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
B. 34.2
C. 5.7
D. 19

Answer

To find the concentration in grams per liter 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-by-Step Solution:

1. **Identify the Given Data:**
- Molecular weight of cane sugar (M1) = 342 g/mol
- Weight of urea (W2) = 6 g
- Molecular weight of urea (M2) = 60 g/mol
- Volume of both solutions (V1 and V2) = 1 L

2. **Use the Isotonic Solution Formula:**
For two isotonic solutions, the relationship can be expressed as:
\[ \frac{W1}{M1} \cdot V1 = \frac{W2}{M2} \cdot V2 \]
Where:
- W1 = weight of cane sugar
- M1 = molecular weight of cane sugar
- W2 = weight of urea
- M2 = molecular weight of urea
- V1 = volume of cane sugar solution
- V2 = volume of urea solution

3. **Substitute the Known Values:**
Since both solutions are 1 L, we can simplify the equation:
\[ \frac{W1}{342} \cdot 1 = \frac{6}{60} \cdot 1 \]

4. **Calculate the Right Side:**
\[ \frac{6}{60} = 0.1 \]

5. **Set Up the Equation:**
Now we have:
\[ \frac{W1}{342} = 0.1 \]

6. **Solve for W1:**
Multiply both sides by 342:
\[ W1 = 0.1 \cdot 342 = 34.2 \text{ g} \]

7. **Conclude the Concentration:**
Since we are asked for the concentration in g/L, the concentration of the cane sugar solution is:
\[ 34.2 \text{ g/L} \]

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