Calculate the vapour pressure , if 0.083 mole of a non-volatile solute is present in 80 g of ethanol at `25^@C` , Vapour pressure of ethanol is 22.45 mm.

Answer

To calculate the vapor pressure of a solution containing a non-volatile solute in ethanol, we can follow these steps:

### Step 1: Calculate the molar mass of ethanol (C2H5OH)
- The atomic masses are:
- Carbon (C) = 12 g/mol
- Hydrogen (H) = 1 g/mol
- Oxygen (O) = 16 g/mol
- Molar mass of ethanol = (2 × 12) + (6 × 1) + (1 × 16) = 24 + 6 + 16 = **46 g/mol**

### Step 2: Calculate the number of moles of ethanol (N2)
- Given mass of ethanol = 80 g
- Molar mass of ethanol = 46 g/mol
- Number of moles of ethanol (N2) = mass / molar mass = 80 g / 46 g/mol = **1.739 moles**

### Step 3: Calculate the number of moles of the solute (N1)
- Given moles of solute = 0.083 moles (as provided in the question).

### Step 4: Calculate the total number of moles (N_total)
- Total number of moles (N_total) = moles of solute (N1) + moles of solvent (N2)
- N_total = 0.083 + 1.739 = **1.822 moles**

### Step 5: Calculate the mole fraction of the solute (X_solute)
- Mole fraction of solute (X_solute) = moles of solute / total moles
- X_solute = N1 / N_total = 0.083 / 1.822 = **0.0455**

### Step 6: Calculate the relative lowering of vapor pressure (ΔP/P)
- The vapor pressure of pure ethanol (P) = 22.45 mmHg
- Relative lowering of vapor pressure (ΔP/P) = mole fraction of solute
- ΔP/P = X_solute = **0.0455**

### Step 7: Calculate the lowering of vapor pressure (ΔP)
- ΔP = P × (ΔP/P) = 22.45 mmHg × 0.0455 = **1.020 mmHg**

### Step 8: Calculate the vapor pressure of the solution (P_solution)
- Vapor pressure of the solution (P_solution) = P - ΔP
- P_solution = 22.45 mmHg - 1.020 mmHg = **21.43 mmHg**

### Final Answer
The vapor pressure of the solution is approximately **21.43 mmHg**.

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