Two solutions each in 100 ml have 4 g glucose and 10 g sucrose respectively. How much urea should be added to one of them in order to make them isotonic?

Options

A. 0.42 g urea in glucose solution
B. 0.77 g urea in glucose solution
C. 0.72 g urea in sucrose solution
D. 0.42 g urea in sucrose solution

Answer

To solve the problem of how much urea should be added to the glucose solution to make it isotonic with the sucrose solution, we can follow these steps:

### Step 1: Understand the Concept of Isotonic Solutions
Isotonic solutions have the same osmotic pressure. For two solutions to be isotonic, their osmotic pressures must be equal.

### Step 2: Write the Formula for Osmotic Pressure
The osmotic pressure (π) can be calculated using the formula:
\[ \pi = iCRT \]
Where:
- \(i\) = van 't Hoff factor (for non-dissociating solutes like glucose, sucrose, and urea, \(i = 1\))
- \(C\) = molarity of the solution
- \(R\) = universal gas constant
- \(T\) = absolute temperature (not needed for this comparison since it cancels out)

### Step 3: Calculate Moles of Glucose and Sucrose
- **For Glucose:**
\[ \text{Moles of glucose} = \frac{\text{mass}}{\text{molar mass}} = \frac{4 \text{ g}}{180 \text{ g/mol}} = 0.0222 \text{ moles} \]

- **For Sucrose:**
\[ \text{Moles of sucrose} = \frac{\text{mass}}{\text{molar mass}} = \frac{10 \text{ g}}{342 \text{ g/mol}} = 0.0292 \text{ moles} \]

### Step 4: Determine Which Solution Needs Urea
Since the sucrose solution has more moles than the glucose solution, we need to add urea to the glucose solution to make them isotonic.

### Step 5: Calculate the Difference in Moles
To find out how many moles of urea are needed to make the glucose solution isotonic with the sucrose solution:
\[ \text{Moles of urea needed} = \text{Moles of sucrose} - \text{Moles of glucose} \]
\[ \text{Moles of urea needed} = 0.0292 - 0.0222 = 0.0070 \text{ moles} \]

### Step 6: Convert Moles of Urea to Mass
Using the molar mass of urea (60 g/mol):
\[ \text{Mass of urea} = \text{Moles of urea} \times \text{Molar mass of urea} \]
\[ \text{Mass of urea} = 0.0070 \text{ moles} \times 60 \text{ g/mol} = 0.42 \text{ g} \]

### Final Answer
To make the glucose solution isotonic with the sucrose solution, **0.42 g of urea should be added** to the glucose solution.

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