Which of the following solutions would have the highest osmotic pressure:

Options

A. `(M)/(10) "" NaCl`
B. `(M)/(10)` Urea
C. `(M)/(10) BaCl_(2)`
D. `(M)/(10)` Glucose

Answer

To determine which solution has the highest osmotic pressure, we will use the formula for osmotic pressure (π):

\[ \pi = iCRT \]

Where:
- \(i\) = van 't Hoff factor (number of particles the solute dissociates into)
- \(C\) = concentration of the solution
- \(R\) = universal gas constant
- \(T\) = temperature (in Kelvin)

We will analyze the osmotic pressure for each solution given in the options.

### Step 1: Analyze NaCl (sodium chloride)

1. **Dissociation**: NaCl dissociates into two ions: Na⁺ and Cl⁻.
- \(i = 2\)
2. **Concentration**: Given as \(C = \frac{m}{10}\).
3. **Osmotic Pressure Calculation**:
\[ \pi_{NaCl} = i \cdot C \cdot R \cdot T = 2 \cdot \frac{m}{10} \cdot R \cdot T = \frac{2m}{10}RT = \frac{m}{5}RT \]

### Step 2: Analyze Urea

1. **Dissociation**: Urea does not dissociate in solution.
- \(i = 1\)
2. **Concentration**: Given as \(C = \frac{m}{10}\).
3. **Osmotic Pressure Calculation**:
\[ \pi_{Urea} = i \cdot C \cdot R \cdot T = 1 \cdot \frac{m}{10} \cdot R \cdot T = \frac{m}{10}RT \]

### Step 3: Analyze BaCl₂ (barium chloride)

1. **Dissociation**: BaCl₂ dissociates into three ions: Ba²⁺ and 2 Cl⁻.
- \(i = 3\)
2. **Concentration**: Given as \(C = \frac{m}{10}\).
3. **Osmotic Pressure Calculation**:
\[ \pi_{BaCl2} = i \cdot C \cdot R \cdot T = 3 \cdot \frac{m}{10} \cdot R \cdot T = \frac{3m}{10}RT \]

### Step 4: Analyze Glucose

1. **Dissociation**: Glucose does not dissociate in solution.
- \(i = 1\)
2. **Concentration**: Given as \(C = \frac{m}{10}\).
3. **Osmotic Pressure Calculation**:
\[ \pi_{Glucose} = i \cdot C \cdot R \cdot T = 1 \cdot \frac{m}{10} \cdot R \cdot T = \frac{m}{10}RT \]

### Step 5: Compare the Osmotic Pressures

Now we have the osmotic pressures for all solutions:

- \( \pi_{NaCl} = \frac{m}{5}RT \)
- \( \pi_{Urea} = \frac{m}{10}RT \)
- \( \pi_{BaCl2} = \frac{3m}{10}RT \)
- \( \pi_{Glucose} = \frac{m}{10}RT \)

To compare:
- \( \frac{m}{5}RT = \frac{2m}{10}RT \)
- \( \frac{3m}{10}RT \)
- \( \frac{m}{10}RT \)

The highest osmotic pressure is from \(BaCl₂\) since \( \frac{3m}{10}RT \) is greater than the others.

### Conclusion

The solution with the highest osmotic pressure is **BaCl₂**.

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