Chemistry: An Atoms-Focused Approach
Chemistry: An Atoms-Focused Approach
14th Edition
ISBN: 9780393912340
Author: Thomas R. Gilbert, Rein V. Kirss, Natalie Foster
Publisher: W. W. Norton & Company
Question
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Chapter 11, Problem 11.44QA
Interpretation Introduction

To find

The concentration of given elements in molality units.

Expert Solution & Answer
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Answer to Problem 11.44QA

Solution:

i. Molality of Al3+ is 1.9 × 10-6 m

ii. Molality of Fe3+ is 7.2 × 10-7 m

iii. Molality of Ca2+ is 3.3 × 10-4 m

iv. Molality of Na+ is 2.3 × 10-4 m

v. Molality of K+ is 3.3 × 10-5 m

vi. Molality of Mg2+ is 1.4 × 10-4 m

Explanation of Solution

1) Concept:

Here we assume 1  kg of river water. With the mass of river water and given concentrations we will find out the mass of each element. From the mass of element and mass of river water we can find out mass of solvent. From the mass and molar mass of element we will find out moles of each element. Finally using moles and mass of solvent in kg we will find out molality of each element.

2) Formula:

Molality= mol of solutemass of solvent in kg

A mole is the SI unit of amount chemical substance. When writing units, it is written as “mol”.

3) Given:

i. Concentration of Al3+ = 0.050 mg/kg

ii. Concentration of Fe3+ = 0.040 mg/kg

iii. Concentration of Ca2+ = 13.4 mg/kg

iv. Concentration of Na+ = 5.2 mg/kg

v. Concentration of K+ = 1.3 mg/kg

vi. Concentration of Mg2+ = 3.4 mg/kg

Conversion factor:

1 kg=1000 g

1 g=1000 mg

4) Calculations:

We will convert mass of river water from kilogram to gram.

1 kg × 1000 g1 kg=1000 g

Calculation of molality of Al3+.

We calculate the mass of Al3+ using 1  kg mass of river water and given concentration of Al3+.

Mass of Al3+=1 kg × 0.050 mg1 kg=0.050 mg

We will convert this mass from mg to kg using the conversion factor between them.

0.050 mg × 1 g1000 mg=5.0 × 10-5 g

From mass of river water and mass of element we will calculate mass of solvent.

Mass of solvent=Mass of solution-Mass of solute

Mass of solvent=1000 g- 5.0 × 10-5 g=999.99995 g

Convert mass of solvent from gram to kilogram using the conversion factor between them.

999.99995 g × 1 kg1000 g=0.99999995 kg

Now we calculate moles of solute using 5.0 × 10-5 g and molar mass of Al3+ (26.982 g/mol)

5.0 × 10-5 g × 1 mol26.982 g=1.853 × 10-6 mol

Finally using mole solute and mass of solvent we can calculate molality of Al3+.

m= 1.853 × 10-6 mol0.99999995 kg= 1.853 × 10-6molkgof Al3+

The molality of Al3+ is 1.9 × 10-6 m.

Calculation of molality of Fe3+.

We calculate the mass of Fe3+ using 1 kg mass of river water and given concentration of Fe3+.

Mass of Fe3+=1 kg × 0.040 mg1 kg=0.040 mg

We will convert this mass from mg to kg using the conversion factor between them.

0.040 mg × 1 g1000 mg=4.0 × 10-5 g

From mass of river water and mass of element we will calculate mass of solvent.

Mass of solvent=Mass of solution-Mass of solute

Mass of solvent=1000 g- 4.0 × 10-5 g=999.99996 g

Convert mass of solvent from gram to kilogram using the conversion factor between them.

999.99996 g × 1 kg1000 g=0.99999996 kg

Now we calculate moles of solute using 4.0 × 10-5 g and molar mass of Fe3+ (55.845 g/mol)

4.0 × 10-5 g × 1 mol55.845 g=7.163 × 10-7 mol

Finally using mole solute and mass of solvent we can calculate molality of Fe3+.

m= 7.163 × 10-7 mol 0.99999996 kg= 7.163 × 10-7 molkgof Fe3+

The molality of Fe3+ is 7.2 × 10-7 m.

Calculation of molality of Ca2+.

We calculate the mass of Ca2+ using 1 kg mass of river water and given concentration of Ca2+.

Mass of Ca2+=1 kg × 13.4 mg1 kg=13.4 mg

We will convert this mass from mg to kg using the conversion factor between them.

13.4 mg × 1 g1000 mg=1.34 × 10-4 g

From mass of river water and mass of element we will calculate mass of solvent.

Mass of solvent=Mass of solution-Mass of solute

Mass of solvent=1000 g- 1.34 × 10-4 g=999.9866 g

Convert mass of solvent from gram to kilogram using the conversion factor between them.

999.9866 g × 1 kg1000 g=0.9999866 kg

Now we calculate moles of solute using 1.34 × 10-4 g and molar mass of Ca2+ (40.078 g/mol)

1.34 × 10-4 g × 1 mol40.078 g=3.34 × 10-4 mol

Finally using mole solute and mass of solvent we can calculate molality of Ca2+.

m= 3.34 × 10-4 mol 0.9999866 kg= 3.34 × 10-4 molkgof Ca2+

The molality of Ca2+ is 3.3 × 10-4 m

Calculation of molality of Na+.

We calculate the mass of Na+ using 1 kg mass of river water and given concentration of Na+.

Mass of Na+=1 kg × 5.2 mg1 kg=5.2 mg

We will convert this mass from mg to kg using the conversion factor between them.

5.2 mg × 1 g1000 mg=5.2 × 10-3 g

From mass of river water and mass of element we will calculate mass of solvent.

Mass of solvent=Mass of solution-Mass of solute

Mass of solvent=1000 g- 5.2 × 10-3 g=999.9948 g

Convert mass of solvent from gram to kilogram using the conversion factor between them.

999.9948 g × 1 kg1000 g=0.9999948 kg

Now we calculate moles of solute using 1.34 × 10-4 g and molar mass of Na+ (22.99 g/mol)

5.2 × 10-3 g × 1 mol22.99 g=2.26 × 10-4 mol

Finally using mole solute and mass of solvent we can calculate molality of Na+.

m= 2.26 × 10-4 mol 0.9999948 kg= 2.26× 10-4 molkgof Na+

The molality of Na+ is 2.3× 10-4 m.

Calculation of molality of K+.

We calculate the mass of K+ using 1 kg mass of river water and given concentration of K+.

Mass of K+=1 kg × 1.3 mg1 kg=1.3 mg

We will convert this mass from mg to kg using the conversion factor between them.

1.3 mg × 1 g1000 mg=1.3 × 10-3 g

From mass of river water and mass of element we will calculate mass of solvent.

Mass of solvent=Mass of solution-Mass of solute

Mass of solvent=1000 g- 1.3 × 10-3 g=999.9987 g

Convert mass of solvent from gram to kilogram using the conversion factor between them.

999.9987 g × 1 kg1000 g=0.9999987 kg

Now we calculate moles of solute using 1.3 × 10-3 g and molar mass of K+ (39.098 g/mol)

1.3 × 10-3 g × 1 mol39.098 g=3.32 × 10-5 mol

Finally using mole solute and mass of solvent we can calculate molality of K+.

m= 3.32 × 10-5 mol 0.9999987 kg= 3.32 × 10-5 molkgof K+

The molality of K+ is 3.3 × 10-5 m.

Calculation of molality of Mg2+.

We calculate the mass of Mg2+ using 1 kg mass of river water and given concentration of Mg2+.

Mass of Mg2+=1 kg × 3.4 mg1 kg=3.4 mg

We will convert this mass from mg to kg using the conversion factor between them.

3.4 mg × 1 g1000 mg=3.4 × 10-3 g

From mass of river water and mass of element we will calculate mass of solvent.

Mass of solvent=Mass of solution-Mass of solute

Mass of solvent=1000 g- 3.4 × 10-3 g=999.9966 g

Convert mass of solvent from gram to kilogram using the conversion factor between them.

999.9966 g × 1 kg1000 g=0.9999966 kg

Now we calculate moles of solute using 3.4 × 10-3 g and molar mass of Mg2+ (24.305 g/mol)

3.4 × 10-3 g × 1 mol24.305 g=1.4 × 10-4 mol

Finally using mole solute and mass of solvent we can calculate molality of Mg2+.

m= 1.4 × 10-4 mol 0.9999966 kg= 1.4 × 10-4 molkgof Mg2+

The molality of Mg2+ is 1.4 × 10-4 m

Conclusion

With the mass of river water and given concentrations of elements we find out the mass of each element. From the mass of element and mass of river water we find out mass of solvent. From the mass and molar mass of element we find out moles of each element. Finally using moles and mass of solvent in kg we find out molality of each element.

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Chapter 11 Solutions

Chemistry: An Atoms-Focused Approach

Ch. 11 - Prob. 11.12QACh. 11 - Prob. 11.13QACh. 11 - Prob. 11.14QACh. 11 - Prob. 11.15QACh. 11 - Prob. 11.16QACh. 11 - Prob. 11.17QACh. 11 - Prob. 11.18QACh. 11 - Prob. 11.19QACh. 11 - Prob. 11.20QACh. 11 - Prob. 11.21QACh. 11 - Prob. 11.22QACh. 11 - Prob. 11.23QACh. 11 - Prob. 11.24QACh. 11 - Prob. 11.25QACh. 11 - Prob. 11.26QACh. 11 - Prob. 11.27QACh. 11 - Prob. 11.28QACh. 11 - Prob. 11.29QACh. 11 - Prob. 11.30QACh. 11 - Prob. 11.31QACh. 11 - Prob. 11.32QACh. 11 - Prob. 11.33QACh. 11 - Prob. 11.34QACh. 11 - Prob. 11.35QACh. 11 - Prob. 11.36QACh. 11 - Prob. 11.37QACh. 11 - Prob. 11.38QACh. 11 - Prob. 11.39QACh. 11 - Prob. 11.40QACh. 11 - Prob. 11.41QACh. 11 - Prob. 11.42QACh. 11 - Prob. 11.43QACh. 11 - Prob. 11.44QACh. 11 - Prob. 11.45QACh. 11 - Prob. 11.46QACh. 11 - Prob. 11.47QACh. 11 - Prob. 11.48QACh. 11 - Prob. 11.49QACh. 11 - Prob. 11.50QACh. 11 - Prob. 11.51QACh. 11 - Prob. 11.52QACh. 11 - Prob. 11.53QACh. 11 - Prob. 11.54QACh. 11 - Prob. 11.55QACh. 11 - Prob. 11.56QACh. 11 - Prob. 11.57QACh. 11 - Prob. 11.58QACh. 11 - Prob. 11.59QACh. 11 - Prob. 11.60QACh. 11 - Prob. 11.61QACh. 11 - Prob. 11.62QACh. 11 - Prob. 11.63QACh. 11 - Prob. 11.64QACh. 11 - Prob. 11.65QACh. 11 - Prob. 11.66QACh. 11 - Prob. 11.67QACh. 11 - Prob. 11.68QACh. 11 - Prob. 11.69QACh. 11 - Prob. 11.70QACh. 11 - Prob. 11.71QACh. 11 - Prob. 11.72QACh. 11 - Prob. 11.73QACh. 11 - Prob. 11.74QACh. 11 - Prob. 11.75QACh. 11 - Prob. 11.76QACh. 11 - Prob. 11.77QACh. 11 - Prob. 11.78QACh. 11 - Prob. 11.79QACh. 11 - Prob. 11.80QACh. 11 - Prob. 11.81QACh. 11 - Prob. 11.82QACh. 11 - Prob. 11.83QACh. 11 - Prob. 11.84QA
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