Question

If the fluid inside a tree is about 0.1M more concentrated in solute than the groundwater that bathes the roots, how high will the column of fluid rise in the tree at 25⁰C? Assume that the density of the fluid is 1.0 g/cm³. The density of mercury is 13.6g/cm³

Short answer

The height of the column till which fluid rise is 25.32 m

Step-by-step solution

Step 1- Calculating the osmotic pressure

Using the formula osmotic pressure= MRT

M= molarity

R= 0.0821 atm mol.K

Temperature= 25C = 298 K

= 0.1 x 0.0821 x 298 = 2.45 atm

Step 2- Calculating pressure

Osmotic pressure x atmospheric pressure x density of the fluid

= 2.45 atm x 760mm Hg/ 1 atm x 1m Hg/10³ mm Hg.

= 1.862 m Hg. This pressure will raise the level of,mercury in the column to a height of 1.862m

Step 3- calculating height

The fluid inside the tree has a low density as compared to mercury so it will rise higher than mercury at the same pressure

Pressure = $\rho gh$

Where g is acceleration due to gravity, h is height and rho is the density

($\rho gh$)_{mercury =}($\rho gh$)_water

(13.6 g/cm³ x 9.8 m/s² x 1.862 m) = (1 g/cm³ x 9.8 m/s²x h)

So, h= 25.32 m