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Chapter 3: Problem 27

(a) What is Avogadro's number, and how is it related to the mole? (b) What is the relationship between the formula weight of a substance and its molar mass?

Short Answer

Expert verified
(a) Avogadro's number (\(N_A\)) is approximately \(6.022 \times 10^{23}\) particles per mole and relates the number of particles in a sample to the mass of the sample using the mole concept. (b) The formula weight of a substance, in atomic mass units (amu), is equal to its molar mass, expressed in grams per mole (g/mol). The relationship between them is: Formula Weight (amu) = Molar Mass (g/mol)

Step by step solution

01

Define Avogadro's Number

Avogadro's number, denoted as \(N_A\), is the number of representative particles (such as atoms, ions, or molecules) in one mole of a substance. It is a fixed value, approximately equal to \( 6.022 \times 10^{23} \) particles per mole.
02

Connect Avogadro's Number to the Mole

The mole is a unit for expressing the amount of a substance. It relates the number of particles in a sample to the mass of the sample. By knowing the molecular weight of a substance, we can determine the number of moles and hence the number of particles in a given mass of the substance using Avogadro's number.
03

Define Formula Weight and Molar Mass

The formula weight (also known as molecular weight) of a substance is the sum of the atomic weights of all the atoms in a chemical formula. It is represented in atomic mass units (amu). Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). Since 1 amu is almost equal to 1 g/mol, you can consider the formula weight of a substance to be numerically equal to its molar mass.
04

Relate Formula Weight to Molar Mass

The relationship between the formula weight of a substance and its molar mass lies in the fact that they have the same numerical value. The formula weight (in amu) represents the mass of one particle of a substance, whereas the molar mass (in g/mol) represents the mass of one mole of a substance, containing Avogadro's number of particles. Thus, the formula weight of a substance is equal to the molar mass, or: Formula Weight (amu) = Molar Mass (g/mol)

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Most popular questions from this chapter

The koala dines exclusively on eucalyptus leaves. Its digestive system detoxifies the eucalyptus oil, a poison to other animals. The chief constituent in eucalyptus oil is a substance called eucalyptol, which contains \(77.87 \% \mathrm{C}\), \(11.76 \% \mathrm{H}\), and the remainder \(\mathrm{O}\). (a) What is the empirical formula for this substance? (b) A mass spectrum of eucalyptol shows a peak at about 154 amu. What is the molecular formula of the substance?

The fermentation of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) produces ethyl alcohol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) and \(\mathrm{CO}_{2}\) : $$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)+2 \mathrm{CO}_{2}(g) $$ (a) How many moles of \(\mathrm{CO}_{2}\) are produced when \(0.400\) mol of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) reacts in this fashion? (b) How many grams of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) are needed to form \(7.50 \mathrm{~g}\) of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) ? (c) How many grams of \(\mathrm{CO}_{2}\) form when \(7.50 \mathrm{~g}\) of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) are produced?

Balance the following equations: (a) \(\mathrm{Li}(s)+\mathrm{N}_{2}(g) \longrightarrow \mathrm{Li}_{3} \mathrm{~N}(s)\) (b) \(\mathrm{La}_{2} \mathrm{O}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{La}(\mathrm{OH})_{3}(a q)\) (c) \(\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (d) \(\mathrm{Ca}_{3} \mathrm{P}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{PH}_{3}(g)\) (e) \(\mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{H}_{3} \mathrm{PO}_{4}(a q) \longrightarrow\) \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l)\) (f) \(\mathrm{AgNO}_{3}(a q)+\mathrm{Na}_{2} \mathrm{SO}_{4}(a q) \longrightarrow\) \(\mathrm{Ag}_{2} \mathrm{SO}_{4}(\mathrm{~s})+\mathrm{NaNO}_{3}(a q)\) (g) \(\mathrm{CH}_{3} \mathrm{NH}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow\) \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{N}_{2}(g)\)

The molecular formula of aspartame, the artificial sweetener marketed as NutraSweet \(^{0}\), is \(\mathrm{C}_{14} \mathrm{H}_{18} \mathrm{~N}_{2} \mathrm{O}_{5}\) (a) What is the molar mass of aspartame? (b) How many moles of aspartame are present in \(1.00 \mathrm{mg}\) of aspartame? (c) How many molecules of aspartame are present in \(1.00 \mathrm{mg}\) of aspartame? (d) How many hydrogen atoms are present in \(1.00 \mathrm{mg}\) of aspartame?

Write a balanced chemical equation for the reaction that occurs when (a) \(\mathrm{Mg}(\mathrm{s})\) reacts with \(\mathrm{Cl}_{2}(g) ;\) (b) barium carbonate decomposes into barium oxide and carbon dioxide gas when heated; (c) the hydrocarbon styrene, \(\mathrm{C}_{8} \mathrm{H}_{8}(l)\), is combusted in air; (d) dimethylether, \(\mathrm{CH}_{3} \mathrm{OCH}_{3}(g)\), is combusted in air.
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