To find the osmotic pressure of a solution containing 0.6 g of urea and 3.42 g of sugar in 100 ml at 27°C, we can follow these steps:
### Step 1: Convert the temperature from Celsius to Kelvin
To convert Celsius to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273.15 \]
For 27°C:
\[ T = 27 + 273.15 = 300.15 \, K \]
### Step 2: Calculate the number of moles of urea and sugar
The number of moles can be calculated using the formula:
\[ \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
- **For urea (NH₂CONH₂)**:
- Molar mass of urea = 60 g/mol
- Moles of urea:
\[ \text{moles of urea} = \frac{0.6 \, g}{60 \, g/mol} = 0.01 \, mol \]
- **For sugar (C₁₂H₂₂O₁₁, assuming sucrose)**:
- Molar mass of sugar = 342 g/mol
- Moles of sugar:
\[ \text{moles of sugar} = \frac{3.42 \, g}{342 \, g/mol} = 0.01 \, mol \]
### Step 3: Calculate the molarity of urea and sugar
Molarity (C) is calculated using the formula:
\[ C = \frac{\text{moles}}{\text{volume (L)}} \]
Since the volume is given in ml, we convert it to liters:
\[ 100 \, ml = 0.1 \, L \]
- **For urea**:
\[ C_1 = \frac{0.01 \, mol}{0.1 \, L} = 0.1 \, M \]
- **For sugar**:
\[ C_2 = \frac{0.01 \, mol}{0.1 \, L} = 0.1 \, M \]
### Step 4: Calculate the osmotic pressure using the formula
The osmotic pressure (π) is given by:
\[ \pi = iCRT \]
Where:
- \( i \) = van 't Hoff factor (for urea and sugar, both are non-electrolytes, so \( i = 1 \))
- \( R \) = ideal gas constant = 0.0821 L·atm/(K·mol)
- \( T \) = temperature in Kelvin = 300.15 K
- \( C \) = total concentration = \( C_1 + C_2 = 0.1 + 0.1 = 0.2 \, M \)
Now substituting the values:
\[ \pi = (1)(0.0821 \, L·atm/(K·mol))(300.15 \, K)(0.2 \, M) \]
### Step 5: Calculate the osmotic pressure
Calculating the above expression:
\[ \pi = 0.0821 \times 300.15 \times 0.2 \]
\[ \pi = 4.92 \, atm \]
### Final Answer
The osmotic pressure of the solution is approximately **4.92 atm**.
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