If a `6.84% (weight//volume)` solution of cane sugar (molecular weight=342) is isotonic with `1.52%(weight//volume)`solution of thiocarbamide, then the molecular weight of thiocarbamide is

Options

A. 152
B. 760
C. 60
D. 180

Explanation

To find the molecular weight of thiocarbamide given that a 6.84% (weight/volume) solution of cane sugar is isotonic with a 1.52% (weight/volume) solution of thiocarbamide, we can follow these steps:

### Step 1: Calculate the number of moles of cane sugar in the solution.
- Given:
- Concentration of cane sugar = 6.84% (weight/volume)
- Molecular weight of cane sugar = 342 g/mol
- For a 100 mL solution:
- Mass of cane sugar = 6.84 g
- Calculate the number of moles of cane sugar:
\[ \text{Number of moles of cane sugar} = \frac{\text{mass}}{\text{molecular weight}} = \frac{6.84 \, \text{g}}{342 \, \text{g/mol}} = 0.02 \, \text{moles} \]

### Step 2: Calculate the molarity of the cane sugar solution.
- Since the volume of the solution is 100 mL (or 0.1 L):
\[ \text{Molarity (C1)} = \frac{\text{moles}}{\text{volume in liters}} = \frac{0.02 \, \text{moles}}{0.1 \, \text{L}} = 0.2 \, \text{M} \]

### Step 3: Calculate the number of moles of thiocarbamide in the solution.
- Given:
- Concentration of thiocarbamide = 1.52% (weight/volume)
- For a 100 mL solution:
- Mass of thiocarbamide = 1.52 g
- Let the molecular weight of thiocarbamide be \( M \).
- Calculate the number of moles of thiocarbamide:
\[ \text{Number of moles of thiocarbamide} = \frac{1.52 \, \text{g}}{M \, \text{g/mol}} = \frac{1.52}{M} \, \text{moles} \]

### Step 4: Calculate the molarity of the thiocarbamide solution.
- Since the volume of the solution is also 100 mL (or 0.1 L):
\[ \text{Molarity (C2)} = \frac{\text{moles}}{\text{volume in liters}} = \frac{\frac{1.52}{M}}{0.1} = \frac{15.2}{M} \, \text{M} \]

### Step 5: Set the molarities equal due to isotonicity.
- Since both solutions are isotonic:
\[ C1 = C2 \implies 0.2 = \frac{15.2}{M} \]

### Step 6: Solve for the molecular weight \( M \).
- Rearranging the equation:
\[ M = \frac{15.2}{0.2} = 76 \, \text{g/mol} \]

### Final Answer:
The molecular weight of thiocarbamide is **76 g/mol**.

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