Concept explainers
(a)
Interpretation:
The solution that has the highest molarity is to be determined.
Concept introduction:
Molarity (M) is one of the concentration terms that determine the number of moles of solute present in per litre of solution. Unit of molarity is mol/L.
The expression to calculate the molarity of solution when moles of solute and volume of solution are given is as follows:
Molarity of solution(M)=moles of solute(mol)volume of solution(L)
(a)
Answer to Problem 4.12P
The solution in beaker B has the highest molarity.
Explanation of Solution
Consider the particles present in the beaker as moles of solute.
The formula to calculate the molarity of solution in beaker is as follows:
Molarity of solution(M)=number of molesvolume of solution (1)
Substitute 8 mol for number of moles and 50.00 mL for volume of solution in the equation (1) to calculate the molarity of solution in beaker A.
Molarity of solution=8 mol50.00 mL(1000 mL1 L)=160 mol/L
Substitute 12 mol for number of moles and 50.00 mL for volume of solution in the equation (1) to calculate the molarity of solution in beaker B.
Molarity of solution=12 mol50.00 mL(1000 mL1 L)=60000 mol/L
Substitute 4 mol for number of moles and 50.00 mL for volume of solution in the equation (1) to calculate the molarity of solution in beaker C.
Molarity of solution=4 mol50.00 mL(1000 mL1 L)=80 mol/L
Substitute 4 mol for number of moles and 50.00 mL for volume of solution in the equation (1) to calculate the molarity of solution in beaker D.
Molarity of solution=4 mol50.00 mL(1000 mL1 L)=80 mol/L
Substitute 2 mol for number of moles and 25.00 mL for volume of solution in the equation (1) to calculate the molarity of solution in beaker E.
Molarity of solution=2 mol25.00 mL(1000 mL1 L)=80 mol/L
Substitute 4 mol for number of moles and 25.00 mL for volume of solution in the equation (1) to calculate the molarity of solution in beaker F.
Molarity of solution=4 mol25.00 mL(1000 mL1 L)=160 mol/L.
Hence, the solution in beaker B has the highest molarity.
Molarity (M) is directly proportional to number of moles and inversely related to the volume of solution.
(b)
Interpretation:
The solutions that have the same molarity are to be determined.
Concept introduction:
Molarity (M) is one of the concentration terms that determine the number of moles of solute present in per litre of solution. Unit of molarity is mol/L.
The expression to calculate the molarity of solution when moles of solute and volume of solution are given is as follows:
Molarity of solution(M)=moles of solute(mol)volume of solution(L)
(b)
Answer to Problem 4.12P
The solution in beaker A and F has the same molarity and solution in beaker C, D and E have the same molarity.
Explanation of Solution
Consider the particles present in the beaker as moles of solute.
The formula to calculate the molarity of solution in beaker is as follows:
Molarity of solution(M)=number of molesvolume of solution (1)
Substitute 8 mol for number of moles and 50.00 mL for volume of solution in the equation (1) to calculate the molarity of solution in beaker A.
Molarity of solution=8 mol50.00 mL(1000 mL1 L)=160 mol/L
Substitute 12 mol for number of moles and 50.00 mL for volume of solution in the equation (1) to calculate the molarity of solution in beaker B.
Molarity of solution=12 mol50.00 mL(1000 mL1 L)=60000 mol/L
Substitute 4 mol for number of moles and 50.00 mL for volume of solution in the equation (1) to calculate the molarity of solution in beaker C.
Molarity of solution=4 mol50.00 mL(1000 mL1 L)=80 mol/L
Substitute 4 mol for number of moles and 50.00 mL for volume of solution in the equation (1) to calculate the molarity of solution in beaker D.
Molarity of solution=4 mol50.00 mL(1000 mL1 L)=80 mol/L
Substitute 2 mol for number of moles and 25.00 mL for volume of solution in the equation (1) to calculate the molarity of solution in beaker E.
Molarity of solution=2 mol25.00 mL(1000 mL1 L)=80 mol/L
Substitute 4 mol for number of moles and 25.00 mL for volume of solution in the equation (1) to calculate the molarity of solution in beaker F.
Molarity of solution=4 mol25.00 mL(1000 mL1 L)=160 mol/L.
The solution in beaker A and F has the same molarity and the value of molarity is 160 mol/L. The solution in beaker C, D and E has the same molarity and the value of molarity is 80 mol/L.
Molarity (M) is directly proportional to number of moles and inversely related to the volume of solution.
(c)
Interpretation:
Whether the mixture of solution A and C have a higher, a lower, or the same molarity as solution B is to be determined.
Concept introduction:
Molarity (M) is one of the concentration terms that determine the number of moles of solute present in per litre of solution. Unit of molarity is mol/L.
The expression to calculate the molarity of solution when moles of solute and volume of solution are given is as follows:
Molarity of solution(M)=moles of solute(mol)volume of solution(L)
(c)
Answer to Problem 4.12P
The mixture of solution A and C has a lower molarity as compared to solution B.
Explanation of Solution
The number of moles in solution A is 8 mol and number of moles in solution C is 4 mol. Therefore the total number of moles in the mixture of A and C is 12 mol.
The formula to calculate the total volume is as follows:
Total volume=VA+VC (2)
Substitute 50.00 mL for VA and 50.00 mL for VC in the equation (2).
Total volume=50.00 mL+50.00 mL=100.00 mL
Substitute 12 mol for number of moles and 100.00 mL for volume of solution in the equation (1) to calculate the molarity of mixture of solution A and C.
Molarity of solution=12 mol100.00 mL(1000 mL1 L)=120 mol/L.
The mixture of solution A and C has lower molarity as compared to solution B.
Molarity (M) is directly proportional to number of moles and inversely related to the volume of solution. The new moles and volume is calculated by the summation of the volumes and moles of the solution that are mixed.
(d)
Interpretation:
Whether the molarity when 50 mL of water is added to solution D is higher, lower, or the same as the molarity of solution F after 75 mL is added to it is to be determined.
Concept introduction:
Molarity (M) is one of the concentration terms that determine the number of moles of solute present in per litre of solution. Unit of molarity is mol/L.
The expression to calculate the molarity of solution when moles of solute and volume of solution are given is as follows:
Molarity of solution(M)=moles of solute(mol)volume of solution(L)
(d)
Answer to Problem 4.12P
The molarity when 50 mL of water is added to solution D is same as the molarity of solution F after 75 mL is added to it.
Explanation of Solution
The volume of solution D is 50.00 mL. The new volume of solution D is calculated as follows:
New volume of solution D=50.00 mL+50.00 mL=100.00 mL
The volume of solution F is 25.00 mL. The new volume of solution F is calculated as follows:
New volume of solution F=25.00 mL+75.00 mL=100.00 mL
Substitute 4 mol for number of moles and 100.00 mL for volume of solution in the equation (1) to calculate the molarity of new solution in beaker D.
Molarity of solution=4 mol100.00 mL(1000 mL1 L)=40 mol/L
Substitute 4 mol for number of moles and 100.00 mL for volume of solution in the equation (1) to calculate the molarity of new solution in beaker F.
Molarity of solution=4 mol100.00 mL(1000 mL1 L)=40 mol/L.
The molarity of solution D is same as the molarity of solution F.
Molarity (M) is directly proportional to number of moles and inversely related to the volume of solution.
(e)
Interpretation:
The solvent must be evaporated from solution E for it to have the same molarity as solution A is to be calculated.
Concept introduction:
Molarity (M) is one of the concentration terms that determine the number of moles of solute present in per litre of solution. Unit of molarity is mol/L.
The expression to calculate the molarity of solution when moles of solute and volume of solution are given is as follows:
Molarity of solution(M)=moles of solute(mol)volume of solution(L)
(e)
Answer to Problem 4.12P
12.5 mL of solvent must be evaporated from solution E for it to have the same molarity as solution A.
Explanation of Solution
The molarity of solution E should be equal to solution A. Therefore the molarity os solution should be 160 mol/L.
The formula to calculate the molarity of solution in beaker is as follows:
Molarity of solution(M)=number of molesvolume of solution (3)
Rearrange the equation (3) to calculate the volume of solution evaporated.
Volume of solution=number of molesMolarity of solution (4)
Substitute 2 mol for number of moles and 160 mol/L for molarity of solution in the equation (4) to calculate the volume of solution.
Volume of solution=2 mol160 mol/L(1000 mL1 L)=12.5 mL.
Therefore to get the same molarity as of the solution A, 2 mol should be present in 12.5 mL. Hence, 12.5 mL of solvent must be evaporated from solution E.
Molarity (M) is directly proportional to number of moles and inversely related to the volume of solution.
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Chapter 4 Solutions
Student Solutions Manual For Silberberg Chemistry: The Molecular Nature Of Matter And Change With Advanced Topics
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