A living cell contains a solution which is isotonic with `0.3`(M) sugar solution .What osmotic pressure develops when the cell is placed in `0.1(M)KCl` solution at body temperature?

Options

A. 5.08 atm
B. 2.54 atm
C. 4.92 atm
D. 2.46 atm

Explanation

To solve the problem, we need to calculate the osmotic pressure that develops when a living cell, which is isotonic with a 0.3 M sugar solution, is placed in a 0.1 M KCl solution at body temperature.

### Step-by-Step Solution:

1. **Understanding Isotonic Solutions**:
- The living cell is isotonic with a 0.3 M sugar solution. This means that the concentration of solute (sugar) inside the cell is 0.3 M.

2. **Identifying the Osmotic Pressure Formula**:
- The osmotic pressure (π) can be calculated using the formula:
\[ \pi = iCRT \]
- Where:
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( C \) = concentration of the solution (in molarity)
- \( R \) = universal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature in Kelvin

3. **Analyzing the KCl Solution**:
- KCl dissociates into two ions: K⁺ and Cl⁻. Therefore, the van 't Hoff factor \( i \) for KCl is 2.
- The concentration \( C \) of the KCl solution is given as 0.1 M.

4. **Converting Body Temperature to Kelvin**:
- Body temperature is approximately 37 °C, which is converted to Kelvin as follows:
\[ T = 37 + 273 = 310 \text{ K} \]

5. **Calculating the Osmotic Pressure of KCl Solution**:
- Using the formula for osmotic pressure:
\[ \pi = iCRT \]
- Substitute the values for KCl:
\[ \pi = 2 \times 0.1 \, \text{M} \times 0.0821 \, \text{L·atm/(K·mol)} \times 310 \, \text{K} \]
- Calculate:
\[ \pi = 2 \times 0.1 \times 0.0821 \times 310 \]
\[ \pi = 2 \times 0.1 \times 25.453 = 0.5086 \, \text{atm} \]

6. **Calculating the Osmotic Pressure of the Sugar Solution**:
- The sugar solution is 0.3 M, and since sugar does not dissociate, \( i = 1 \):
\[ \pi_{\text{sugar}} = 1 \times 0.3 \, \text{M} \times 0.0821 \, \text{L·atm/(K·mol)} \times 310 \, \text{K} \]
- Calculate:
\[ \pi_{\text{sugar}} = 0.3 \times 0.0821 \times 310 = 7.6693 \, \text{atm} \]

7. **Finding the Net Osmotic Pressure**:
- The net osmotic pressure when the cell is placed in the KCl solution can be calculated as:
\[ \Delta \pi = \pi_{\text{sugar}} - \pi_{\text{KCl}} \]
- Substitute the values:
\[ \Delta \pi = 7.6693 - 0.5086 = 7.1607 \, \text{atm} \]

### Final Answer:
The osmotic pressure that develops when the cell is placed in a 0.1 M KCl solution at body temperature is approximately **7.16 atm**.