The plot of osmotic pressure (π) vs concentration (mol L^–1 ) for a solution gives a straight line with slope 25.73 L bar mol^–1 . The temperature at which the osmotic pressure measurement is done is

(Use R = 0.083 L bar mol^–1 K^–1 )

The correct option is 37°C.

To find the temperature at which the osmotic pressure measurement is carried out, we can use the van 't Hoff equation for osmotic pressure:

$\pi =CRT$

where:
- $\pi$ is the osmotic pressure (in bar),
- $C$ is the molar concentration of the solution (in mol L^-1),
- $R$ is the universal gas constant (0.083 L bar mol^-1 K^-1),
- $T$ is the absolute temperature (in Kelvin).

The equation can be rearranged in the slope-intercept form of a straight line, $y=mx$, where $y=\pi$ and $x=C$:

$\pi =\left(RT\right)C$

Thus, a plot of osmotic pressure ($\pi$) versus concentration ($C$) gives a straight line passing through the origin with a slope ($m$) equal to:

$\text{Slope}=RT$

Given that the slope of the line is 25.73 L bar mol^-1, we can write:

$RT=25.73$

Now, substitute the value of $R=0.083{\text{L bar mol}}^{-1}{\text{K}}^{-1}$ into the equation to calculate the temperature $T$ in Kelvin:

$T=\frac{25.73}{0.083}$

$T\approx 310\text{K}$

To convert the absolute temperature to degrees Celsius (°C), we subtract 273 from the temperature in Kelvin:

$t{\text{(°C)}}^{}=T\text{(K)}-273$

$t=310-273=37{\text{°C}}^{}$

Therefore, the temperature at which the osmotic pressure measurement is done is 37°C.