Sea water is `3.5%`by mass of a salt and has a density `1.04gcm^(-3)` at `293K`.Assuming the salt to be sodium chloride ,calculate the osmotic pressure of sea water.Assume complete ionisation of the salt-

Options

A. 25.45 atm
B. 11.56 atm
C. 29.98 atm
D. 30.20 atm

Answer

To calculate the osmotic pressure of sea water, we will follow these steps:

### Step 1: Assume the mass of the solution
Let's assume the mass of the sea water solution to be 100 grams. This simplifies our calculations.

### Step 2: Calculate the mass of salt (NaCl)
Given that sea water is 3.5% by mass of salt, we can calculate the mass of NaCl in our assumed 100 grams of solution:
\[ \text{Mass of NaCl} = 3.5\% \text{ of } 100 \text{ g} = 3.5 \text{ g} \]

### Step 3: Calculate the volume of the solution
Using the density of the solution (1.04 g/cm³), we can calculate the volume of the solution:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{100 \text{ g}}{1.04 \text{ g/cm}^3} = 96.154 \text{ cm}^3 = 0.096154 \text{ L} \]

### Step 4: Calculate the number of moles of NaCl
The molar mass of NaCl is approximately 58.5 g/mol. We can find the number of moles of NaCl:
\[ \text{Number of moles (n)} = \frac{\text{Mass of NaCl}}{\text{Molar mass of NaCl}} = \frac{3.5 \text{ g}}{58.5 \text{ g/mol}} \approx 0.0599 \text{ mol} \]

### Step 5: Calculate the concentration (C) of the solution
The concentration (C) in mol/L can be calculated as:
\[ C = \frac{n}{V} = \frac{0.0599 \text{ mol}}{0.096154 \text{ L}} \approx 0.623 \text{ mol/L} \]

### Step 6: Determine the Van't Hoff factor (i)
Since NaCl completely ionizes in solution, the Van't Hoff factor (i) is:
\[ i = 2 \]

### Step 7: Use the osmotic pressure formula
The osmotic pressure (π) can be calculated using the formula:
\[ \pi = i \cdot C \cdot R \cdot T \]
Where:
- \( R = 0.0821 \text{ L atm/(K mol)} \)
- \( T = 293 \text{ K} \)

Substituting the values:
\[ \pi = 2 \cdot 0.623 \text{ mol/L} \cdot 0.0821 \text{ L atm/(K mol)} \cdot 293 \text{ K} \]

### Step 8: Calculate the osmotic pressure
Calculating the above expression:
\[ \pi \approx 2 \cdot 0.623 \cdot 0.0821 \cdot 293 \approx 29.98 \text{ atm} \]

### Final Answer
The osmotic pressure of sea water is approximately **29.98 atm**.

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