What elevation in boiling point of alcohol is to be expected when 5 g of urea (molar mass = 60) are dissolved in 75 g of it ? The molal elevation constant for alcohol is `1.15^(@)C`.

Explanation

To solve the problem of determining the elevation in boiling point of alcohol when 5 g of urea is dissolved in 75 g of it, we will follow these steps:

### Step 1: Identify the given values
- Mass of urea (solute) = 5 g
- Molar mass of urea = 60 g/mol
- Mass of alcohol (solvent) = 75 g
- Molal elevation constant (K_b) for alcohol = 1.15 °C

### Step 2: Calculate the number of moles of urea
To find the number of moles of urea (n), we use the formula:
\[ n = \frac{\text{mass of solute}}{\text{molar mass of solute}} \]
Substituting the values:
\[ n = \frac{5 \, \text{g}}{60 \, \text{g/mol}} = \frac{5}{60} = \frac{1}{12} \, \text{mol} \]

### Step 3: Convert the mass of the solvent to kilograms
Since molality (m) is defined as moles of solute per kilogram of solvent, we need to convert the mass of alcohol from grams to kilograms:
\[ \text{mass of solvent} = 75 \, \text{g} = \frac{75}{1000} \, \text{kg} = 0.075 \, \text{kg} \]

### Step 4: Calculate the molality of the solution
Molality (m) is calculated using the formula:
\[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \]
Substituting the values:
\[ m = \frac{\frac{1}{12} \, \text{mol}}{0.075 \, \text{kg}} = \frac{1}{12 \times 0.075} = \frac{1}{0.9} \approx 1.111 \, \text{mol/kg} \]

### Step 5: Determine the van 't Hoff factor (i)
Since urea is a non-electrolyte and does not dissociate in solution, the van 't Hoff factor (i) is:
\[ i = 1 \]

### Step 6: Calculate the elevation in boiling point (ΔT_b)
Using the formula for elevation in boiling point:
\[ \Delta T_b = i \cdot K_b \cdot m \]
Substituting the known values:
\[ \Delta T_b = 1 \cdot 1.15 \, °C \cdot 1.111 \approx 1.277 \, °C \]

### Step 7: Round the result
Rounding to two decimal places, we get:
\[ \Delta T_b \approx 1.28 \, °C \]

### Final Answer
The expected elevation in the boiling point of alcohol when 5 g of urea is dissolved in 75 g of it is **1.28 °C**.

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