Chemistry for Today: General, Organic, and Biochemistry
Chemistry for Today: General, Organic, and Biochemistry
9th Edition
ISBN: 9781305960060
Author: Spencer L. Seager, Michael R. Slabaugh, Maren S. Hansen
Publisher: Cengage Learning
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Chapter 7, Problem 7.30E

Calculate the concentration in % ( w / w ) of the following solutions. Assume water has a density of 1.00 g / mL .

a. 20.0 g of salt is dissolved in 250. mL of water.

b. 0.100 mol of solid glucose ( C 6 H 12 O 6 ) is dissolved in 100. mL of water.

c. 120 g of solid is dissolved in 100. mL of water.

d. 10.0 mL of ethyl alcohol (density = 0.789 g / mL ) is mixed with 10.0 mL of water.

Expert Solution
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Interpretation Introduction

(a)

Interpretation:

The concentration in %(w/w) of 20.0g of salt dissolved in 250.mL of water is to be calculated.

Concept introduction:

A solution is prepared by mixing proper amount of solute and solvent. The concentration of solution when measured on the basis of solution volume, is expressed in terms of percent weight by volume (%w/v), percent volume by volume (%v/v) and molarity (M). When concentration is measured on the basis of mass of solvent, it is expressed in terms of percent weight by weight (%w/w).

Answer to Problem 7.30E

The concentration in %(w/w) of 20.0g of salt dissolved in 250.mL of water is 7.41%w/w.

Explanation of Solution

The formula to calculate concentration in %(w/w) is given below as,

%(w/w)=SoluteMassSolutionMass×100

The density of water is 1.00g/mL. Thus, the mass of water is equal to its volume. Hence in this case the mass of solution is taken as 250.g. Substitute the value of mass of salt and mass of solution in the above equation as follows.

%(w/w)=Massof saltSolutionMass×100=20.0g(250+20)g×100=20g270g×100=7.41%w/w

Conclusion

The concentration in %(w/w) of 20.0g of salt dissolved in 250.mL of water is 7.41%w/w.

Expert Solution
Check Mark
Interpretation Introduction

(b)

Interpretation:

The concentration in %(w/w) of 0.100mol of solid glucose (C6H12O6) dissolved in 100.mL of water is to be calculated.

Concept introduction:

A solution is prepared by mixing proper amount of solute and solvent. The concentration of solution when measured on the basis of solution volume, is expressed in terms of percent weight by volume (%w/v), percent volume by volume (%v/v) and molarity (M). When concentration is measured on the basis of mass of solvent, it is expressed in terms of percent weight by weight (%w/w).

Answer to Problem 7.30E

The concentration in %(w/w) of 0.100mol of solid glucose (C6H12O6) dissolved in 100.mL of water is 15.27%w/w.

Explanation of Solution

The formula to calculate number of moles of solutes is given below as,

Molesofsolute=MassofsoluteMolarmassofsolute

Rearrange the above equation for mass of solute as follows.

Molesofsolute=MassofsoluteMolarmassofsoluteMassofsolute=Molesofsolute×Molarmassofsolute …(1)

The molar mass of glucose can be calculated as follows.

C6H12O6=(6×C)+(12×H)+(6×O)=(6×12)+(12×1)+(6×16)=180g/mol

Substitute the values in the equation (1) as follows.

MassofC6H12O6=MolesofC6H12O6×MolarmassofC6H12O6=0.100mol×180g/molg/mol=18.0g

The formula to calculate concentration in %(w/w) is given below as,

%(w/w)=SoluteMassSolutionMass×100

The density of water is 1.00g/mL. Thus, the mass of water is equal to its volume. Hence in this case the mass of solution is taken as 100.g. Substitute the value of mass of solute and mass of solution in the above equation as follows.

%(w/w)=MassofC6H12O6SolutionMass×100=18.02g(100+18.0)g×100=18.02g118.0g×100=15.27%w/w

Conclusion

The concentration in %(w/w) of 0.100mol of solid glucose (C6H12O6) dissolved in 100.mL of water is 15.27%w/w.

Expert Solution
Check Mark
Interpretation Introduction

(c)

Interpretation:

The concentration in %(w/w) of 120g of solid dissolved in 100.mL of water is to be calculated.

Concept introduction:

A solution is prepared by mixing proper amount of solute and solvent. The concentration of solution when measured on the basis of solution volume, is expressed in terms of percent weight by volume (%w/v), percent volume by volume (%v/v) and molarity (M). When concentration is measured on the basis of mass of solvent, it is expressed in terms of percent weight by weight (%w/w).

Answer to Problem 7.30E

The concentration in %(w/w) of 120g of solid dissolved in 100.mL of water is 54.55%w/w.

Explanation of Solution

The formula to calculate concentration in %(w/w) is given below as,

%(w/w)=SoluteMassSolutionMass×100

The density of water is 1.00g/mL. Thus, the mass of water is equal to its volume. Hence in this case the mass of solution is taken as 100.g. Substitute the value of mass of solute and mass of solution in the above equation as follows.

%(w/w)=SoluteMassSolutionMass×100=120g(100+120)g×100=120g220g×100=54.55%w/w

Conclusion

The concentration in %(w/w) of 120g of solid dissolved in 100.mL of water is 54.55%w/w.

Expert Solution
Check Mark
Interpretation Introduction

(d)

Interpretation:

The concentration in %(w/w) of 10.0mL of ethyl alcohol (density =0.789g/mL) mixed with 10.0mL of water is to be calculated.

Concept introduction:

A solution is prepared by mixing proper amount of solute and solvent. The concentration of solution when measured on the basis of solution volume, is expressed in terms of percent weight by volume (%w/v), percent volume by volume (%v/v) and molarity (M). When concentration is measured on the basis of mass of solvent, it is expressed in terms of percent weight by weight (%w/w).

Answer to Problem 7.30E

The concentration in %(w/w) of 10.0mL of ethyl alcohol (density =0.789g/mL) mixed with 10.0mL of water is 44.10%w/w.

Explanation of Solution

The formula to calculate concentration in %(w/w) is given below as,

%(w/w)=SoluteMassSolutionMass×100 …(1)

The formula to calculate density is given below as,

d=mV

Where,

m is the mass of the substance.

V is the volume of the substance.

d is the density of the substance.

The density of water is 1.00g/mL. Thus, the mass of water is equal to its volume. Hence in this case the mass of solution is taken as 10.g. But the density of ethyl alcohol is 0.789g/mL. Thus, the mass of 10.0mL of ethyl alcohol can be calculated as follows.

d=mVm=d×V=0.789g/mL×10.0mL=7.89g

Substitute the value of mass of ethyl alcohol and mass of solution in the equation (1) as follows.

%(w/w)=Massofethyl alcoholSolutionMass×100=7.89g(10+7.89)g×100=7.89g17.89g×100=44.10%w/w

Conclusion

The concentration in %(w/w) of 10.0mL of ethyl alcohol (density =0.789g/mL) mixed with 10.0mL of water is 44.10%w/w.

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Chapter 7 Solutions

Chemistry for Today: General, Organic, and Biochemistry

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Solutions: Crash Course Chemistry #27; Author: Crash Course;https://www.youtube.com/watch?v=9h2f1Bjr0p4;License: Standard YouTube License, CC-BY