At a certain temperature, the value of the slope of the plot of osmotic pressure `(pi)` against concentration (`"C in mol L"^(-1)`) of a certain polymer solution is 291R. The temperature at which osmotic pressure is measured is (R is gas constant)

Options

A. `271^(@)C`
B. `18^(@)C`
C. 564 K
D. 18 K

Explanation

To solve the problem, we need to find the temperature at which the osmotic pressure is measured, given that the slope of the plot of osmotic pressure (π) against concentration (C) is 291R.

### Step-by-Step Solution:

1. **Understand the Relation**:
The relationship between osmotic pressure (π), concentration (C), and temperature (T) is given by the formula:
\[ \pi = CRT \]
where:
- π = osmotic pressure
- C = concentration in mol/L
- R = gas constant
- T = temperature in Kelvin

2. **Identify the Slope**:
The slope of the plot of osmotic pressure (π) against concentration (C) can be derived from the equation:
\[ \text{slope} = \frac{\Delta \pi}{\Delta C} = RT \]
According to the problem, the slope is given as:
\[ \text{slope} = 291R \]

3. **Set Up the Equation**:
From the slope equation, we can equate:
\[ RT = 291R \]

4. **Cancel R**:
Since R is a common factor on both sides of the equation, we can cancel it out (assuming R ≠ 0):
\[ T = 291 \]

5. **Determine the Temperature**:
The temperature T is found to be:
\[ T = 291 \text{ K} \]

6. **Convert to Celsius**:
To convert Kelvin to Celsius, we use the formula:
\[ T(°C) = T(K) - 273 \]
Thus:
\[ T(°C) = 291 - 273 = 18 °C \]

### Final Answer:
The temperature at which the osmotic pressure is measured is **18 °C**.