   Chapter 13, Problem 80GQ

Chapter
Section
Textbook Problem

A tree is 10.0 m tall. (a) What must be the total molarity of the solutes if sap rises to the top of the tree by osmotic pressure at 20 °C? Assume the groundwater outside the tree is pure water and that the density of the sap is 1.0 g/mL. (1 mm Hg = 13.6 mm H2O.) (b) If the only solute in the sap is sucrose, C12H22O11, what is its percent by mass?

(a)

Interpretation Introduction

Interpretation: The total molarity of the solutes if a sap rises to the top of the tree by osmotic pressure at 20°C has to be determined.

Concept introduction:

Colligative properties: Properties of solutions which having influence on the concentration of the solute in it. Colligative properties are,

• Decrease in the vapor pressure
• Increase in the boiling point
• Decline in the freezing point
• Osmotic pressure

Osmotic pressure: The pressure created by the column of solution for the system at equilibrium is a measure of the osmotic pressure.

π=icRT

where,

c is the molar concentration

i is the van’t Hoff factor

The number of moles of any substance can be determined using the equation

Numberofmole=GivenmassofthesubstanceMolarmass

Percentage by mass: ratio of amount of solute to amount of solution and multiplied with 100.

percentbymass=amountofsoluteamountofsolute+amountofsolvent×100%

Explanation

Given,

R=0.08206L.atm K1mol1T=200C=(20+273.15)K=293.15KHeightoftree=10m=10×103mm=10000mm

Density of the solution is 1.0g/mL

Given that 1mmHg=13.6mmH2O

The osmotic pressure is,

The osmotic pressure=(heightofcolumn)×(1mmHg13

(b)

Interpretation Introduction

Interpretation: The percentage by mass of sucrose in the sap has to be determined.

Concept introduction:

Colligative properties: Properties of solutions which having influence on the concentration of the solute in it. Colligative properties are,

• Decrease in the vapor pressure
• Increase in the boiling point
• Decline in the freezing point
• Osmotic pressure

Change in freezing point is calculated by using the equation,

ΔTfp=Kfpmsolute

where,

Kfp is the molal freezing point depression constant.

The number of moles of any substance can be determined using the equation

Numberofmole=GivenmassofthesubstanceMolarmass

Percentage by mass: ratio of amount of solute to amount of solution and multiplied with 100.

percentbymass=amountofsoluteamountofsolute+amountofsolvent×100%

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