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Chapter 3: Problem 24

Avogadro's number, molar mass, and the chemical formula of a compound are three useful conversion factors. What unit conversions can be accomplished using these conversion factors?

Short Answer

Expert verified
Using Avogadro's number, molar mass, and the chemical formula of a compound, we can accomplish six different unit conversions: 1. Moles to Number of Particles: Number of particles = Number of moles 脳 Avogadro's number 2. Number of Particles to Moles: Number of moles = Number of particles / Avogadro's number 3. Grams to Moles: Number of moles = Mass in grams / Molar mass 4. Moles to Grams: Mass in grams = Number of moles 脳 Molar mass 5. Number of Particles to Grams: Number of moles = Number of particles / Avogadro's number, then Mass in grams = Number of moles 脳 Molar mass 6. Grams to Number of Particles: Number of moles = Mass in grams / Molar mass, then Number of particles = Number of moles 脳 Avogadro's number

Step by step solution

01

Understanding Avogadro's number, molar mass, and chemical formula

Avogadro's number (N鈧�) is the number of particles (atoms, molecules, ions, etc.) in one mole of a substance. It is a constant and is approximately equal to 6.022 x 10虏鲁 particles per mole. Molar mass is the mass of one mole of a substance, and it is expressed in grams per mole (g/mol). The chemical formula of a compound describes the number and type of atoms in a molecule of that compound.
02

Conversion 1: Moles to Number of Particles

Using Avogadro's number, we can convert the number of moles of a substance to the number of particles. To do this, we will multiply the given number of moles by Avogadro's number: Number of particles = Number of moles 脳 Avogadro's number
03

Conversion 2: Number of Particles to Moles

We can also convert the number of particles to moles using Avogadro's number. To find the number of moles, we will divide the given number of particles by Avogadro's number: Number of moles = Number of particles / Avogadro's number
04

Conversion 3: Grams to Moles

Using molar mass, we can convert the mass of a substance in grams to the number of moles. To do this, we will divide the given mass in grams by the molar mass of the substance: Number of moles = Mass in grams / Molar mass
05

Conversion 4: Moles to Grams

We can also convert the number of moles of a substance to its mass in grams using molar mass. To find the mass in grams, we will multiply the given number of moles by the molar mass of the substance: Mass in grams = Number of moles 脳 Molar mass
06

Conversion 5: Number of Particles to Grams (Combining steps)

It is often useful to convert the number of particles of a substance to its mass in grams. This can be done by first converting the number of particles to moles (Conversion 2), and then converting moles to grams (Conversion 4): Number of moles = Number of particles / Avogadro's number Mass in grams = Number of moles 脳 Molar mass
07

Conversion 6: Grams to Number of Particles (Combining steps)

Similarly, we can convert the mass of a substance in grams to the number of particles. First, we need to convert the mass in grams to moles (Conversion 3), and then convert moles to the number of particles (Conversion 1): Number of moles = Mass in grams / Molar mass Number of particles = Number of moles 脳 Avogadro's number In conclusion, we can accomplish six different unit conversions using Avogadro's number, molar mass, and the chemical formula of a compound: moles to number of particles, number of particles to moles, grams to moles, moles to grams, number of particles to grams, and grams to number of particles.

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Most popular questions from this chapter

Many cereals are made with high moisture content so that the cereal can be formed into various shapes before it is dried. A cereal product containing \(58 \% \mathrm{H}_{2} \mathrm{O}\) by mass is produced at the rate of \(1000 . \mathrm{kg} / \mathrm{h} .\) What mass of water must be evaporated per hour if the final product contains only \(20 . \%\) water?

A new grill has a mass of \(30.0 \mathrm{~kg}\). You put \(3.0 \mathrm{~kg}\) of charcoal in the grill. You burn all the charcoal and the grill has a mass of \(30.0 \mathrm{~kg}\). What is the mass of the gases given off? Explain.

Dimethylnitrosamine, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{~N}_{2} \mathrm{O}\), is a carcinogenic (cancercausing) 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 \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{~N}_{2} \mathrm{O}\) molecules are present in \(250 \mathrm{mg}\) dimethylnitrosamine? c. What is the mass of \(0.050\) mol dimethylnitrosamine? d. How many atoms of hydrogen are in \(1.0 \mathrm{~mol}\) dimethylnitrosamine? e. What is the mass of \(1.0 \times 10^{6}\) molecules of dimethylnitrosamine? f. What is the mass in grams of one molecule of dimethylnitrosamine?

Aspartame is an artificial sweetener that is 160 times sweeter than sucrose (table sugar) when dissolved in water. It is marketed as Nutra-Sweet. The molecular formula of aspartame is \(\mathrm{C}_{14} \mathrm{H}_{18} \mathrm{~N}_{2} \mathrm{O}_{5}\) a. Calculate the molar mass of aspartame. b. What amount (moles) of molecules are present in \(10.0 \mathrm{~g}\) aspartame? c. Calculate the mass in grams of \(1.56\) mol aspartame. d. What number of molecules are in \(5.0 \mathrm{mg}\) aspartame? e. What number of atoms of nitrogen are in \(1.2 \mathrm{~g}\) aspartame? f. What is the mass in grams of \(1.0 \times 10^{9}\) molecules of aspartame? g. What is the mass in grams of one molecule of aspartame?

Maleic acid is an organic compound composed of \(41.39 \% \mathrm{C}\), \(3.47 \% \mathrm{H}\), and the rest oxygen. If \(0.129 \mathrm{~mol}\) of maleic acid has a mass of \(15.0 \mathrm{~g}\), what are the empirical and molecular formulas of maleic acid?
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