Chapter 13, Problem 79GQ

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
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,

â€‚Â Molal freezing point depression constant of water is â€‰âˆ’1.860C/m

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

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

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

â€‚Â Numberâ€‰ofâ€‰moleâ€‰=Givenâ€‰massâ€‰ofâ€‰theâ€‰substanceMolarâ€‰massâ€‰

â€‚Â Numberâ€‰ofâ€‰molesâ€‰ofâ€‰Clâˆ’â€‰=â€‰1.95â€‰Ã—â€‰104â€‰g35.45â€‰g/mol=â€‰550.0â€‰mol

Number of moles of Clâˆ’ is 550.0â€‰mol

â€‚Â Numberâ€‰ofâ€‰molesâ€‰ofâ€‰Na+â€‰=â€‰1.08â€‰Ã—â€‰104â€‰g22.99â€‰g/mol=â€‰469.8â€‰mol

Number of moles of Na+ is 469.8â€‰mol

â€‚Â Numberâ€‰ofâ€‰molesâ€‰ofâ€‰Mg+â€‰=â€‰1.29â€‰Ã—â€‰103â€‰g24.31â€‰g/mol=â€‰53.06â€‰mol

Number of moles of Mg+ is â€‰53.06â€‰mol

â€‚Â Numberâ€‰ofâ€‰molesâ€‰ofâ€‰SO43âˆ’â€‰=â€‰9.05â€‰Ã—â€‰102â€‰g96.06â€‰g/mol=â€‰9.421â€‰mol

Number of moles of â€‰SO43âˆ’ is â€‰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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