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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

At least \(25 \mu \mathrm{g}\) of tetrahydrocannabinol (THC), the active ingredient in marijuana, is required to produce intoxication. The molecular formula of \(\mathrm{THC}\) is \(\mathrm{C}_{21} \mathrm{H}_{30} \mathrm{O}_{2}\). How many moles of THC does this \(25 \mu \mathrm{g}\) represent? How many molecules?

A mixture of \(\mathrm{N}_{2}(\mathrm{~g})\) and \(\mathrm{H}_{2}(\mathrm{~g})\) reacts in a closed container to form ammonia, \(\mathrm{NH}_{3}(g)\). The reaction ceases before either reactant has been totally consumed. At this stage \(3.0 \mathrm{~mol} \mathrm{~N}_{2}, 3.0 \mathrm{~mol} \mathrm{H}_{2}\), and \(3.0 \mathrm{~mol} \mathrm{NH}_{3}\) are present. How many moles of \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) were present originally?

If Avogadro's number of pennies is divided equally among the 300 million men, women, and children in the United States, how many dollars would each receive? How does this compare with the gross domestic product of the United States, which was \(\$ 13.5\) trillion in 2006 ? (The GDP is the total market value of the nation's goods and services.)

Hydrofluoric acid, \(\mathrm{HF}(a q)\), cannot be stored in glass bottles because compounds called silicates in the glass are attacked by the \(\mathrm{HF}(a q) .\) Sodium silicate \(\left(\mathrm{Na}_{2} \mathrm{SiO}_{3}\right)\), for example, reacts as follows: $$ \mathrm{Na}_{2} \mathrm{SiO}_{3}(s)+8 \mathrm{HF}(a q) \longrightarrow $$ (a) How many moles of \(\mathrm{HF}\) are needed to react with \(0.300 \mathrm{~mol}\) of \(\mathrm{Na}_{2} \mathrm{SiO}_{3} ?\) (b) How many grams of NaF form when \(0.500 \mathrm{~mol}\) of HF reacts with excess \(\mathrm{Na}_{2} \mathrm{SiO}_{3} ?\) (c) How many grams of \(\mathrm{Na}_{2} \mathrm{SiO}_{3}\) can react with \(0.800 \mathrm{~g}\) of \(\mathrm{HF}\) ?

(a) Define the terms limiting reactant and excess reactant. (b) Why are the amounts of products formed in a reaction determined only by the amount of the limiting reactant? (c) Why should you base your choice of what compound is the limiting reactant on its number of initial moles, not on its initial mass in grams?
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