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Answer true or false. (a) The mole is a counting unit, just as a dozen is a counting unit. (b) Avogadro's number is the number of formula units in one mole. (c) Avogadro's number, to three significant figures, is \(6.02 \times 10^{23}\) formula units per mole. (d) \(1 \mathrm{mol}\) of \(\mathrm{H}_{2} \mathrm{O}\) contains \(3 \times 6.02 \times 10^{23}\) formula units. (e) \(1 \mathrm{mol}\) of \(\mathrm{H}_{2} \mathrm{O}\) has the same number of molecules as \(1 \mathrm{mol}\) of \(\mathrm{H}_{2} \mathrm{O}_{2}\) (f) The molar mass of a compound is its formula weight expressed in amu. (g) The molar mass of \(\mathrm{H}_{2} \mathrm{O}\) is \(18 \mathrm{g} / \mathrm{mol}\). (h) \(1 \mathrm{mol}\) of \(\mathrm{H}_{2} \mathrm{O}\) has the same molar mass as \(1 \mathrm{mol}\) of \(\mathrm{H}_{2} \mathrm{O}_{2}\) (i) 1 mol of ibuprofen, \(C_{13} H_{18} O_{2},\) contains 33 mol of atoms. (j) To convert moles to grams, multiply by Avogadro's number. (k) To convert grams to moles, divide by molar mass. (1) \(1 \mathrm{mol}\) of \(\mathrm{H}_{2} \mathrm{O}\) contains \(1 \mathrm{mol}\) of hydrogen atoms and one mol of oxygen atoms. \((\mathrm{m}) 1 \mathrm{mol}\) of \(\mathrm{H}_{2} \mathrm{O}\) contains \(2 \mathrm{g}\) of hydrogen atoms and 1 g of oxygen atoms. (n) 1 mole of \(\mathrm{H}_{2} \mathrm{O}\) contains \(18.06 \times 10^{23}\) atoms.

Step by step solution

01

Comparison of Counting Units

Both a mole and a dozen are counting units. A dozen always refers to 12 items, while a mole refers to approximately \(6.022 \times 10^{23}\) entities. Therefore, statement (a) is true.

02

Definition of Avogadro's Number

Avogadro's number is defined as the number of elementary entities (atoms, molecules, etc.) per mole of substance. This corresponds with statement (b), which describes the number of formula units in one mole, making statement (b) true.

03

Scientific Notation for Avogadro's Number

Avogadro's number, rounded to three significant figures, is correctly written as \(6.02 \times 10^{23}\). This makes statement (c) true.

04

Calculating Moles of Atoms in a Compound

For statement (d), \(1 \text{ mole of } \text{H}_2\text{O}\) consists of 1 mole of water molecules, which includes 2 moles of hydrogen atoms and 1 mole of oxygen atoms. Therefore, \(3 \times 6.02 \times 10^{23}\) formula units is correct, making statement (d) true.

05

Molecular Consistency Across Substances

Statement (e) holds true as 1 mole of any substance contains the same number of molecules, \(6.022 \times 10^{23}\), irrespective of their chemical nature. Hence, (e) is true.

06

Definition of Molar Mass

Molar mass is the mass of one mole of a substance, measured in grams, not amu. Therefore, statement (f) is false.

07

Calculation of Water Molar Mass

The molar mass of \(\text{H}_2\text{O}\) is calculated as 2*(1 g/mol) for hydrogen + 16 g/mol for oxygen, totaling 18 g/mol. Therefore, statement (g) is true.

08

Comparison of Molar Masses in Compounds

Statement (h) is false as \(1 \text{ mol of } \text{H}_2\text{O}_2\) (hydrogen peroxide) has a different molar mass due to the additional oxygen atom, resulting in a higher total molar mass than water.

09

Counting Atoms in a Mole

In statement (i), 1 mole of ibuprofen contains 13 moles of carbon, 18 moles of hydrogen, and 2 moles of oxygen, totaling 33 moles of atoms. Therefore, this statement is true.

10

Converting Moles to Mass

To convert moles to grams, multiply by the molar mass, not Avogadro's number. Therefore, statement (j) is false.

11

Converting Mass to Moles

To convert grams to moles, divide by the molar mass, as correctly stated in (k). Therefore, statement (k) is true.

12

Chemical Composition of Water

Statement (l) is false because 1 mole of \(\text{H}_2\text{O}\) contains 2 moles of hydrogen atoms (not 1) and 1 mole of oxygen atoms.

13

Massing Elements in Water

For statement (m), 1 mol of \(\text{H}_2\text{O}\) actually contains 2 grams of hydrogen (from the two hydrogen atoms) and 16 grams of oxygen, so this is false.

14

Counting Atoms in Water

In statement (n), 1 mole of water contains \(6.022\times 10^{23}\) molecules, which is \(18.066\times 10^{23}\) atoms (with 3 atoms per molecule), making this true.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Avogadro's number

Avogadro's number is a fundamental concept in chemistry, representing the quantity of atoms, molecules, or other entities in one mole of a substance. Just like a dozen refers to 12 items, one mole refers to approximately \(6.022 \times 10^{23}\) entities. This large number arises from the tiny scale of atoms. Even a tiny amount of a substance like a gram of hydrogen contains billions of atoms.
Understanding Avogadro's number is crucial, as it allows chemists to count these minuscule entities in practical, large-scale amounts.

• It defines the mole as a counting unit in chemistry, originating from Avogadro's hypothesis that equal volumes of gases at the same temperature and pressure contain an equal number of molecules.
• While Avogadro's number is often rounded to \(6.02 \times 10^{23}\) for simplicity, it provides a solid basis for converting between microscopic entities and macroscopic quantities useful in laboratory settings.

Molar mass calculations

Molar mass is the mass of one mole of a substance expressed in grams per mole (g/mol). This concept is vital for translating between masses in an experiment and the number of moles involved in chemical reactions.
To determine the molar mass of a compound, you sum the atomic masses of its elements, each weighted by the number of times the element appears in the compound. For example, the molar mass of water \( ext{H}_2 ext{O}\) is calculated as:
\[2 \times (1 \, ext{g/mol for H}) + 16 \, ext{g/mol for O} = 18 \, ext{g/mol}\]

• When converting from moles to grams, multiply the number of moles by the molar mass.
• When converting from grams to moles, divide the mass of the substance by its molar mass.
• Consistent use of the correct molar masses is essential in calculations for stoichiometry and balancing chemical equations.

Chemical composition of compounds

Understanding the chemical composition of compounds allows chemists to predict how they will react. Compounds are made of atoms from different elements, bonded together in specific ratios, which are represented by their chemical formulas.
For example, in the compound water (\( ext{H}_2 ext{O}\)), each molecule consists of two hydrogen atoms and one oxygen atom. This ratio directly affects the compound's properties and how it interacts chemically.

• The chemical formula gives insight into the compound's molar mass, as explained in the molar mass calculations.
• One mole of any compound will have Avogadro's number of molecules, allowing easy conversion between the number of molecules and the mass of the sample.
• Understanding chemical compositions is critical for predicting the outcome of reactions, especially in determining how much of each reactant is needed and the amounts of products formed.