A solution containing 3 g of solute A (M=60 g/mol) in 1L solution is isotonic with a solution containing 8.55 g of solute B in 500 mL solution. What is the molar mass of B?

Answer

To solve the problem, we need to find the molar mass of solute B using the information given about the isotonic solutions. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the concept of isotonic solutions
Isotonic solutions have the same osmotic pressure. Therefore, the osmotic pressure of solution A must equal the osmotic pressure of solution B.

### Step 2: Write the formula for osmotic pressure
The osmotic pressure (π) can be expressed as:
\[ \pi = C \cdot R \cdot T \]
where:
- \(C\) is the molarity (concentration in moles per liter),
- \(R\) is the universal gas constant,
- \(T\) is the temperature in Kelvin.

Since both solutions are isotonic, we can set the osmotic pressures equal to each other:
\[ \pi_A = \pi_B \]

### Step 3: Calculate the molarity of solution A
Given:
- Mass of solute A = 3 g
- Molar mass of A = 60 g/mol
- Volume of solution A = 1 L

First, we calculate the number of moles of solute A:
\[ \text{Number of moles of A} = \frac{\text{mass}}{\text{molar mass}} = \frac{3 \text{ g}}{60 \text{ g/mol}} = 0.05 \text{ mol} \]

Next, we find the molarity of solution A:
\[ C_A = \frac{\text{Number of moles of A}}{\text{Volume of solution in L}} = \frac{0.05 \text{ mol}}{1 \text{ L}} = 0.05 \text{ mol/L} \]

### Step 4: Calculate the molarity of solution B
Given:
- Mass of solute B = 8.55 g
- Volume of solution B = 500 mL = 0.5 L

Let the molar mass of B be \(M_B\). The number of moles of solute B is:
\[ \text{Number of moles of B} = \frac{8.55 \text{ g}}{M_B} \]

Now, we can calculate the molarity of solution B:
\[ C_B = \frac{\text{Number of moles of B}}{\text{Volume of solution in L}} = \frac{8.55 \text{ g}/M_B}{0.5 \text{ L}} = \frac{17.1 \text{ g}}{M_B} \]

### Step 5: Set the molarities equal to each other
Since the solutions are isotonic:
\[ C_A = C_B \]
This gives us:
\[ 0.05 = \frac{17.1}{M_B} \]

### Step 6: Solve for \(M_B\)
Rearranging the equation to solve for \(M_B\):
\[ M_B = \frac{17.1}{0.05} = 342 \text{ g/mol} \]

### Conclusion
The molar mass of solute B is **342 g/mol**.