   Chapter 13, Problem 79GQ

Chapter
Section
Textbook Problem

The following table lists the concentrations of the principal ions in seawater: (a) Calculate the freezing point of seawater. (b) Calculate the osmotic pressure of seawater at 25 °C. What is the minimum pressure needed to purify seawater by reverse osmosis?

(a)

Interpretation Introduction

Interpretation: The freezing point of seawater 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

Freezing point depression: The freezing point of the solution varies with the solute concentration.

Freezing point depression = ΔTfp= Kfp. msolute,where,Kfp=molal freezing point depression constant,msolute= molality of solute.

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

Numberofmole=GivenmassofthesubstanceMolarmass

Explanation

Given,

Molal freezing point depression constant of water is 1.860C/m

The value 1ppm means, it contains 1g of solute in 106g of solution.

Hence, the concentration given in ppm can be taken as the mass of each of the ions on 106g of water.

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

Numberofmole=GivenmassofthesubstanceMolarmass

NumberofmolesofCl=1.95×104g35.45g/mol=550.0mol

Number of moles of Cl is 550.0mol

NumberofmolesofNa+=1.08×104g22.99g/mol=469.8mol

Number of moles of Na+ is 469.8mol

NumberofmolesofMg+=1.29×103g24.31g/mol=53.06mol

Number of moles of Mg+ is 53.06mol

NumberofmolesofSO43=9.05×102g96.06g/mol=9.421mol

Number of moles of SO43 is 9

(b)

Interpretation Introduction

Interpretation: The osmotic pressure of seawater at 250C has to be determined. Minimum pressure needed to purify the seawater using reverse osmosis method has to be calculated.

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 and is calculated by using the equation,

π=cRT

where,

c is the molar concentration

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

Numberofmole=GivenmassofthesubstanceMolarmass

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