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Consider the problem of how plants might lift water from ground level to their leaves. Assume that there us a semipermeable membrane at the roots, with pure water on the outside, and an ideal solution inside a small cylindrical capillary inside the plant. The solute mole fraction inside the capillary is x = 0.001. The radius of the capillary is 0.1 mm. Assuming the density of the solution = 1 g/mL, what is the height of the solution at 298 K? Can osmotic pressure account for raising this water?

Consider the problem of how plants might lift water from ground level to their leaves. Assume that there us a semipermeable membrane at the roots, with pure water on the outside, and an ideal solution inside a small cylindrical capillary inside the plant. The solute mole fraction inside the capillary is x = 0.001. The radius of the capillary is 0.1 mm. Assuming the density of the solution = 1 g/mL, what is the height of the solution at 298 K? Can osmotic pressure account for raising this water?

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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**Problem Description: Lifting Water in Plants** **Concept:** The challenge is to understand how plants transport water from the ground to their leaves. This involves examining a scenario where a semipermeable membrane at the plant roots separates pure water outside from an ideal solution within the plant's cylindrical capillaries. **Given Information:** - **Semipermeable Membrane:** Present at the roots. - **Outside:** Pure water environment. - **Inside:** Ideal solution with the solute mole fraction (\(x\)) of 0.001 in a capillary. - **Capillary Radius:** 0.1 mm. - **Solution Density:** 1 g/mL. - **Temperature:** 298 K (Kelvin). **Questions:** 1. What is the height that the solution can achieve? 2. Can osmotic pressure alone account for this water movement? **Analysis Approach:** - Consider the effects of osmotic pressure across the membrane. - Use principles of capillary action and the physical properties given to determine the potential height of water rise. This scenario explores the physical principles of water transport in plants, focusing on osmotic pressure and its impact within a simplified model.
Transcribed Image Text:**Problem Description: Lifting Water in Plants** **Concept:** The challenge is to understand how plants transport water from the ground to their leaves. This involves examining a scenario where a semipermeable membrane at the plant roots separates pure water outside from an ideal solution within the plant's cylindrical capillaries. **Given Information:** - **Semipermeable Membrane:** Present at the roots. - **Outside:** Pure water environment. - **Inside:** Ideal solution with the solute mole fraction (\(x\)) of 0.001 in a capillary. - **Capillary Radius:** 0.1 mm. - **Solution Density:** 1 g/mL. - **Temperature:** 298 K (Kelvin). **Questions:** 1. What is the height that the solution can achieve? 2. Can osmotic pressure alone account for this water movement? **Analysis Approach:** - Consider the effects of osmotic pressure across the membrane. - Use principles of capillary action and the physical properties given to determine the potential height of water rise. This scenario explores the physical principles of water transport in plants, focusing on osmotic pressure and its impact within a simplified model.
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