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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 × 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 × Molar mass 5. Number of Particles to Grams: Number of moles = Number of particles / Avogadro's number, then Mass in grams = Number of moles × Molar mass 6. Grams to Number of Particles: Number of moles = Mass in grams / Molar mass, then Number of particles = Number of moles × Avogadro's number

Step by step solution

01

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

Avogadro's number (Nₐ) 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 10²³ 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 × 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 × 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 × 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 × 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

In 1987 the first substance to act as a superconductor at a temperature above that of liquid nitrogen \((77 \mathrm{~K})\) was discovered. The approximate formula of this substance is \(\mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{7} .\) Calculate the percent composition by mass of this material.

A potential fuel for rockets is a combination of \(\mathrm{B} \cdot \mathrm{H}_{9}\) and \(\mathrm{O}_{-}\) The two react according to the following balanced equation: $$ 2 \mathrm{~B}_{5} \mathrm{H}_{9}(l)+12 \mathrm{O}_{2}(g) \longrightarrow 5 \mathrm{~B}_{2} \mathrm{O}_{3}(s)+9 \mathrm{H}_{2} \mathrm{O}(g) $$ If one tank in a rocket holds \(126 \mathrm{~g} \mathrm{~B}_{5} \mathrm{H}_{9}\) and another tank holds \(192 \mathrm{~g} \mathrm{O}_{2}\), what mass of water can be produced when the entire contents of each tank react together?

Consider a mixture of potassium chloride and potassium nitrate that is \(43.2 \%\) potassium by mass. What is the percent \(\mathrm{KCl}\) by mass of the original mixture?

Bacterial digestion is an economical method of sewage treatment. The reaction \(5 \mathrm{CO}_{2}(g)+55 \mathrm{NH}_{4}^{+}(a q)+76 \mathrm{O}_{2}(g)\) \(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2} \mathrm{~N}(s)+54 \mathrm{NO}_{2}^{-}(a q)+52 \mathrm{H}_{2} \mathrm{O}(l)+109 \mathrm{H}^{+}(a q)\)

With the advent of techniques such as scanning tunneling microscopy, it is now possible to "write" with individual atoms by manipulating and arranging atoms on an atomic surface. a. If an image is prepared by manipulating iron atoms and their total mass is \(1.05 \times 10^{-20} \mathrm{~g}\), what number of iron atoms were used? b. If the image is prepared on a platinum surface that is exactly 20 platinum atoms high and 14 platinum atoms wide, what is the mass (grams) of the atomic surface? c. If the atomic surface were changed to ruthenium atoms and the same surface mass as determined in part \(\mathrm{b}\) is used, what number of ruthenium atoms is needed to construct the surface?
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