The osmotic pressure of solution at `0^(@)C` is 4 atm what will be its osmotic pressure at 546 K. Under similar conditions

Options

A. 4 atm
B. 2 atm
C. 1 atm
D. 8 atm

Explanation

To solve the problem of finding the osmotic pressure of a solution at 546 K given that its osmotic pressure at 0°C is 4 atm, we can use the formula for osmotic pressure, which is given by:

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

Where:
- \(\pi\) = osmotic pressure
- \(C\) = concentration of the solution (constant in this case)
- \(R\) = universal gas constant (constant)
- \(T\) = absolute temperature in Kelvin

### Step 1: Identify the initial conditions
- The initial osmotic pressure (\(\pi_1\)) is 4 atm at \(T_1 = 0°C\).
- Convert \(T_1\) to Kelvin:
\[ T_1 = 0 + 273 = 273 \, K \]

### Step 2: Identify the final conditions
- The final temperature (\(T_2\)) is given as 546 K.
- We need to find the final osmotic pressure (\(\pi_2\)).

### Step 3: Establish the relationship between osmotic pressures and temperatures
Since the concentration \(C\) and the gas constant \(R\) remain constant, we can establish the relationship:
\[ \frac{\pi_1}{\pi_2} = \frac{T_1}{T_2} \]

### Step 4: Rearranging the formula to find \(\pi_2\)
Rearranging the above equation gives us:
\[ \pi_2 = \pi_1 \cdot \frac{T_2}{T_1} \]

### Step 5: Substitute the known values
Substituting the known values into the equation:
\[ \pi_2 = 4 \, \text{atm} \cdot \frac{546 \, K}{273 \, K} \]

### Step 6: Calculate \(\pi_2\)
Calculating the right side:
\[ \pi_2 = 4 \, \text{atm} \cdot 2 = 8 \, \text{atm} \]

### Conclusion
Thus, the osmotic pressure at 546 K is:
\[ \pi_2 = 8 \, \text{atm} \]

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