Compered to 1M sucrose solution, the `Psi_(omega)` of 1M sodium chloride solution is

Options

A. High
B. Same
C. Lower
D. None of the above

Answer

To determine the water potential (Ψ) of a 1M sodium chloride (NaCl) solution compared to a 1M sucrose solution, we need to understand how the presence of solutes affects water potential.

### Step-by-Step Solution:

1. **Understand Water Potential (Ψ)**:
Water potential is a measure of the potential energy of water in a system and is influenced by solute concentration and pressure. It is represented by the formula:
\[ Ψ = Ψ_s + Ψ_p \]
where Ψ_s is the solute potential and Ψ_p is the pressure potential.

2. **Calculate Solute Potential (Ψ_s)**:
The solute potential can be calculated using the formula:
\[ Ψ_s = -iCRT \]
where:
- \(i\) = ionization constant (number of particles the solute dissociates into)
- \(C\) = molar concentration of the solution
- \(R\) = pressure constant (0.0831 liter bar per mole per Kelvin)
- \(T\) = temperature in Kelvin (assume room temperature, approximately 298 K)

3. **Analyze the Ionization of Solutes**:
- For sucrose, which does not dissociate into ions, \(i = 1\).
- For sodium chloride (NaCl), which dissociates into two ions (Na⁺ and Cl⁻), \(i = 2\).

4. **Calculate Ψ_s for 1M Solutions**:
- For 1M sucrose:
\[ Ψ_s(\text{sucrose}) = -1 \times 1 \times 0.0831 \times 298 = -24.6 \text{ bars} \]
- For 1M sodium chloride:
\[ Ψ_s(\text{NaCl}) = -2 \times 1 \times 0.0831 \times 298 = -49.2 \text{ bars} \]

5. **Compare Water Potentials**:
Since pressure potential (Ψ_p) is generally assumed to be zero in this context (for comparison purposes), we can directly compare the solute potentials:
- Ψ_s for sucrose = -24.6 bars
- Ψ_s for NaCl = -49.2 bars

6. **Conclusion**:
Since the solute potential of the sodium chloride solution is more negative than that of the sucrose solution, the water potential (Ψ) of the 1M sodium chloride solution is lower than that of the 1M sucrose solution.

### Final Answer:
The water potential (Ψ) of 1M sodium chloride solution is **lower** compared to the 1M sucrose solution.

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