Chemistry: An Atoms First Approach
Chemistry: An Atoms First Approach
2nd Edition
ISBN: 9781305079243
Author: Steven S. Zumdahl, Susan A. Zumdahl
Publisher: Cengage Learning
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Chapter 5, Problem 72E

Dimethylnitrosamine, (CH3)2N2O , is a carcinogenic (cancer-causing) substance that may be formed in foods, beverages, or gastric juices from the reaction of nitrite ion (used as a food preservative) with other substances.

a. What is the molar mass of dimethylnitrosamine?

b. How many moles of (CH3h N20 molecules are present in 250 mg dimethylnitrosamine?

c. What is the mass of 0.050 mole of dimethylnitrosamine?

d. How many atoms of hydrogen are in 1.0 mole of dimethylnitrosamine?

e. What is the mass of 1.0 × 106 molecules of dimethylnitrosamine?

f. What is the mass in grams of one molecule of dimethylnitrosamine?

(a)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The answers are to be given for the given options.

Concept introduction: The atomic mass is defined as the sum of number of protons and number of neutrons.

Molar mass of a substance is defined as the mass of the substance in gram of one mole of that compound.

The molar mass of any compound can be calculated by adding of atomic weight of individual atoms present in it.

The amount of substance containing 12g of pure carbon is called a mole. One mole of atoms always contains 6.022×1023 molecules. The number of molecules in one mole is also called Avogadro’s number.

Explanation of Solution

To determine: The molar mass of Dimethylnitrosamine [(CH3)2N2O] .

The atomic weight of carbon (C) is 12.01g/mol .

The atomic weight of oxygen (O) is 16.00g/mol .

The atomic weight of hydrogen (H) is 1.008g/mol .

The atomic weight of nitrogen (N) is 14.01g/mol .

In a compound (CH3)2N2O , two carbon, one oxygen, two nitrogen and six hydrogen atoms are present. Hence, molar mass of (CH3)2N2O is calculated as,

[6(1.008g/mol)+2(12.01g/mol)+(16.00g/mol)+2(14.01g/mol)]=74.09g/mol_

The molar mass of (CH3)2N2O is 74.09g/mol_ .

Conclusion

Molar mass is defined as mass of 6.022×1023 atoms, molecules of that substance.

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The answers are to be given for the given options.

Concept introduction: The atomic mass is defined as the sum of number of protons and number of neutrons.

Molar mass of a substance is defined as the mass of the substance in gram of one mole of that compound.

The molar mass of any compound can be calculated by adding of atomic weight of individual atoms present in it.

The amount of substance containing 12g of pure carbon is called a mole. One mole of atoms always contains 6.022×1023 molecules. The number of molecules in one mole is also called Avogadro’s number.

To determine: The number of moles in 250mg of (CH3)2N2O .

Explanation of Solution

Given

The mass of C2H3Cl3O2 is 250mg .

The molar mass of (CH3)2N2O is 74.09g/mol .

The conversion of milligram (mg) into gram (g) is done as,

1mg=103g

Hence, the conversion of 250mg into gram is,

250mg=(250×103)g=0.25g

Formula

The number of moles in (CH3)2N2O is calculated as,

Molesof(CH3)2N2O=Massof(CH3)2N2OMolarmassof(CH3)2N2O

Substitute the values of mass and molar mass of (CH3)2N2O in above equation,

Molesof(CH3)2N2O=Massof(CH3)2N2OMolarmassof(CH3)2N2O=0.25g74.09g/mol=3.37×103mol_

The number of moles in 250mg of (CH3)2N2O is 3.37×103mol_ .

Conclusion

Number of moles is calculated by dividing the given mass with the molar mass of that compound.

(c)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The answers are to be given for the given options.

Concept introduction: The atomic mass is defined as the sum of number of protons and number of neutrons.

Molar mass of a substance is defined as the mass of the substance in gram of one mole of that compound.

The molar mass of any compound can be calculated by adding of atomic weight of individual atoms present in it.

The amount of substance containing 12g of pure carbon is called a mole. One mole of atoms always contains 6.022×1023 molecules. The number of molecules in one mole is also called Avogadro’s number.

To determine: The mass of 0.050mol (CH3)2N2O .

Explanation of Solution

Given

The moles of (CH3)2N2O is 0.050mol .

The molar mass of (CH3)2N2O is 74.09g/mol .

Formula

The mass of (CH3)2N2O is calculated as,

Molesof(CH3)2N2O=Massof(CH3)2N2OMolarmassof(CH3)2N2OMassof(CH3)2N2O=Molesof(CH3)2N2O×Molarmassof(CH3)2N2O

Substitute the values of moles and molar mass of (CH3)2N2O in above equation.

Massof(CH3)2N2O=Molesof(CH3)2N2O×Molarmassof(CH3)2N2O=74.09g/mol×0.050mol=3.7g_

The mass of 0.050mol (CH3)2N2O is 3.7g_ .

Conclusion

Mass of molecule is calculated by multiplying the number of moles and molar mass of that molecule.

(d)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The answers are to be given for the given options.

Concept introduction: The atomic mass is defined as the sum of number of protons and number of neutrons.

Molar mass of a substance is defined as the mass of the substance in gram of one mole of that compound.

The molar mass of any compound can be calculated by adding of atomic weight of individual atoms present in it.

The amount of substance containing 12g of pure carbon is called a mole. One mole of atoms always contains 6.022×1023 molecules. The number of molecules in one mole is also called Avogadro’s number.

To determine: The number of hydrogen (H) atoms in 1.00mol of (CH3)2N2O .

Explanation of Solution

Given

The moles of (CH3)2N2O is 1.00mol .

Since, one mole of (CH3)2N2O is equal to six moles of hydrogen. Therefore, 1.00mol of (CH3)2N2O is equal to

6×1.00mol=6.00mol of hydrogen (H) .

Formula

The number of hydrogen atoms in (CH3)2N2O is calculated using the formula,

NumberofHatom=MolesofHatom×6.022×1023

Substitute the value of number of moles of H atom in above equation,

NumberofHatom=MolesofHatom×6.022×1023=6.00mol×6.022×1023=3.6×1024atoms_

The number of hydrogen (H) atoms in 1.00mol of (CH3)2N2O is 3.6×1024atoms_ .

Conclusion

The number of atoms is calculated by multiplying the number of moles with Avogadro’s number.

(e)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The answers are to be given for the given options.

Concept introduction: The atomic mass is defined as the sum of number of protons and number of neutrons.

Molar mass of a substance is defined as the mass of the substance in gram of one mole of that compound.

The molar mass of any compound can be calculated by adding of atomic weight of individual atoms present in it.

The amount of substance containing 12g of pure carbon is called a mole. One mole of atoms always contains 6.022×1023 molecules. The number of molecules in one mole is also called Avogadro’s number.

To determine: The mass of exactly 1.0×106molecules of (CH3)2N2O .

Explanation of Solution

Given

The total molecules in (CH3)2N2O is 1.0×106molecules .

The molar mass of (CH3)2N2O is 74.09g/mol .

Since one mole of atoms always contains 6.022×1023 molecules. Therefore, number of moles in 1.0×106molecules is,

1.0×1066.022×1023mol=1.6×1018mol

Formula

The mass of (CH3)2N2O is calculated as,

Molesof(CH3)2N2O=Massof(CH3)2N2OMolarmassof(CH3)2N2OMassof(CH3)2N2O=Molesof(CH3)2N2O×Molarmassof(CH3)2N2O

Substitute the values of moles and molar mass of (CH3)2N2O in above equation.

Massof(CH3)2N2O=Molesof(CH3)2N2O×Molarmassof(CH3)2N2O=74.09×1.6×1018mol=1.2×1016g_

The mass of exactly 1.0×106molecules of (CH3)2N2O is 1.2×1016g_ .

Conclusion

Mass of molecule is calculated by multiplying the number of moles and molar mass of that molecule.

(f)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The answers are to be given for the given options.

Concept introduction: The atomic mass is defined as the sum of number of protons and number of neutrons.

Molar mass of a substance is defined as the mass of the substance in gram of one mole of that compound.

The molar mass of any compound can be calculated by adding of atomic weight of individual atoms present in it.

The amount of substance containing 12g of pure carbon is called a mole. One mole of atoms always contains 6.022×1023 molecules. The number of molecules in one mole is also called Avogadro’s number.

To determine: The mass of exactly 1.0molecules of (CH3)2N2O .

Explanation of Solution

Given

The total molecules in (CH3)2N2O is 1.0molecules .

The molar mass of (CH3)2N2O is 74.09g/mol .

Since one mole of atoms always contains 6.022×1023 molecules. Therefore, number of moles in 1.0molecules is,

1.06.022×1023mol=1.6×1023mol

Formula

The mass of (CH3)2N2O is calculated as,

Molesof(CH3)2N2O=Massof(CH3)2N2OMolarmassof(CH3)2N2OMassof(CH3)2N2O=Molesof(CH3)2N2O×Molarmassof(CH3)2N2O

Substitute the values of moles and molar mass of (CH3)2N2O in above equation.

Massof(CH3)2N2O=Molesof(CH3)2N2O×Molarmassof(CH3)2N2O=74.09×1.6×1023mol=1.2×1022g_

The mass of exactly 1.0molecules of (CH3)2N2O is 1.2×1022g_ .

Conclusion

Mass of molecule is calculated by multiplying the number of moles and molar mass of that molecule.

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Chapter 5 Solutions

Chemistry: An Atoms First Approach

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