Based upon the technique of reverse osmosis the approximate pressure required to desalinate sea water containing 2.5% (mass/volume)`KNO_(3)` at `27^(@)`C will be

Options

A. 10.5 atm
B. 21 atm
C. 12.2 atm
D. 6.09 atm

Answer

To find the approximate pressure required to desalinate seawater containing 2.5% (mass/volume) KNO3 at 27°C using the technique of reverse osmosis, we will calculate the osmotic pressure using the formula:

\[ \pi = C \cdot R \cdot T \cdot i \]

where:
- \(\pi\) = osmotic pressure
- \(C\) = concentration of the solute in moles per liter
- \(R\) = gas constant (0.0821 L·atm/(K·mol))
- \(T\) = temperature in Kelvin
- \(i\) = Van't Hoff factor (number of particles the solute dissociates into)

### Step 1: Convert the mass/volume percentage to grams and volume
Given that the solution is 2.5% (mass/volume) KNO3, this means there are 2.5 grams of KNO3 in 100 mL of solution.

### Step 2: Calculate the number of moles of KNO3
To find the number of moles, we use the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

The molar mass of KNO3 is calculated as follows:
- Potassium (K) = 39 g/mol
- Nitrogen (N) = 14 g/mol
- Oxygen (O) = 16 g/mol × 3 = 48 g/mol

Thus, the molar mass of KNO3 = 39 + 14 + 48 = 101 g/mol.

Now, calculate the number of moles in 2.5 g of KNO3:

\[ \text{Number of moles} = \frac{2.5 \text{ g}}{101 \text{ g/mol}} \approx 0.02475 \text{ mol} \]

### Step 3: Convert the volume from mL to L
Since we have 100 mL of solution, we convert this to liters:

\[ \text{Volume in L} = \frac{100 \text{ mL}}{1000} = 0.1 \text{ L} \]

### Step 4: Calculate the concentration (C) in moles per liter
Now we can find the concentration \(C\):

\[ C = \frac{\text{Number of moles}}{\text{Volume in L}} = \frac{0.02475 \text{ mol}}{0.1 \text{ L}} = 0.2475 \text{ mol/L} \]

### Step 5: Determine the Van't Hoff factor (i)
KNO3 dissociates into two ions: K\(^+\) and NO3\(^-\). Therefore, the Van't Hoff factor \(i\) is 2.

### Step 6: Convert temperature to Kelvin
The temperature given is 27°C. To convert this to Kelvin:

\[ T = 27 + 273 = 300 \text{ K} \]

### Step 7: Calculate the osmotic pressure (\(\pi\))
Now we can substitute all the values into the osmotic pressure formula:

\[ \pi = C \cdot R \cdot T \cdot i \]

Substituting the values:

\[ \pi = 0.2475 \text{ mol/L} \cdot 0.0821 \text{ L·atm/(K·mol)} \cdot 300 \text{ K} \cdot 2 \]

Calculating this step-by-step:

1. Calculate \(C \cdot R \cdot T\):
\[ 0.2475 \cdot 0.0821 \cdot 300 \approx 6.086 \]

2. Multiply by \(i\):
\[ \pi \approx 6.086 \cdot 2 \approx 12.172 \text{ atm} \]

### Step 8: Round the result
Rounding 12.172 atm gives approximately 12.2 atm.

### Final Answer
The approximate pressure required to desalinate seawater containing 2.5% KNO3 at 27°C is **12.2 atm**.

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