Question

5. Tree sap can be a very concentrated solution of solutes in water. These are mostly sugars, with van’t Hoff factors of 1. The root system provides a semi-permeable membrane across which water moves to “dilute” the sap, providing a significant osmotic pressure.

a. If a tree sap has an effective concentration of 37 Molar, what pressure is generate at 298K across the endodermis root membrane? R = 0.08216 L.atm/mol.K.

b. If an osmotic pressure of 1.0 atm can raise a volume of water 10.33 meters high, how high can the sap of this tree rise?

Answer 1

a)905,89 atm of pressure will be generated at 298K.

b)The sap of tree can rise upto 9,357.84 meters.

Step-by-step explanation:

a)

Effective concentration of sap = c = 37 M

Osmotic pressure generate at 298K =
`\pi`

Temperature ,T = 298 K

`\pi =cRT`

`\pi =37 mol/L* 0.08216 atm L/mol L* 298 K`

`\pi =905.89 atm`

905,89 atm of pressure will be generated at 298K across the endodermis root membrane.

b)

Given that 1.0 at of pressure raises the volume of water upto height of 10.33 m

Then 905.89 atm of pressure will raise the height of water upto:

`(10.33)/(1.0)* 905.89 m=9,357.84 m`

The sap of the tree can rise upto 9,357.84 meter.