At a certain temperature the values of the slope of the plot of osmotic pressure (π) against concentration (C in mol $L^{-1}$) of a certain polymer solution is 291 R. The temperature at which osmotic pressure measured is -

18°C

The correct answer is Option (2) → 18°C.

To determine the temperature at which the osmotic pressure is measured, we can use van't Hoff's law for osmotic pressure:

\(\pi = C R T\)

Where:

\(\pi\) is the osmotic pressure,

\(C\) is the concentration (in mol/L),

\(R\) is the universal gas constant,

\(T\) is the temperature (in Kelvin).

The slope of the plot of osmotic pressure \(\pi\) versus concentration \(C\) is given as 291 R. From the equation \(\pi = C R T\), we can observe that:

\(\text{slope} = R T\)

Given that the slope is \(291 R\), we can write:

\(291 R = R T\)

Canceling \(R\) from both sides:

\(T = 291 \, \text{K}\)

Now, we need to convert the temperature from Kelvin to Celsius. The conversion formula is:

\(T(\degree C) = T(K) - 273\)

So,

\(T(\degree C) = 291 - 273 = 18^\degree C\)

Conclusion:

The temperature at which the osmotic pressure was measured is 18°C, which corresponds to option 2.