The concentration in `g//L` of a solution of cane sugar (Molecular weight = 342) which is isotonic with a solution containing 6 g of urea (Molecular weight = 60) per litre is

Options

A. `3.42 g//L`
B. `34.2 g//L`
C. `5.7 g//L`
D. `19 g//L`

Answer

To find the concentration of a solution of cane sugar that is isotonic with a solution containing 6 g of urea per liter, we can follow these steps:

### Step 1: Understand the concept of isotonic solutions
Isotonic solutions have the same osmotic pressure. This means that the number of solute particles in both solutions must be equal when compared at the same volume and temperature.

### Step 2: Set up the equation for osmotic pressure
The osmotic pressure (π) can be expressed using the formula:
\[ \pi = C \cdot R \cdot T \]
Where:
- \( C \) = concentration of the solution (in mol/L)
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

Since both solutions are isotonic, we can write:
\[ C_{\text{sugar}} = C_{\text{urea}} \]

### Step 3: Calculate the concentration of urea
The concentration of urea can be calculated using the formula:
\[ C = \frac{W}{M \cdot V} \]
Where:
- \( W \) = weight of the solute (in grams)
- \( M \) = molecular weight of the solute (in g/mol)
- \( V \) = volume of the solution (in liters)

For urea:
- \( W = 6 \, \text{g} \)
- \( M = 60 \, \text{g/mol} \)
- \( V = 1 \, \text{L} \)

Substituting the values:
\[ C_{\text{urea}} = \frac{6 \, \text{g}}{60 \, \text{g/mol} \cdot 1 \, \text{L}} = \frac{6}{60} = 0.1 \, \text{mol/L} \]

### Step 4: Calculate the concentration of cane sugar
Since the solutions are isotonic, the concentration of cane sugar will also be 0.1 mol/L. Now, we need to convert this concentration into grams per liter.

The molecular weight of cane sugar is 342 g/mol. Therefore, we can find the weight of cane sugar in 1 L of solution:
\[ W_{\text{sugar}} = C_{\text{sugar}} \cdot M_{\text{sugar}} \cdot V \]
Substituting the values:
\[ W_{\text{sugar}} = 0.1 \, \text{mol/L} \cdot 342 \, \text{g/mol} \cdot 1 \, \text{L} = 34.2 \, \text{g} \]

### Step 5: Conclusion
The concentration of cane sugar in grams per liter, which is isotonic with the urea solution, is 34.2 g/L.

### Final Answer:
The concentration of the cane sugar solution is **34.2 g/L**.

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