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 making two solutions isotonic, we need to follow these steps:

### Step 1: Calculate the moles of glucose and sucrose in their respective solutions.

1. **For Glucose:**
- Given mass = 4 g
- Molar mass of glucose (C6H12O6) = 180 g/mol
- Moles of glucose = Given mass / Molar mass = 4 g / 180 g/mol = 0.0222 moles

2. **For Sucrose:**
- Given mass = 10 g
- Molar mass of sucrose (C12H22O11) = 342 g/mol
- Moles of sucrose = Given mass / Molar mass = 10 g / 342 g/mol = 0.0292 moles

### Step 2: Set up the equation for isotonic solutions.

To make the glucose solution isotonic with the sucrose solution, we need to add urea to the glucose solution. The osmotic pressure of both solutions must be equal.

- Let \( x \) be the moles of urea added to the glucose solution.
- The total moles in the glucose solution after adding urea will be \( 0.0222 + x \).
- The concentration of the glucose solution (after adding urea) will be \( \frac{0.0222 + x}{0.1} \) (since the volume is 100 ml or 0.1 L).

For the sucrose solution, the concentration will be:
- \( \frac{0.0292}{0.1} \)

### Step 3: Set the concentrations equal to each other.

To achieve isotonicity, we set the concentrations equal:
\[ \frac{0.0222 + x}{0.1} = \frac{0.0292}{0.1} \]

### Step 4: Solve for \( x \).

Since the volumes are the same, we can cancel out the \( 0.1 \):
\[ 0.0222 + x = 0.0292 \]
\[ x = 0.0292 - 0.0222 \]
\[ x = 0.007 moles \]

### Step 5: Calculate the mass of urea needed.

Now we need to convert the moles of urea to grams:
- Molar mass of urea (NH2CONH2) = 60 g/mol
- Mass of urea = moles × molar mass = \( 0.007 \, \text{moles} \times 60 \, \text{g/g} = 0.42 \, \text{g} \)

### 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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