Question

Sap rises in maple trees as a result of the osmotic pressure difference between the sugar solution within the tree and the water in the ground around the roots. The sap contains 1% by weight of sucrose in water. Assuming the temperature is 27 degrees Celsius, find:

a) concentration in mol/m^3
b) the osmotic pressure
c) the height the sap rises

Answer 1

1% of sucrose in water indicates 1 g of sucrose in 100g of water.

From density of water 1g = 1cm^3

volume of water = 100 cm^3

molarity = mass of solute/molar mass of solute * 1000/volume of solution in mL

concentraion in molarity = 1/342 * 1000/100 cm^3

                         = 1/342 * 1000/100 * (10^-2m)^3

Concentration = 29239.7 mol/m^3

b)

Osmotic pressure = C * S * T

C = concentration of the solution

S = solution constant

T = temperature of the solution in K

Osmotic pressure = 29239.7 mol/m^3 * 0.0831 L atm/mol K * (27 +273)K

Osmotic pressure = 29239.7 mol/1000L * 0.0831 L atm/mol K * (27+273) K

Osmotic pressure = 728.945 atm

c)

Height of the saps from the formula ,

P = d * h * g

P = Pressure difference in pascals

d = density in kg/m^3

h = height in m

g = gravitational field strength in Newtons/Kg

Pressure = 728.945 atm = 728.945 * 1.0132 * 10^5 pascal

d = 29239.7 mol/m^3 = 29239.7 * 342 * 10^-3 kg/m^3 =   9999.9 kg/m^3

g = gravitational force = 9.8 Newtons/kg

height h = 728.945 * 1.0132 * 10^5/(9999.9 * 9.8)

height h = 753.647 m