Question

P1. Giant sequoias, an indigenous species of California, are among the tallest trees on Earth. Some individuals live to be 3500 years old. Water entering at the roots must be transported up some 300 m of xylem in order to nourish cells at the top of the tree. Calculate the work done against gravity in transporting a single water molecule this distance.

Answer 1

Work done in lifting one water molecule = change in the potential energy from ground to top at 300 m

1 mole of water = 6.023*10²³ molecules of water

1 mole of water weighs = 18 g

1 molecule of water weighs = 18/6.023 * 10²³ = 2.988 * 10^-23 g

in terms of Kgs,

1 molecule of water = 2.988 * 10^-26 Kg

h = h2 - h1 = 300 - 0 = 300m

g = 9.81

Potential energy change = mgh = 2.988 * 10^-26 * 300 * 9.81 = 8.793 * 10^-23 J

Work done in transporting a single molecule of water =  8.793 * 10^-23 J