
\]
Thus, gas B is \( C_2H_6 \) (ethane).
### Step 8: Determine the structure of organic halide (A)
Since A produces ethane (C2H6) when reacted with sodium, it must be a methyl halide. The molecular formula for A can be represented as \( CH_3X \), where X is a halogen.
### Step 9: Calculate the halogen in A
The molar mass of A is 142 g/mol. The molar mass of \( CH_3 \) is 15 g/mol. Therefore:
\[
X = 142 - 15 = 127 \, \text{g/mol}
\]
The only halogen with a molar mass of approximately 127 g/mol is iodine (I).
### Conclusion
Thus, the organic halide (A) is methyl iodide, represented as \( CH_3I \).
### Final Answer
The compound A is \( CH_3I \) (methyl iodide).
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