Chapter 21, Problem 128SCQ

### 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

# (a) Magnesium is obtained from seawater. If the concentration of Mg2+ in seawater is 0.050 M, what volume of seawater (in liters) must be treated to obtain 1.00 kg of magnesium met.il? What mass of lime (CaO; in kilograms) must be used to precipitate the magnesium in this volume of seawater?(b) When 1.2 × 103 kg of molten MgCl2 is electrolyzed to produce magnesium, what mass (in kilograms) of metal is produced at the cathode? What is produced at the anode? What is the mass of this product? What is the total number of Faradays of electricity used in the process?(c) One industrial process has an energy consumption of 18.5 kWh/kg of Mg. How many joules are required per mole (1 kWh = 1 kilowatt-hour = 3.6 × 106 J)? How does this energy compare with the energy of the following process?

(a)

Interpretation Introduction

Interpretation:

To estimate the mass of lime required to precipitate magneisum from sea water.

Concept introduction:

Magnesium is an alkaline earth metal and is prsent in sea water. The magnesium present in sea water can be extracted by precipitating it with either CaO or Ca(OH)2. The pure metal from the salt obtained can be obtained by the process of electrolysis.

Numberofmoles=MassMolecularmass

Mass=Numberofmoles×Molecularmass

Explanation

The mass of lime that must be used to precipitate magnesium from sea water is calculated below.

Given:

The given reaction is,

Â Â Â Â Mg2+(aq)+CaO(s)+H2O(l)â†’Mg(OH)2(aq)+Ca2+

It is given that the concentration of magnesium ions in sea water is 0.050Â M.

Thus, the number of moles of magnesium in 1Â L of sea water is 0.050Â moles.

Thus, the mass of magnesium ions present is calculated by multiplying the atomic mass of magnesium with the number of moles present which is equal to 1.2Â g.

Thus,

1.2Â g of magnesium is present in 1Â L of sea water

(b)

Interpretation Introduction

Interpretation:

To estimate the mass of product produced at anode and cathode on electrolysis of MgCl2 and also total number of Faradays of electricity used.

Concept introduction:

Magnesium is an alkaline earth metal and is prsent in sea water. The magnesium present in sea water can be extracted by precipitating it with either CaO or Ca(OH)2. The pure metal from the salt obtained can be obtained by the process of electrolysis.

The reduction happens at cathode

The oxidation happens at anode.

Numberofmoles=MassMolecularmass

Mass=Numberofmoles×Molecularmass

The total number of Faradays of electricity used is calculated by the number of electrons involved in the reaction

(c)

Interpretation Introduction

Interpretation:

To estimate how many Joules are required per mole for the given industrial process

Concept introduction:

Magnesium is an alkaline earth metal and is prsent in sea water. The magnesium present in sea water can be extracted by precipitating it with either CaO or Ca(OH)2. The pure metal from the salt obtained can be obtained by the process of electrolysis.

Numberofmoles=MassMolecularmass

Mass=Numberofmoles×Molecularmass

1kWh=1kilowatthour=3.6×106J

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