Osmotic pressure of a 0.01 M solution is 0.7 atm at `27^(@)C`, its van't Hoff factor will be

Options

A. 2.76
B. 2.7
C. 2.84
D. 2.6

Answer

To find the van't Hoff factor (i) for the given solution, we can use the formula for osmotic pressure:

\[ \pi = iCRT \]

Where:
- \(\pi\) = osmotic pressure (in atm)
- \(i\) = van't Hoff factor
- \(C\) = concentration of the solution (in molarity)
- \(R\) = universal gas constant (0.0821 atm L/mol K)
- \(T\) = temperature (in Kelvin)

### Step-by-Step Solution:

1. **Identify Given Values**:
- Osmotic pressure, \(\pi = 0.7 \, \text{atm}\)
- Concentration, \(C = 0.01 \, \text{M}\)
- Temperature, \(T = 27^\circ C\)

2. **Convert Temperature to Kelvin**:
\[ T(K) = 273 + 27 = 300 \, K \]

3. **Substitute Values into the Osmotic Pressure Formula**:
\[ 0.7 = i \times 0.01 \times 0.0821 \times 300 \]

4. **Calculate the Right Side**:
First, calculate \(0.01 \times 0.0821 \times 300\):
\[ 0.01 \times 0.0821 = 0.000821 \]
\[ 0.000821 \times 300 = 0.2463 \]

5. **Rearrange the Equation to Solve for \(i\)**:
\[ i = \frac{0.7}{0.2463} \]

6. **Calculate \(i\)**:
\[ i \approx 2.84 \]

### Final Answer:
The van't Hoff factor \(i\) is approximately **2.84**.

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